symbolicCircuits.ipynb

{
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    "# author: Jhonathan Romero Fontalvo\n",
    "#         BK and JW transformations (April 30, 2015)\n",
    "#         Revised version (August 11, 2016)\n",
    "#         Circuits (August 30, 2015)\n",
    "#         Commutators (December 2, 2015)\n",
    "#         Routines to write inputs for qHipster (December 13, 2015)\n",
    "#         Revised version (December 14, 2016)\n",
    "\n",
    "import time\n",
    "import numpy as np\n",
    "import scipy\n",
    "from scipy.optimize import minimize\n",
    "import warnings\n",
    "#import commutators\n",
    "import scipy.sparse\n",
    "import scipy.optimize\n",
    "import scipy.sparse.linalg\n",
    "from itertools import combinations\n",
    "from sys import argv\n",
    "import resource\n",
    "import itertools\n",
    "import commutators #(Ryan Babbush)\n",
    "from qutip import *\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.ticker as mtick\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Symbolic Bravyi-Kitaev (BK) and Jordan-Wigner (JW) transformations.\n",
    "\n",
    "The next cells have routines that perform the tasks requires for the Jordan-Wigner and the Bravyi-Kitaev transformation."
   ]
  },
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   "source": [
    "def generateBKSets(qubits):\n",
    "    \"\"\" Generate the sets parity (P), update (U), flip (F) and remaining (R) sets\n",
    "        required for the BK transformation.\n",
    "        \n",
    "        References: Seeley et al. JCP, 137, 224109 (2012) \n",
    "        \n",
    "        Returns\n",
    "        -------\n",
    "            Lists of P, U, F and R for n qubits. Handles up to 10 qubits.\n",
    "    \"\"\"\n",
    "    dic={0:1,1:2,2:4,3:8,4:16,5:32,6:64,7:128,8:256,9:512,10:1024}\n",
    "    for n in range(0,11):\n",
    "        if dic[n]>=qubits:\n",
    "            power2=n\n",
    "            break\n",
    "    beta=1.\n",
    "    invbeta=1.\n",
    "    size=2**power2\n",
    "    pi=np.zeros((size,size))\n",
    "    for n in range(0,size):\n",
    "        pi[n,0:n]=1\n",
    "    I = np.array([[1, 0], [0, 1]])\n",
    "    for n in range(0,power2):\n",
    "        l1=2**n\n",
    "        beta=np.kron(I,beta)\n",
    "        invbeta=np.kron(I,invbeta)\n",
    "        for m in range(0,l1):\n",
    "            beta[2*l1-1,m]=1.0\n",
    "        invbeta[2*l1-1,l1-1]=1.0\n",
    "    #print np.linalg.inv(beta)\n",
    "    parity=np.remainder(np.dot(pi,invbeta),2)\n",
    "    P={}\n",
    "    for n in range(0,qubits):\n",
    "        s=[]\n",
    "        for m in range(0,n):\n",
    "            if parity[n,m]==1:\n",
    "                s.append(m)\n",
    "        P[n]=s\n",
    "    R={}\n",
    "    for n in range(0,qubits):\n",
    "        s=[]\n",
    "        for m in range(0,n):\n",
    "            if parity[n,m]==1:\n",
    "                s.append(m)\n",
    "        R[n]=s\n",
    "    F={}\n",
    "    for n in range(0,qubits):\n",
    "        set=[]\n",
    "        for m in range(0,n):\n",
    "            if invbeta[n,m]==1:\n",
    "                set.append(m)\n",
    "        F[n]=set\n",
    "    U={}\n",
    "    for n in range(0,qubits):\n",
    "        set=[]\n",
    "        for m in range(n+1,qubits):\n",
    "            if beta[m,n]==1:\n",
    "                set.append(m)\n",
    "        U[n]=set\n",
    "    for n in range(0,qubits):\n",
    "        for x in F[n]:\n",
    "            if x in R[n]:\n",
    "                R[n].remove(x)\n",
    "    return beta,P,U,F,R"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Class term"
   ]
  },
  {
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    "def chunkIt(seq, num):\n",
    "    \"\"\"Create chunks of a list\"\"\"\n",
    "    avg = len(seq) / float(num)\n",
    "    out = []\n",
    "    last = 0.0\n",
    "    \n",
    "    while last < len(seq):\n",
    "        out.append(seq[int(last):int(last + avg)])\n",
    "        last += avg\n",
    "    return out\n",
    "\n",
    "class term:\n",
    "    \"\"\" Class Term: Defines symbolically a product of Pauli Matrices\n",
    "        The term is saved as a dictionary, with each qubit having a list of terms\n",
    "    \"\"\"\n",
    "    def __init__(self,nqubits,alpha=0.0):\n",
    "        string={}\n",
    "        for n in range(0,nqubits):\n",
    "            string[n]=['I']\n",
    "        self.c = 1.0 # coefficient of the term\n",
    "        self.pl = string # dictionary containing n strings, one per each qubit\n",
    "        self.matrix=[] # matrix form of the term\n",
    "        self.l=nqubits # length: number of qubits\n",
    "        self.alpha=alpha #\n",
    "        \n",
    "    def reduceTerm(self):\n",
    "        \"\"\"\n",
    "            Reduces a product of Pauli Matrices\n",
    "        \"\"\"\n",
    "        dic1={'ZZ':'I','YY':'I','XX':'I','II':'I','XY':'Z','XZ':'Y','YX':'Z','YZ':'X','ZX':'Y',\n",
    "              'ZY':'X','IX':'X','IY':'Y','IZ':'Z','ZI':'Z','YI':'Y','XI':'X'}\n",
    "        dic2={'ZZ':1.0,'YY':1.0,'XX':1.0,'II':1.0,'XY':1.0j,'XZ':-1.0j,'YX':-1.0j,'YZ':1.0j,'ZX':1.0j,\n",
    "              'ZY':-1.0j,'IX':1.0,'IY':1.0,'IZ':1.0,'ZI':1.0,'YI':1.0,'XI':1.0}\n",
    "        factor=1.0 \n",
    "        for x in self.pl:\n",
    "            t=self.pl[x]\n",
    "            length=len(t)\n",
    "            while length>1:\n",
    "                pair=''.join(t[:2])\n",
    "                del t[:2]\n",
    "                t.insert(0,dic1[pair])\n",
    "                factor=factor*dic2[pair]\n",
    "                length=len(t)\n",
    "            self.pl[x]=t\n",
    "        self.c=factor*self.c\n",
    "    \n",
    "    def printTerm(self):\n",
    "        \"\"\"\n",
    "            Routine to print term. N 1.\n",
    "            \n",
    "            Returns\n",
    "            -------\n",
    "                Coefficient and string representing the term\n",
    "        \"\"\"\n",
    "        vprint=[]\n",
    "        for x in self.pl:\n",
    "            vprint += self.pl[x]\n",
    "            vprint += str(x)\n",
    "        vprint=''.join(vprint)\n",
    "        return self.c,vprint\n",
    "    \n",
    "    def printTerm2(self):\n",
    "        \"\"\"\n",
    "            Routine to print term. N 2.\n",
    "            \n",
    "            Returns\n",
    "            -------\n",
    "                Coefficient and string representing the term\n",
    "        \"\"\"\n",
    "        vprint=[]\n",
    "        for x in self.pl:\n",
    "            vprint += self.pl[x]\n",
    "        return self.c,vprint\n",
    "    \n",
    "    def printTerm3(self):\n",
    "        \"\"\"\n",
    "            Routine to print term. N 3.\n",
    "            \n",
    "            Returns\n",
    "            -------\n",
    "                Coefficient and string representing the term\n",
    "                In addition counds the number of cnot, swap, single qubits and control z\n",
    "                gates required to implement the evolution of the terms.\n",
    "                Used to estimate number of gates for the superconducting qubit devices of John Martinis. \n",
    "        \"\"\"\n",
    "        vprint=[]\n",
    "        counter=0\n",
    "        n_swaps=0\n",
    "        n_x=0; n_y=0\n",
    "        maxi=0\n",
    "        mini=self.l\n",
    "        for x in self.pl:\n",
    "            if self.pl[x] != ['Y']:\n",
    "                n_y += 1\n",
    "            if self.pl[x] != ['X']:\n",
    "                n_x += 1\n",
    "            if self.pl[x] != ['I']:\n",
    "                counter=counter+1\n",
    "                vprint += self.pl[x]\n",
    "                if x>maxi:\n",
    "                    maxi=x\n",
    "                if x<mini:\n",
    "                    mini=x\n",
    "                vprint += str(x)\n",
    "            elif self.pl[x] == ['I']:\n",
    "                vprint += [' ']\n",
    "        for n in range(mini,maxi+1):\n",
    "            if self.pl[n] == ['I']:\n",
    "                n_swaps += 2\n",
    "        vprint=''.join(vprint)\n",
    "        n_cnots=2*(maxi-mini)-n_swaps\n",
    "        sqcount=n_x*2+n_y*2+2*n_cnots+6*n_swaps\n",
    "        czcount=1*(n_cnots)+3*n_swaps\n",
    "        return self.c,vprint,8-counter,n,sqcount,czcount,n_swaps,n_cnots\n",
    "    \n",
    "    def printTerm4(self):\n",
    "        \"\"\"\n",
    "            Routine to print term. N 4.\n",
    "            \n",
    "            Returns\n",
    "            -------\n",
    "                Coefficient, string representing the term in latex notation and number of \n",
    "                Pauli matrices in the string\n",
    "        \"\"\"\n",
    "        vprint=[]\n",
    "        counter=0\n",
    "        for x in self.pl:\n",
    "            if self.pl[x] != ['I']:\n",
    "                counter=counter+1\n",
    "                vprint += '\\sigma_'\n",
    "                cosa=self.pl[x][0]\n",
    "                vprint += self.pl[x]\n",
    "                vprint += '^'\n",
    "                vprint += str(x)\n",
    "        vprint=''.join(vprint)\n",
    "        return self.c,vprint,counter\n",
    "\n",
    "    def printCircuit(self,f1):\n",
    "        \"\"\"\n",
    "            Returns\n",
    "            -------\n",
    "                Circuit implementation of exp(-i\\theta Term) using CNOTs and single rotations\n",
    "\n",
    "        \"\"\"\n",
    "        list_of_qubits = []\n",
    "        coefficient = self.c.imag\n",
    "        if coefficient == 0.0:\n",
    "            coefficient = self.c.real\n",
    "        for x in self.pl:\n",
    "            if self.pl[x] != ['I']:\n",
    "                list_of_qubits.append(x)\n",
    "            if self.pl[x] == ['Y']:\n",
    "                f1.write('\\tRx\\tq'+str(x)+'\\n')\n",
    "            elif self.pl[x] == ['X']:\n",
    "                f1.write('\\tH\\tq'+str(x)+'\\n')\n",
    "        for n in range(1,len(list_of_qubits)):\n",
    "            f1.write('\\tcnot\\tq'+str(n)+',q'+str(n+1)+'\\n')\n",
    "        f1.write('\\tRz\\tq'+str(list_of_qubits[-1])+'\\t'+str(coefficient)+'\\n')\n",
    "        for n in range(1,len(list_of_qubits))[::-1]:\n",
    "            f1.write('\\tcnot\\tq'+str(n-1)+',q'+str(n)+'\\n')\n",
    "        for x in self.pl:\n",
    "            if self.pl[x] == ['Y']:\n",
    "                f1.write('\\tRxt\\tq'+str(x)+'\\n')\n",
    "            elif self.pl[x] == ['X']:\n",
    "                f1.write('\\tH\\tq'+str(x)+'\\n')\n",
    "\n",
    "    def getListOfOperations(self):\n",
    "        \"\"\"\n",
    "                Get the information necessary to print the string in the \n",
    "                format proposed by Gian for qHipster\n",
    "        \"\"\"\n",
    "        list_of_qubits = []\n",
    "        list_of_operations = []\n",
    "        for x in self.pl:\n",
    "            if self.pl[x] != ['I']:\n",
    "                list_of_qubits.append(x)\n",
    "                if self.pl[x] == ['X']:\n",
    "                    list_of_operations.append(1)\n",
    "                elif self.pl[x] == ['Y']:\n",
    "                    list_of_operations.append(2)\n",
    "                elif self.pl[x] == ['Z']:\n",
    "                    list_of_operations.append(3)\n",
    "        self.nonIcount = len(list_of_qubits)\n",
    "        self.list_of_qubits = list_of_qubits\n",
    "        self.list_of_operations = list_of_operations\n",
    "    \n",
    "    def printString(self,f1):\n",
    "        \"\"\"\n",
    "                Print the string in the \n",
    "                format proposed by Gian for qHipster\n",
    "        \"\"\"\n",
    "        if not hasattr(self, 'nonIcount'):\n",
    "            self.getListOfOperations()\n",
    "        coefficient = self.c.imag\n",
    "        #print(coefficient)\n",
    "        if coefficient == 0.0:\n",
    "            coefficient = self.c.real\n",
    "            #print(coefficient)\n",
    "        f1.write('{0:.8f}\\t{1}\\t{2}\\n'.format(coefficient,' '.join(str(x) for x in self.list_of_qubits),\n",
    "                                              ' '.join(str(x) for x in self.list_of_operations)))\n",
    "\n",
    "    def getMatrix(self):       \n",
    "        \"\"\"\n",
    "            Routine to print term. N 4.\n",
    "            \n",
    "            Returns\n",
    "            -------\n",
    "                A qutip quantum object (QUTIP) that corresponds to the Pauli term\n",
    "        \"\"\"\n",
    "        pauli={'I':identity(2),'X':sigmax(),'Y':sigmay(),'Z':sigmaz()}\n",
    "        counter=-1\n",
    "        l=[]\n",
    "        for t in self.pl:\n",
    "            counter += 1\n",
    "            l.append(pauli[self.pl[t][0]])\n",
    "        m = tensor(l)\n",
    "        self.matrix=self.c*m\n",
    "        return self.c*m\n",
    "    \n",
    "def simplifyTerms(products):\n",
    "    \"\"\"        \n",
    "    Input: products, a list of terms with the same size (number of qubits), that might have repeated terms.\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "        A simplified list of terms, without repetitions.    \n",
    "        \n",
    "    Note\n",
    "    -------\n",
    "        The routine also discards terms with small coefficients.\n",
    "        THIS ROUTINE IS PRETTY SLOW, WE MUST MAKE IT MORE EFFICIENT\n",
    "        CHECK FOR ALGORITHMS TO COMPARE LIST ELEMENTS\n",
    "    \"\"\"\n",
    "    error=10**(-12) # threshold to discard terms\n",
    "    ss=[]\n",
    "    products2=[]\n",
    "    indexes=range(0,len(products))\n",
    "    counter=0\n",
    "    removed=[]\n",
    "    for p in indexes:\n",
    "        if (p in removed)==False:\n",
    "            s=[]\n",
    "            s += [p]; removed += [p]; counter +=1\n",
    "            for q in indexes:\n",
    "                if (q in removed)==False:\n",
    "                    addTerm = True\n",
    "                    for x in products[p].pl:\n",
    "                        if products[p].pl[x] != products[q].pl[x]:\n",
    "                            addTerm = False\n",
    "                            break\n",
    "                    if addTerm:\n",
    "                        s += [q]; removed += [q]; counter +=1\n",
    "            ss += [s]\n",
    "        if counter == len(products):\n",
    "            break\n",
    "    # calculating sums and eliminating repeated terms\n",
    "    for x in ss:\n",
    "        value=0.0\n",
    "        for y in x:\n",
    "            value=value+products[y].c\n",
    "        if abs(value)>error:\n",
    "            products[x[0]].c=value\n",
    "            products2.append(products[x[0]])\n",
    "    del products\n",
    "    return products2\n",
    "\n",
    "def returnBKform(operator,P,U,F,R):\n",
    "    \"\"\"        \n",
    "    Input: operator of the form [i,j,-k,-l] that represents a^{/dag}_i a^{/dag}_j a_k a_l. Any length.\n",
    "            P, U, F and R sets of the corresponding size.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "        The representation of the operator in the BK form\n",
    "    \n",
    "    \"\"\"\n",
    "    # P, U and F must have the same number of elements = nqubits\n",
    "    l=len(operator)\n",
    "    size=2*l\n",
    "    nqubits=len(P)\n",
    "    BKform=[]\n",
    "    counter=-1\n",
    "    for a in operator:\n",
    "        counter += 1\n",
    "        s1=term(nqubits)\n",
    "        s2=term(nqubits)\n",
    "        j=abs(a)-1\n",
    "        # case j is even\n",
    "        if j%2==0:\n",
    "            s1.pl[j] += 'X'\n",
    "            #print U[j], P[j], R[j]\n",
    "            for k in U[j]:\n",
    "                s1.pl[k] += 'X'\n",
    "                #print k\n",
    "            for k in P[j]:\n",
    "                #print k\n",
    "                s1.pl[k] += 'Z'\n",
    "            s2.pl[j] += 'Y'\n",
    "            for k in U[j]:\n",
    "                s2.pl[k] += 'X'\n",
    "                #print k\n",
    "            for k in P[j]:\n",
    "                s2.pl[k] += 'Z'\n",
    "                #print k\n",
    "            # annihilator\n",
    "            if a<0:\n",
    "                s1.c=0.5\n",
    "                s2.c=0.5j\n",
    "            # creator\n",
    "            elif a>0:\n",
    "                s1.c=0.5\n",
    "                s2.c=-0.5j              \n",
    "            BKform += [s1]\n",
    "            BKform += [s2]\n",
    "            s1.reduceTerm()\n",
    "            s2.reduceTerm()\n",
    "        # case j is odd\n",
    "        elif j%2==1:\n",
    "            s1.pl[j] += 'X'\n",
    "            #print U[j], P[j], R[j]\n",
    "            for k in U[j]:\n",
    "                s1.pl[k] += 'X'\n",
    "                #print k\n",
    "            for k in P[j]:\n",
    "                s1.pl[k] += 'Z'\n",
    "                #print k\n",
    "            s2.pl[j] += 'Y'\n",
    "            for k in U[j]:\n",
    "                s2.pl[k] += 'X'\n",
    "                #print k\n",
    "            for k in R[j]:\n",
    "                s2.pl[k] += 'Z'\n",
    "                #print k\n",
    "            # annihilator\n",
    "            if a<0:\n",
    "                s1.c=0.5\n",
    "                s2.c=0.5j\n",
    "            # creator\n",
    "            elif a>0:\n",
    "                s1.c=0.5\n",
    "                s2.c=-0.5j \n",
    "            s1.reduceTerm()\n",
    "            s2.reduceTerm()\n",
    "            BKform += [s1]\n",
    "            BKform += [s2]\n",
    "        #print s1.printTerm()\n",
    "        #print s2.printTerm()\n",
    "        del s1; del s2\n",
    "    products=[]\n",
    "    iterables = chunkIt(range(size), size/2)\n",
    "    counter = 0\n",
    "    for element in itertools.product(*iterables):\n",
    "        counter += 1\n",
    "        s=term(nqubits)\n",
    "        for t in element:\n",
    "            for k in range(0,nqubits):\n",
    "                s.pl[k] += BKform[t].pl[k]\n",
    "            s.c=s.c*BKform[t].c\n",
    "        s.reduceTerm()\n",
    "        products += [s]\n",
    "        del s\n",
    "    # finding terms that are equivalent\n",
    "    products2=simplifyTerms(products)\n",
    "    return products2\n",
    "\n",
    "def returnJWform(operator,nqubits):\n",
    "    \"\"\"        \n",
    "    Input: operator of the form [i,j,-k,-l] that represents a^{/dag}_i a^{/dag}_j a_k a_l. Any length.\n",
    "            Number of qubits. \n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "        The representation of the operator in the JW form\n",
    "    \n",
    "    \"\"\"\n",
    "    l=len(operator)\n",
    "    size=2*l\n",
    "    BKform=[]\n",
    "    counter=-1\n",
    "    for a in operator:\n",
    "        counter += 1\n",
    "        s1=term(nqubits) \n",
    "        s2=term(nqubits)\n",
    "        j=abs(a)-1\n",
    "        # case j is even\n",
    "        s1.pl[j] += 'X'\n",
    "        #print U[j], P[j], R[j]\n",
    "        for k in range(0,j):\n",
    "            s1.pl[k] += 'Z'\n",
    "        s2.pl[j] += 'Y'\n",
    "        for k in range(0,j):\n",
    "            s2.pl[k] += 'Z'\n",
    "        # annihilator\n",
    "        if a<0:\n",
    "            s1.c=0.5\n",
    "            s2.c=0.5j\n",
    "        # creator\n",
    "        elif a>0:\n",
    "            s1.c=0.5\n",
    "            s2.c=-0.5j \n",
    "        s1.reduceTerm()\n",
    "        s2.reduceTerm()\n",
    "        BKform += [s1]\n",
    "        BKform += [s2]\n",
    "        #print s1.printTerm()\n",
    "        #print s2.printTerm()\n",
    "        del s1; del s2\n",
    "    products=[]\n",
    "    iterables = chunkIt(range(size), size/2)\n",
    "    counter = 0\n",
    "    for element in itertools.product(*iterables):\n",
    "        counter += 1\n",
    "        s=term(nqubits)\n",
    "        for t in element:\n",
    "            for k in range(0,nqubits):\n",
    "                s.pl[k] += BKform[t].pl[k]\n",
    "            s.c=s.c*BKform[t].c\n",
    "        s.reduceTerm()\n",
    "        products += [s]\n",
    "        del s\n",
    "    # finding terms that are equivalent\n",
    "    products2=simplifyTerms(products)\n",
    "    return products2\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hamiltonian and ansatz manipulation\n",
    "\n",
    "Functions that transform a Hamiltonian in second quantization to sum of strings of Pauli Matrices. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T09:10:23.562122",
     "start_time": "2016-12-14T09:10:23.405631"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def reduceHamiltonian(hamiltonian):\n",
    "    \"\"\"        \n",
    "    Input: Hamiltonian with repeated terms. \n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "        Hamiltonian without repeated terms.\n",
    "        \n",
    "    Note\n",
    "    -------\n",
    "        THIS ROUTINE NEEDS ACCELERATION\n",
    "    \n",
    "    \"\"\"    \n",
    "    check_term={}\n",
    "    result=True\n",
    "    new_nqubits=0\n",
    "    # remove qubit if the operations for all of them are identities\n",
    "    for n in range(0,hamiltonian[0].l):\n",
    "        counter=0\n",
    "        for x in hamiltonian:\n",
    "            if x.pl[n]==['I']:\n",
    "                counter+=1\n",
    "        if counter==len(hamiltonian):\n",
    "            check_term[n]=False\n",
    "        else:\n",
    "            check_term[n]=True\n",
    "        result=result*check_term[n]\n",
    "        new_nqubits += check_term[n]\n",
    "    products=[]\n",
    "    print (check_term)\n",
    "    if result==0:\n",
    "        for x in hamiltonian:\n",
    "            y=term(int(new_nqubits))\n",
    "            counter=-1\n",
    "            y.c=x.c\n",
    "            for n in range(0,len(check_term)):\n",
    "                if check_term[n]==True:\n",
    "                    counter += 1\n",
    "                    y.pl[counter]=x.pl[n]\n",
    "            products.append(y)\n",
    "        #products2=simplifyTerms(products)\n",
    "        return products\n",
    "    else:\n",
    "        return hamiltonian\n",
    "\n",
    "def getBKHamiltonian(coefficients,terms,P,U,F,R):\n",
    "    \"\"\"        \n",
    "    Input: A second quantized hamiltonian represented as a list of coeffficients \n",
    "            and terms in second quantization. P, U, F and R sets\n",
    "            for a given number of qubits.\n",
    "    \n",
    "    The notation for terms in second quantization is: [i,j,-k,-l] \n",
    "    that represents a^{/dag}_i a^{/dag}_j a_k a_l. Any length.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "        The Hamiltonian in BK form\n",
    "    \n",
    "    \"\"\"\n",
    "    products=[]\n",
    "    conteo=0\n",
    "    start_time = time.time()\n",
    "    for c,t in zip(coefficients,terms):    \n",
    "        #print c,t\n",
    "        cosa = returnBKform(t,P,U,F,R)\n",
    "        conteo=conteo+len(cosa)\n",
    "        for element in cosa:\n",
    "            element.c=c*element.c\n",
    "            #print element.printTerm()\n",
    "        products.extend(cosa)\n",
    "    # finding terms that are equivalent\n",
    "    total_time = time.time() - start_time\n",
    "    print(\"Time for transformation:\",total_time)\n",
    "    print(\"length of products:\",len(products))\n",
    "    start_time = time.time()\n",
    "    products2=simplifyTerms(products)\n",
    "    total_time = time.time() - start_time\n",
    "    print(\"Time for simplification:\",total_time)\n",
    "    print(\"length of products2:\",len(products2))\n",
    "    return products2  \n",
    "\n",
    "def getJWHamiltonian(coefficients, terms, nqubits, num=20):\n",
    "    \"\"\"        \n",
    "    Input: A second quantized hamiltonian represented as a list of coeffficients \n",
    "            and terms in second quantization. Number of qubits. \n",
    "    \n",
    "    The notation for terms in second quantization is: [i,j,-k,-l] \n",
    "    that represents a^{/dag}_i a^{/dag}_j a_k a_l. Any length.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "        The Hamiltonian in JW form\n",
    "    \n",
    "    \"\"\"\n",
    "    error=10**(-12)\n",
    "    #coefficients, terms = commutators.GetHamiltonianTerms(molecule, basis, add_conjugates=True)\n",
    "    products=[]\n",
    "    conteo=0\n",
    "    start_time = time.time()\n",
    "    for c,t in zip(coefficients,terms):    \n",
    "        #print c,t\n",
    "        cosa = returnJWform(t,nqubits)\n",
    "        conteo=conteo+len(cosa)\n",
    "        for element in cosa:\n",
    "            element.c=c*element.c\n",
    "            #print element.printTerm()\n",
    "        products.extend(cosa)\n",
    "    # finding terms that are equivalent\n",
    "    total_time = time.time() - start_time\n",
    "    print(\"Time for transformation:\",total_time)\n",
    "    print(\"length of products:\",len(products))\n",
    "    start_time = time.time()\n",
    "    #chunks = chunkIt(products, num)\n",
    "    #products2 = []\n",
    "    #for chunk in chunks:\n",
    "    #    chunk2 = simplifyTerms(chunk)\n",
    "    #    products2.extend(chunk)\n",
    "    products3 = simplifyTerms(products)\n",
    "    total_time = time.time() - start_time\n",
    "    print(\"Time for simplification:\",total_time)\n",
    "    print(\"length of products3:\",len(products3))\n",
    "    return products3\n",
    "\n",
    "def createExcitations(nocc,total,N):\n",
    "    \"\"\"\n",
    "        Return \n",
    "        ------\n",
    "            Create excitation operators up to order N for a given number of occupied orbitals (nocc)\n",
    "            and total orbitals (total)\n",
    "    \"\"\"\n",
    "    occ=range(1,nocc+1)\n",
    "    vir=range(nocc+1,total+1)\n",
    "    operators=[]\n",
    "    for n in range(1,N+1):\n",
    "        for cosa1 in itertools.combinations(occ,n):\n",
    "            for cosa2 in itertools.combinations(vir,n):\n",
    "                cosita=[]\n",
    "                cosita.extend(cosa2[::-1])\n",
    "                cosita.extend([x * -1 for x in cosa1[::-1]])\n",
    "                operators.append(cosita)\n",
    "    return operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T09:10:24.474405",
     "start_time": "2016-12-14T09:10:24.387028"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def checkCommutation(term1,term2):\n",
    "    \"\"\"        \n",
    "    Input: 2 TERMS\n",
    "    Returns\n",
    "    -------\n",
    "        Logical value. False or TrueHamiltonian without repeated terms.\n",
    "    Note\n",
    "    -------\n",
    "        THIS ROUTINE NEEDS ACCELERATION\n",
    "    \"\"\"    \n",
    "    nqubits1=max(term1.l,term2.l)\n",
    "    nqubits2=min(term1.l,term2.l)\n",
    "    product1=term(nqubits1)\n",
    "    product2=term(nqubits1)\n",
    "    for x in range(0,nqubits2):\n",
    "        product1.pl[x] += term1.pl[x]\n",
    "        product1.pl[x] += term2.pl[x]\n",
    "        product2.pl[x] += term2.pl[x]\n",
    "        product2.pl[x] += term1.pl[x]\n",
    "    product1.reduceTerm(); product2.reduceTerm();\n",
    "    commute=False\n",
    "    if product1.c==product2.c:\n",
    "        commute=True\n",
    "    return commute\n",
    "\n",
    "def checkCommutation2(term1,term2):\n",
    "    \"\"\"        \n",
    "    Input: 2 TERMS\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "        Logical value. False or TrueHamiltonian without repeated terms.\n",
    "        \n",
    "    Note\n",
    "    -------\n",
    "        THIS SHOULD BE FASTER\n",
    "    \n",
    "    \"\"\"    \n",
    "    if term1.l != term2.l:\n",
    "        raise ValueError('The Pauli strings to be compared must act on the same number of qubits')\n",
    "    counter = 0\n",
    "    for a, b in zip(term1.pl,term2.pl):\n",
    "        if term1.pl[a]!=term2.pl[b] and term1.pl[a]!=['I'] and term2.pl[b]!=['I']:\n",
    "            #print(a,b,term1.pl[a],term2.pl[b])\n",
    "            counter += 1\n",
    "    if counter%2 == 1:\n",
    "        commute = False\n",
    "    else:\n",
    "        commute = True\n",
    "    #print(counter)\n",
    "    return commute\n",
    "\n",
    "def getHam_JW(molecule,basis,path,num=20):\n",
    "    \"\"\"        \n",
    "    Gets a hamiltonian from file. Uses commutators.py\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "        Hamiltonian in JW form\n",
    "    \"\"\"  \n",
    "    fci_energy, repulsion, coefficients, terms = commutators.GetHamiltonianTerms(molecule, basis, add_conjugates=True, path=path)\n",
    "    N = commutators.OrbitalCount(terms)\n",
    "    hamiltonian=getJWHamiltonian(coefficients,terms,N,num)\n",
    "    return hamiltonian\n",
    "\n",
    "def getHam_BK(molecule,basis,path):\n",
    "    \"\"\"        \n",
    "    Gets a hamiltonian from file. Uses commutators.py\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "        Hamiltonian in BK form\n",
    "    \"\"\"  \n",
    "    fci_energy, repulsion, coefficients, terms = commutators.GetHamiltonianTerms(molecule, basis, add_conjugates=True, path=path)\n",
    "    N = commutators.OrbitalCount(terms)\n",
    "    hamiltonian=getBKHamiltonian(coefficients,terms,N)\n",
    "    return hamiltonian\n",
    "\n",
    "def getHamiltonianObject(ham):\n",
    "    \"\"\"        \n",
    "    Gets a qutip quantum object from a Hamiltonian consisting of a list of objects of type term. \n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "        Qobj\n",
    "    \"\"\"  \n",
    "    qobject = ham[0].getMatrix()\n",
    "    for n in range(1,len(ham)):\n",
    "        qobject = qobject + ham[n].getMatrix()\n",
    "    return qobject\n",
    "\n",
    "#compBasis={'1':basis(2,1),'0':basis(2,0)}\n",
    "#pauli={'I':qeye(2),'Z':sigmaz(),'X':sigmax(),'Y':sigmay()}\n",
    "\n",
    "def genNqubitState(state):\n",
    "    l=[]\n",
    "    for x in state:\n",
    "        l.append(compBasis[x])\n",
    "    result=tensor(l)\n",
    "    return result    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T09:10:25.336130",
     "start_time": "2016-12-14T09:10:25.324421"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def diffJW(example1,nqubits):\n",
    "    \"\"\"\n",
    "    Returns\n",
    "    -------\n",
    "        JW form of an antihermitian UCC operator\n",
    "    \"\"\"\n",
    "    example2=example1[::-1]\n",
    "    example2 = [x * -1 for x in example2]\n",
    "    expression=getJWHamiltonian([1.0,-1.0],[example1,example2],nqubits)\n",
    "    return expression\n",
    "\n",
    "def diffBK(example1,P,U,F,R):\n",
    "    \"\"\"\n",
    "    Returns\n",
    "    -------\n",
    "        BK form of an antihermitian UCC operator\n",
    "    \"\"\"\n",
    "    example2=example1[::-1]\n",
    "    example2 = [x * -1 for x in example2]\n",
    "    expression=getBKHamiltonian([1.0,-1.0],[example1,example2],P,U,F,R)\n",
    "    return expression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Routines to print circuits for qHipster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T09:10:27.334168",
     "start_time": "2016-12-14T09:10:27.149030"
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   "outputs": [],
   "source": [
    "def orderAndPrintHamiltonian(hamiltonian,name):\n",
    "    \"\"\"\n",
    "        Print hamiltonian using Gian's convention:\n",
    "        - First line has n+1 numbers, q_i. q_i is the number of terms\n",
    "        with length i.\n",
    "        - Lines describe:\n",
    "            coefficient \\t qubits \\t pauli strings (1=X,2=Y,Z=3)\n",
    "        Example: -0.98 Z1Z3X4Y5\n",
    "        -0.98 \\t 1 3 4 5 \\t 3 3 1 2\n",
    "        Strings are ordered from the shortest to the longest\n",
    "    \"\"\"\n",
    "    f1 = open(name,'w')\n",
    "    lengthCount = []\n",
    "    for h in hamiltonian:\n",
    "        h.getListOfOperations()\n",
    "        lengthCount.append(h.nonIcount)\n",
    "    sort_index = np.argsort(np.array(lengthCount))\n",
    "    ks = np.zeros(hamiltonian[0].l+1)\n",
    "    for n in range(hamiltonian[0].l+1):\n",
    "        ks[n]=lengthCount.count(n)\n",
    "    f1.write('{0}\\n'.format(' '.join(str(int(k)) for k in ks)))\n",
    "    for x in sort_index:\n",
    "        hamiltonian[x].printString(f1)\n",
    "    print(sort_index)\n",
    "    print(lengthCount)\n",
    "    f1.close()\n",
    "    \n",
    "def writeUCC(coefficients,ham_terms,f1,nqubits,mapping='JW'):\n",
    "    \"\"\"\n",
    "        Takes a set of coefficients and excitation operators and \n",
    "        return the corresponding circuit using CNOTs and arbitrary qubit rotations\n",
    "    \"\"\"\n",
    "    f1.write('--- Ansatz preparation ---\\n')\n",
    "    n=-1\n",
    "    for c,t in zip(coefficients, ham_terms):\n",
    "        if mapping=='JW':\n",
    "            subterms = diffJW(t,nqubits)\n",
    "        if mapping=='BK':\n",
    "            subterms = diffBK(t,nqubits)\n",
    "        n+=1\n",
    "        f2.write('b{0}\\t{1:.12f}\\n'.format(n,c))\n",
    "        for subterm in subterms:\n",
    "            print(subterm)\n",
    "            subterm.printCircuit(f1,'b'+str(n))\n",
    "\n",
    "def writeQASM(coefficients,ham_terms,nqubits,filepath,mapping='JW'):\n",
    "    \"\"\"\n",
    "        Write qasm circuit of MPS+GUCCI for qHipster\n",
    "    \"\"\"\n",
    "    f1 = open(filepath+'.qasm','w')\n",
    "    f2 = open(filepath+'-b.out','w')\n",
    "    n=-1\n",
    "    f1.write('--- initialization ---\\n')\n",
    "    for n in range(8):\n",
    "        f1.write('\\tqubit\\tq'+str(n)+',0\\n')\n",
    "    f1.write('--- MPS preparation ---\\n')\n",
    "    f1.write('\\tRy\\tq0\\ta5\\n')\n",
    "    f1.write('\\tcnot\\tq0,q7\\n')\n",
    "\n",
    "    f1.write('\\tRy\\tq6\\ta4\\n')\n",
    "    f1.write('\\tcnot\\tq0,q6\\n')\n",
    "    f1.write('\\tRy\\tq6\\t-a4\\n')    \n",
    "    f1.write('\\tcnot\\tq0,q6\\n')\n",
    "    \n",
    "    f1.write('\\tX\\tq0\\n')    \n",
    "    f1.write('\\tcnot\\tq0,q5\\n')    \n",
    "    f1.write('\\tX\\tq0\\n')    \n",
    "\n",
    "    f1.write('\\tRy\\tq4\\ta1\\n')\n",
    "    f1.write('\\tcnot\\tq0,q4\\n')\n",
    "    f1.write('\\tRy\\tq4\\t-a1\\n')\n",
    "    f1.write('\\tcnot\\tq0,q4\\n')\n",
    "\n",
    "    f1.write('\\tRy\\tq4\\ta2\\n')\n",
    "    f1.write('\\tcnot\\tq0,q4\\n')\n",
    "    f1.write('\\tRy\\tq4\\t-a2\\n')\n",
    "    f1.write('\\tcnot\\tq0,q4\\n')\n",
    "\n",
    "    f1.write('\\tRy\\tq0\\ta0\\n')\n",
    "    f1.write('\\tcnot\\tq0,q3\\n')\n",
    "\n",
    "    f1.write('\\tcnot\\tq0,q2\\n')\n",
    "\n",
    "    f1.write('\\tX\\tq0\\n')    \n",
    "    f1.write('\\tcnot\\tq0,q1\\n')    \n",
    "\n",
    "    writeUCC(coefficients,ham_terms, f1, nqubits, mapping)\n",
    "\n",
    "    f1.close()\n",
    "    \n",
    "    \n",
    "def writeHamiltonian(coefficients,ham_terms,filepath):\n",
    "    hamiltonian = getJWHamiltonian(coefficients, ham_terms, 8)\n",
    "    orderAndPrintHamiltonian(hamiltonian,filepath+'.ham')\n",
    "    f1.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Routines to divide Hamiltonian into commuting groups"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T10:35:33.005778",
     "start_time": "2016-12-14T10:35:32.816511"
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    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def canBeMerge(group1,group2):\n",
    "    merge = True\n",
    "    for x in group1:\n",
    "        for y in group2:\n",
    "            #print(\"Terms:\",x.printTerm(),y.printTerm())\n",
    "            if checkCommutation(x,y)==False:\n",
    "                merge = False\n",
    "                break\n",
    "        else:\n",
    "            continue\n",
    "        break\n",
    "    return merge\n",
    "\n",
    "def canBeMerge2(group1,group2):\n",
    "    merge = True\n",
    "    for x in group1:\n",
    "        for y in group2:\n",
    "            #print(\"Terms:\",x.printTerm(),y.printTerm())\n",
    "            if checkCommutation2(x,y)==False:\n",
    "                merge = False\n",
    "                break\n",
    "        else:\n",
    "            continue\n",
    "        break\n",
    "    return merge\n",
    "\n",
    "def sweepStep(hamGroups):\n",
    "    length = len(hamGroups)\n",
    "    for n in range(length):      \n",
    "        x = hamGroups[n]\n",
    "        for m in range(n+1,length):  \n",
    "            y = hamGroups[m]\n",
    "            if canBeMerge(x,y) == True:\n",
    "                #print(n,m,\"YES\")\n",
    "                y.extend(x)\n",
    "                hamGroups.remove(x)\n",
    "                break\n",
    "        else:\n",
    "            continue\n",
    "        break\n",
    "\n",
    "def sweepStep2(hamGroups):\n",
    "    length = len(hamGroups)\n",
    "    for n in range(length):      \n",
    "        x = hamGroups[n]\n",
    "        for m in range(n+1,length):  \n",
    "            y = hamGroups[m]\n",
    "            if canBeMerge2(x,y) == True:\n",
    "                #print(n,m,\"YES\")\n",
    "                y.extend(x)\n",
    "                hamGroups.remove(x)\n",
    "                break\n",
    "        else:\n",
    "            continue\n",
    "        break\n",
    "        \n",
    "def groupHamiltonian(ham):\n",
    "    hamGroups = []\n",
    "    for x in ham:\n",
    "        hamGroups.append([x])\n",
    "    start_time = time.time()\n",
    "    nelements = len(hamGroups)\n",
    "    nelements2 = 0\n",
    "    while nelements>nelements2:\n",
    "        nelements = len(hamGroups)\n",
    "        sweepStep(hamGroups)\n",
    "        nelements2 = len(hamGroups)\n",
    "        #print(nelements,nelements2)\n",
    "    total_time = time.time() - start_time\n",
    "    total_memory = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss / 1000\n",
    "    return hamGroups, total_time, total_memory\n",
    "\n",
    "def groupHamiltonian(ham):\n",
    "    hamGroups = []\n",
    "    for x in ham:\n",
    "        hamGroups.append([x])\n",
    "    start_time = time.time()\n",
    "    nelements = len(hamGroups)\n",
    "    nelements2 = 0\n",
    "    while nelements>nelements2:\n",
    "        nelements = len(hamGroups)\n",
    "        sweepStep2(hamGroups)\n",
    "        nelements2 = len(hamGroups)\n",
    "        #print(nelements,nelements2)\n",
    "    total_time = time.time() - start_time\n",
    "    total_memory = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss / 1000\n",
    "    return hamGroups, total_time, total_memory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T09:05:58.810825",
     "start_time": "2016-12-14T09:05:58.806571"
    }
   },
   "source": [
    "## Hubbard hamiltonians"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T09:10:30.760836",
     "start_time": "2016-12-14T09:10:30.536541"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def constructSymbolicHubbard2(hdim,vdim,t,U):\n",
    "    \"\"\"\n",
    "        Generates the Hamiltonian for a Hubbard model in a grid structure\n",
    "        with hdim and vdim sites in the horizontal and the vertical dimensions, respectively\n",
    "        \n",
    "        The system in periodic in the horizontal dimension and \n",
    "        open in the vertical dimension\n",
    "        \n",
    "        Inputs: number of sites (nsites), t and U (parameters of the model)\n",
    "        \n",
    "        t: hopping parameters. A positive t must be provided\n",
    "        U: repulsion parameters\n",
    "        \n",
    "        \n",
    "    \"\"\"\n",
    "    hdim = hdim*2\n",
    "    nqubits = vdim*hdim\n",
    "    # first horizontal line of sites\n",
    "    firstLine = range(1,hdim-1)\n",
    "    spinDownList = [x for x in firstLine if x % 2 == 1]\n",
    "    coefficients=[]\n",
    "    operators=[]\n",
    "    # Generating the horizontal contributions to the hamiltonian\n",
    "    for j in range(0,vdim):\n",
    "        offset = j*hdim\n",
    "        for i in spinDownList:\n",
    "            #print(i)\n",
    "            operators.append([i+offset,-i-2-offset])\n",
    "            coefficients.append(-t)\n",
    "            operators.append([i+1+offset,-i-3-offset])\n",
    "            coefficients.append(-t)            \n",
    "        # periodic boundary conditions\n",
    "        if hdim > 2:\n",
    "            operators.append([hdim-1+offset,-1-offset])\n",
    "            coefficients.append(-t)\n",
    "            operators.append([hdim+offset,-2-offset])\n",
    "            coefficients.append(-t)     \n",
    "    #print(\"spinDownList\",spinDownList)\n",
    "    #print(\"horizontal contributions:\",operators)\n",
    "\n",
    "    # Generating the vertical contributions to the hamiltonian\n",
    "    # open boundary conditions\n",
    "    firstLine = range(1,hdim+1)\n",
    "    spinDownList = [x for x in firstLine if x % 2 == 1]\n",
    "    #print(\"spinDownList\",spinDownList)\n",
    "    for j in range(1,vdim):\n",
    "        offset1 = (j-1)*hdim\n",
    "        offset2 = j*hdim\n",
    "        for i in spinDownList:\n",
    "            #print(i)\n",
    "            operators.append([i+offset1,-i-offset2])\n",
    "            coefficients.append(-t)\n",
    "            operators.append([i+1+offset1,-i-1-offset2])\n",
    "            coefficients.append(-t)            \n",
    "    #print(\"vertical contributions:\",operators)\n",
    "    \n",
    "    # repulsion terms\n",
    "    allQubits = range(1,nqubits+1)\n",
    "    spinDownListAll = [x for x in allQubits if x % 2 == 1]\n",
    "    for i in spinDownListAll:\n",
    "        operators.append([i,-i,i+1,-i-1])\n",
    "        coefficients.append(U)\n",
    "    \n",
    "    #print(\"repulsion contributions:\",operators)\n",
    "    return operators, coefficients, nqubits\n",
    "\n",
    "compBasis={'1':basis(2,1),'0':basis(2,0)}\n",
    "pauli={'I':qeye(2),'Z':sigmaz(),'X':sigmax(),'Y':sigmay()}\n",
    "\n",
    "def constructNumberOperator(nqubits,transformation='JW'):\n",
    "    operators = []\n",
    "    coefficients = []\n",
    "    for n in range(1,nqubits+1):\n",
    "        operators.append([n,-n])\n",
    "        coefficients.append(1.0)\n",
    "    if transformation == 'JW':\n",
    "        number_op = getHamiltonianObject(getJWHamiltonian(coefficients, operators, nqubits))\n",
    "    elif transformation == 'BK': \n",
    "        number_op = getHamiltonianObject(getBKHamiltonian(coefficients, operators, nqubits))\n",
    "    return number_op\n",
    "\n",
    "def genNqubitState(state):\n",
    "    l=[]\n",
    "    for x in state:\n",
    "        l.append(compBasis[x])\n",
    "    result=tensor(l)\n",
    "    return result   \n",
    "\n",
    "def pickSubspace(numberOfParticles,eigenvals,eigenvecs):\n",
    "    eigenvalsN = []\n",
    "    eigenvecsN = []\n",
    "    nqubits = int(np.log2(eigenvecs[0].shape[0]))\n",
    "    print(nqubits)\n",
    "    number_op = constructNumberOperator(nqubits,transformation)\n",
    "    for vector, value in zip(eigenvecs,eigenvals):\n",
    "        if int(expect(number_op,vector)) == numberOfParticles:\n",
    "            eigenvecsN.append(vector)\n",
    "            eigenvalsN.append(value)\n",
    "    return eigenvalsN, eigenvecsN\n",
    "\n",
    "def getFockStateNumber(state):\n",
    "    nonZeroEntries=[]\n",
    "    for n in range(state.shape[0]):\n",
    "        if abs(state[n])>0.0:\n",
    "            nonZeroEntries.append(state[n]**2.0)\n",
    "    return nonZeroEntries,len(nonZeroEntries),np.std(np.array(nonZeroEntries))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: getting the representation of the Unitary Coupled Cluster operators (JW and BK representations)\n",
    "\n",
    "This operators are excitation operators minus their conjugates. For example: $a_i^{\\dagger}a_j^{\\dagger}a_ka_l-a_l^{\\dagger}a_k^{\\dagger}a_ka_i$ (double excitation). The double excitation is represented as: [i,j,-k,-l]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T09:10:32.716431",
     "start_time": "2016-12-14T09:10:32.532393"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time for transformation: 0.023927927017211914\n",
      "length of products: 32\n",
      "Time for simplification: 0.009505033493041992\n",
      "length of products2: 8\n",
      "{0: ['X'], 1: ['I'], 2: ['Y'], 3: ['I'], 4: ['I'], 5: ['I'], 6: ['I'], 7: ['I']}\n",
      "1 0.125j X0I1Y2I3I4I5I6I7\n",
      "{0: ['X'], 1: ['Z'], 2: ['Y'], 3: ['I'], 4: ['I'], 5: ['I'], 6: ['I'], 7: ['I']}\n",
      "2 0.125j X0Z1Y2I3I4I5I6I7\n",
      "{0: ['Y'], 1: ['I'], 2: ['X'], 3: ['I'], 4: ['I'], 5: ['I'], 6: ['I'], 7: ['I']}\n",
      "3 -0.125j Y0I1X2I3I4I5I6I7\n",
      "{0: ['Y'], 1: ['Z'], 2: ['X'], 3: ['I'], 4: ['I'], 5: ['I'], 6: ['I'], 7: ['I']}\n",
      "4 -0.125j Y0Z1X2I3I4I5I6I7\n",
      "{0: ['Y'], 1: ['Z'], 2: ['X'], 3: ['Z'], 4: ['I'], 5: ['I'], 6: ['I'], 7: ['I']}\n",
      "5 -0.125j Y0Z1X2Z3I4I5I6I7\n",
      "{0: ['Y'], 1: ['I'], 2: ['X'], 3: ['Z'], 4: ['I'], 5: ['I'], 6: ['I'], 7: ['I']}\n",
      "6 -0.125j Y0I1X2Z3I4I5I6I7\n",
      "{0: ['X'], 1: ['Z'], 2: ['Y'], 3: ['Z'], 4: ['I'], 5: ['I'], 6: ['I'], 7: ['I']}\n",
      "7 0.125j X0Z1Y2Z3I4I5I6I7\n",
      "{0: ['X'], 1: ['I'], 2: ['Y'], 3: ['Z'], 4: ['I'], 5: ['I'], 6: ['I'], 7: ['I']}\n",
      "8 0.125j X0I1Y2Z3I4I5I6I7\n"
     ]
    }
   ],
   "source": [
    "# Example for $a_8^{\\dagger}a_7^{\\dagger}a_6a_5-a_5^{\\dagger}a_6^{\\dagger}7_ka_8$ for a system with 8 qubits.\n",
    "b,P,U,F,R=generateBKSets(8)\n",
    "e=diffBK([4,3,-2,-1],P,U,F,R)\n",
    "counter=0\n",
    "for x in e:\n",
    "    counter += 1\n",
    "    print(x.pl)\n",
    "    c,t=x.printTerm()\n",
    "    print(counter,c, t)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T09:10:33.912099",
     "start_time": "2016-12-14T09:10:33.851013"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "f1=open('exampleCircuit','w')\n",
    "e[4].printCircuit(f1)\n",
    "f1.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T09:10:34.953764",
     "start_time": "2016-12-14T09:10:34.933255"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time for transformation: 0.0033349990844726562\n",
      "length of products: 32\n",
      "Time for simplification: 0.0004329681396484375\n",
      "length of products3: 8\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_X^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_X^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_X^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_X^3', 4) (-0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_X^3', 4) (0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_X^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_X^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_X^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_X^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_X^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_X^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_X^3', 4) (-0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_X^3', 4) (0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_X^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_X^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_X^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_X^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_X^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_X^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_X^3', 4) (-0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_X^3', 4) (0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_X^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_X^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_X^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_X^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_X^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_X^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_X^3', 4) (-0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_X^3', 4) (0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_X^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_X^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_X^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_Y^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_Y^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_Y^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_Y^3', 4) (-0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_Y^3', 4) (0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_Y^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_Y^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_Y^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_Y^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_Y^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_Y^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_Y^3', 4) (-0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_Y^3', 4) (0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_Y^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_Y^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_Y^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_Y^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_Y^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_Y^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_Y^3', 4) (-0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_Y^3', 4) (0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_Y^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_Y^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_Y^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_Y^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_Y^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_Y^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_Y^3', 4) (-0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_X^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_Y^3', 4) (0.125j, '\\\\sigma_Y^0\\\\sigma_X^1\\\\sigma_Y^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_Y^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_Y^1\\\\sigma_Y^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_Y^3', 4) (0.125j, '\\\\sigma_X^0\\\\sigma_X^1\\\\sigma_X^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n",
      "(-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_Y^3', 4) (-0.125j, '\\\\sigma_Y^0\\\\sigma_Y^1\\\\sigma_X^2\\\\sigma_Y^3', 4)\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "x=diffJW([4,3,-2,-1],8)\n",
    "for y in x:\n",
    "    print\n",
    "    for z in x:\n",
    "        print(y.printTerm4(), z.printTerm4())\n",
    "        print(checkCommutation(z,y))\n",
    "        print(checkCommutation2(z,y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Getting all the single and double operators for a system with 8 molecular orbitals in 8 qubits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T09:10:36.979852",
     "start_time": "2016-12-14T09:10:36.976519"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[3, -1], [4, -1], [5, -1], [6, -1], [3, -2], [4, -2], [5, -2], [6, -2], [4, 3, -2, -1], [5, 3, -2, -1], [6, 3, -2, -1], [5, 4, -2, -1], [6, 4, -2, -1], [6, 5, -2, -1]]\n"
     ]
    }
   ],
   "source": [
    "x=createExcitations(2,6,2)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Here we also count the number of SWAPS and CNOTs required to simulate the first term in the sum representing every excitation operator (excitation operators are sums of at least 2 products of Pauli matrices in the BK representation :P)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T09:10:38.543453",
     "start_time": "2016-12-14T09:10:38.537066"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#operators=[]\n",
    "#totalCZ=0\n",
    "#totalSQ=0\n",
    "#for y in x:\n",
    "#    op=diffJW(y,6)\n",
    "#    operators += op\n",
    "#    print(y)\n",
    "#    for cosa in op:\n",
    "#        a,b,c,d,e,f,g,h=cosa.printTerm3()\n",
    "#        print(a,b,c,d,e,f,g,h)\n",
    "#        print(cosa.printTerm())\n",
    "#        totalSQ += e\n",
    "#        totalCZ += f\n",
    "#        print\n",
    "#    print('total SQ:', totalSQ, 'total CZ:',totalCZ)\n",
    "#    print"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: reading the hamiltonian of H2. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T09:10:41.192081",
     "start_time": "2016-12-14T09:10:41.083228"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inside commutators: path integrals/H2/H2_0.75-STO6G-NMO.int\n",
      "commutators path: integrals/H2/H2_0.75-STO6G-NMO.int\n",
      "The FCIenergy from integrals file is: -1.1457416723\n",
      "Time for transformation: 0.01692485809326172\n",
      "length of products: 144\n",
      "Time for simplification: 0.06097698211669922\n",
      "length of products3: 15\n",
      "(-0.8229486547799898+0j) I0I1I2I3\n",
      "(0.17176868595639527+0j) Z0I1I2I3\n",
      "(0.1717686859563953+0j) I0Z1I2I3\n",
      "(-0.21736788612184887+0j) I0I1Z2I3\n",
      "(-0.21736788612184887+0j) I0I1I2Z3\n",
      "(0.16819661852139073+0j) Z0Z1I2I3\n",
      "(0.12014567801253387+0j) Z0I1Z2I3\n",
      "(0.16566073965958383+0j) I0Z1Z2I3\n",
      "(0.16566073965958383+0j) Z0I1I2Z3\n",
      "(0.12014567801253387+0j) I0Z1I2Z3\n",
      "(0.17433760124527048+0j) I0I1Z2Z3\n",
      "(0.04551506164704997+0j) Y0X1X2Y3\n",
      "(-0.04551506164704997+0j) X0X1Y2Y3\n",
      "(-0.04551506164704997+0j) Y0Y1X2X3\n",
      "(0.04551506164704997+0j) X0Y1Y2X3\n",
      "\n"
     ]
    }
   ],
   "source": [
    "molecule='H2'\n",
    "basis='0.75-STO6G-NMO'\n",
    "#path = '/home/jonathan/exacta/integrals/H2/H2_0.75-STO6G-NMO.int'\n",
    "path = 'integrals/H2/H2_0.75-STO6G-NMO.int'\n",
    "hamiltonianH2=getHam_JW(molecule,basis,path)\n",
    "\n",
    "counter=0\n",
    "for x in hamiltonianH2:\n",
    "    counter += 1\n",
    "    c,t=x.printTerm()\n",
    "    print(c,t)\n",
    "print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Grouping terms in the Hamiltonian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T09:13:06.318998",
     "start_time": "2016-12-14T09:13:06.304912"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.009736061096191406 96632.832\n",
      "2 15\n"
     ]
    }
   ],
   "source": [
    "groupedHamH2,a,b = groupHamiltonian(hamiltonianH2)\n",
    "print(a,b)\n",
    "print(len(groupedHamH2),len(hamiltonianH2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T09:13:08.571182",
     "start_time": "2016-12-14T09:13:08.567057"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "((0.17433760124527048+0j), 'I0I1Z2Z3')\n",
      "((0.12014567801253387+0j), 'I0Z1I2Z3')\n",
      "((0.16566073965958383+0j), 'Z0I1I2Z3')\n",
      "((0.16566073965958383+0j), 'I0Z1Z2I3')\n",
      "((0.12014567801253387+0j), 'Z0I1Z2I3')\n",
      "((0.16819661852139073+0j), 'Z0Z1I2I3')\n",
      "((-0.21736788612184887+0j), 'I0I1I2Z3')\n",
      "((-0.21736788612184887+0j), 'I0I1Z2I3')\n",
      "((0.1717686859563953+0j), 'I0Z1I2I3')\n",
      "((0.17176868595639527+0j), 'Z0I1I2I3')\n",
      "((-0.8229486547799898+0j), 'I0I1I2I3')\n"
     ]
    }
   ],
   "source": [
    "for x in groupedHamH2[0]:\n",
    "    print(x.printTerm())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T09:13:18.179652",
     "start_time": "2016-12-14T09:13:18.169944"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n"
     ]
    }
   ],
   "source": [
    "for x in groupedHamH2[0]:\n",
    "    for y in groupedHamH2[1]:\n",
    "        print(checkCommutation(x,y),checkCommutation2(x,y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T09:36:05.846675",
     "start_time": "2016-12-14T09:25:14.449814"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inside commutators: path integrals/various/HF-CMO.int\n",
      "commutators path: integrals/various/HF-CMO.int\n",
      "The FCIenergy from integrals file is: -99.5302667207\n",
      "Time for transformation: 1.6452889442443848\n",
      "length of products: 6912\n",
      "Time for simplification: 649.5523002147675\n",
      "length of products3: 631\n"
     ]
    }
   ],
   "source": [
    "# with simplification for each term\n",
    "# one step simplification for the whole hamiltonian\n",
    "molecule='HF'\n",
    "basis='CMO'\n",
    "#path = '/home/jonathan/exacta/integrals/H2/H2_0.75-STO6G-NMO.int'\n",
    "path = 'integrals/various/HF-CMO.int'\n",
    "hamiltonianHF=getHam_JW(molecule,basis,path)\n",
    "\n",
    "#counter=0\n",
    "#for x in hamiltonian:\n",
    "#    counter += 1\n",
    "#    c,t=x.printTerm()\n",
    "#    print(c,t)\n",
    "#print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T10:30:21.579829",
     "start_time": "2016-12-14T10:28:57.773258"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "83.79119396209717 102957.056\n",
      "45 631\n"
     ]
    }
   ],
   "source": [
    "groupedHamHF,a,b = groupHamiltonian(hamiltonianHF)\n",
    "print(a,b)\n",
    "print(len(groupedHamHF),len(hamiltonianHF))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T10:35:50.364715",
     "start_time": "2016-12-14T10:35:45.430423"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.928544044494629 102957.056\n",
      "45 631\n"
     ]
    }
   ],
   "source": [
    "groupedHamHF_2,a,b = groupHamiltonian2(hamiltonianHF)\n",
    "print(a,b)\n",
    "print(len(groupedHamHF_2),len(hamiltonianHF))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T10:36:15.403146",
     "start_time": "2016-12-14T10:36:15.168690"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
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      "False False\n",
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      "False False\n",
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      "False False\n",
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      "True True\n",
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      "True True\n",
      "True True\n",
      "False False\n",
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      "True True\n",
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      "True True\n",
      "True True\n",
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      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "False False\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n",
      "True True\n"
     ]
    }
   ],
   "source": [
    "for x in groupedHamHF_2[0]:\n",
    "    for y in groupedHamHF_2[1]:\n",
    "        print(checkCommutation(x,y),checkCommutation2(x,y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T10:36:32.507147",
     "start_time": "2016-12-14T10:36:32.501865"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OK 0\n",
      "OK 1\n",
      "OK 2\n",
      "OK 3\n",
      "OK 4\n",
      "OK 5\n",
      "OK 6\n",
      "OK 7\n",
      "OK 8\n",
      "OK 9\n",
      "OK 10\n",
      "OK 11\n",
      "OK 12\n",
      "OK 13\n",
      "OK 14\n",
      "OK 15\n",
      "OK 16\n",
      "OK 17\n",
      "OK 18\n",
      "OK 19\n",
      "OK 20\n",
      "OK 21\n",
      "OK 22\n",
      "OK 23\n",
      "OK 24\n",
      "OK 25\n",
      "OK 26\n",
      "OK 27\n",
      "OK 28\n",
      "OK 29\n",
      "OK 30\n",
      "OK 31\n",
      "OK 32\n",
      "OK 33\n",
      "OK 34\n",
      "OK 35\n",
      "OK 36\n",
      "OK 37\n",
      "OK 38\n",
      "OK 39\n",
      "OK 40\n",
      "OK 41\n",
      "OK 42\n",
      "OK 43\n",
      "OK 44\n"
     ]
    }
   ],
   "source": [
    "for n in range(45):\n",
    "    if len(groupedHamHF[n])!=len(groupedHamHF_2[n]):\n",
    "        print(\"UPS\",n)\n",
    "    else:\n",
    "        print(\"OK\",n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-11-25T15:09:44.964135",
     "start_time": "2016-11-25T15:09:44.959740"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-6.305142059700003\n",
      "-6.964669032858822\n"
     ]
    }
   ],
   "source": [
    "print(-76.05864148+69.7534994203)\n",
    "print(-75.954194566436+68.9895255335771793)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-10-10T11:39:20.316490",
     "start_time": "2016-10-10T11:39:20.311891"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#molecule='H4'\n",
    "#basis='90.00-STO-6G'\n",
    "#path = '/home/jonathan/integrals/H4-PES-STO6G-int/H4-90.00-STO-6G.int'\n",
    "#hamiltonian2=getHam_JW(molecule,basis,path)\n",
    "\n",
    "#counter=0\n",
    "#for x in hamiltonian:\n",
    "#    counter += 1\n",
    "#    c,t=x.printTerm()\n",
    "#    print(c,t)\n",
    "#print()\n",
    "\n",
    "#print(\"Hamiltonian Qobj:\")\n",
    "#hamo2=getHamiltonianObject(hamiltonian2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#print(hamo2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#molecule='H2'\n",
    "#basis='0.75-STO6G-NMO'\n",
    "#path = '/home/jonathan/exacta/integrals/various/H2-321G-NMO.int'\n",
    "#hamiltonian=getHam_JW(molecule,basis,path)\n",
    "\n",
    "#counter=0\n",
    "#for x in hamiltonian:\n",
    "#    counter += 1\n",
    "#    c,t=x.printTerm()\n",
    "#    print c,t\n",
    "#print"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Hubbard model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T10:37:25.412856",
     "start_time": "2016-12-14T10:37:23.308913"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time for transformation: 0.0074770450592041016\n",
      "length of products: 24\n",
      "Time for simplification: 0.00032901763916015625\n",
      "length of products3: 13\n",
      "[[1, -3], [2, -4], [3, -5], [4, -6], [5, -1], [6, -2], [7, -9], [8, -10], [9, -11], [10, -12], [11, -7], [12, -8], [1, -7], [2, -8], [3, -9], [4, -10], [5, -11], [6, -12], [1, -1, 2, -2], [3, -3, 4, -4], [5, -5, 6, -6], [7, -7, 8, -8], [9, -9, 10, -10], [11, -11, 12, -12]]\n",
      "[-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0]\n",
      "12\n",
      "Time for transformation: 0.02306509017944336\n",
      "length of products: 96\n",
      "Time for simplification: 0.013802051544189453\n",
      "length of products3: 91\n",
      "Symbolic Hamiltonian:\n",
      "(0.25j, 'Y0Z1X2I3I4I5I6I7I8I9I10I11')\n",
      "((-0.25+0j), 'Y0Z1Y2I3I4I5I6I7I8I9I10I11')\n",
      "((-0.25+0j), 'X0Z1X2I3I4I5I6I7I8I9I10I11')\n",
      "(-0.25j, 'X0Z1Y2I3I4I5I6I7I8I9I10I11')\n",
      "(0.25j, 'I0Y1Z2X3I4I5I6I7I8I9I10I11')\n",
      "((-0.25+0j), 'I0Y1Z2Y3I4I5I6I7I8I9I10I11')\n",
      "((-0.25+0j), 'I0X1Z2X3I4I5I6I7I8I9I10I11')\n",
      "(-0.25j, 'I0X1Z2Y3I4I5I6I7I8I9I10I11')\n",
      "(0.25j, 'I0I1Y2Z3X4I5I6I7I8I9I10I11')\n",
      "((-0.25+0j), 'I0I1Y2Z3Y4I5I6I7I8I9I10I11')\n",
      "((-0.25+0j), 'I0I1X2Z3X4I5I6I7I8I9I10I11')\n",
      "(-0.25j, 'I0I1X2Z3Y4I5I6I7I8I9I10I11')\n",
      "(0.25j, 'I0I1I2Y3Z4X5I6I7I8I9I10I11')\n",
      "((-0.25+0j), 'I0I1I2Y3Z4Y5I6I7I8I9I10I11')\n",
      "((-0.25+0j), 'I0I1I2X3Z4X5I6I7I8I9I10I11')\n",
      "(-0.25j, 'I0I1I2X3Z4Y5I6I7I8I9I10I11')\n",
      "(-0.25j, 'Y0Z1Z2Z3X4I5I6I7I8I9I10I11')\n",
      "((-0.25+0j), 'X0Z1Z2Z3X4I5I6I7I8I9I10I11')\n",
      "((-0.25+0j), 'Y0Z1Z2Z3Y4I5I6I7I8I9I10I11')\n",
      "(0.25j, 'X0Z1Z2Z3Y4I5I6I7I8I9I10I11')\n",
      "(-0.25j, 'I0Y1Z2Z3Z4X5I6I7I8I9I10I11')\n",
      "((-0.25+0j), 'I0X1Z2Z3Z4X5I6I7I8I9I10I11')\n",
      "((-0.25+0j), 'I0Y1Z2Z3Z4Y5I6I7I8I9I10I11')\n",
      "(0.25j, 'I0X1Z2Z3Z4Y5I6I7I8I9I10I11')\n",
      "(0.25j, 'I0I1I2I3I4I5Y6Z7X8I9I10I11')\n",
      "((-0.25+0j), 'I0I1I2I3I4I5Y6Z7Y8I9I10I11')\n",
      "((-0.25+0j), 'I0I1I2I3I4I5X6Z7X8I9I10I11')\n",
      "(-0.25j, 'I0I1I2I3I4I5X6Z7Y8I9I10I11')\n",
      "(0.25j, 'I0I1I2I3I4I5I6Y7Z8X9I10I11')\n",
      "((-0.25+0j), 'I0I1I2I3I4I5I6Y7Z8Y9I10I11')\n",
      "((-0.25+0j), 'I0I1I2I3I4I5I6X7Z8X9I10I11')\n",
      "(-0.25j, 'I0I1I2I3I4I5I6X7Z8Y9I10I11')\n",
      "(0.25j, 'I0I1I2I3I4I5I6I7Y8Z9X10I11')\n",
      "((-0.25+0j), 'I0I1I2I3I4I5I6I7Y8Z9Y10I11')\n",
      "((-0.25+0j), 'I0I1I2I3I4I5I6I7X8Z9X10I11')\n",
      "(-0.25j, 'I0I1I2I3I4I5I6I7X8Z9Y10I11')\n",
      "(0.25j, 'I0I1I2I3I4I5I6I7I8Y9Z10X11')\n",
      "((-0.25+0j), 'I0I1I2I3I4I5I6I7I8Y9Z10Y11')\n",
      "((-0.25+0j), 'I0I1I2I3I4I5I6I7I8X9Z10X11')\n",
      "(-0.25j, 'I0I1I2I3I4I5I6I7I8X9Z10Y11')\n",
      "(-0.25j, 'I0I1I2I3I4I5Y6Z7Z8Z9X10I11')\n",
      "((-0.25+0j), 'I0I1I2I3I4I5X6Z7Z8Z9X10I11')\n",
      "((-0.25+0j), 'I0I1I2I3I4I5Y6Z7Z8Z9Y10I11')\n",
      "(0.25j, 'I0I1I2I3I4I5X6Z7Z8Z9Y10I11')\n",
      "(-0.25j, 'I0I1I2I3I4I5I6Y7Z8Z9Z10X11')\n",
      "((-0.25+0j), 'I0I1I2I3I4I5I6X7Z8Z9Z10X11')\n",
      "((-0.25+0j), 'I0I1I2I3I4I5I6Y7Z8Z9Z10Y11')\n",
      "(0.25j, 'I0I1I2I3I4I5I6X7Z8Z9Z10Y11')\n",
      "(0.25j, 'Y0Z1Z2Z3Z4Z5X6I7I8I9I10I11')\n",
      "((-0.25+0j), 'Y0Z1Z2Z3Z4Z5Y6I7I8I9I10I11')\n",
      "((-0.25+0j), 'X0Z1Z2Z3Z4Z5X6I7I8I9I10I11')\n",
      "(-0.25j, 'X0Z1Z2Z3Z4Z5Y6I7I8I9I10I11')\n",
      "(0.25j, 'I0Y1Z2Z3Z4Z5Z6X7I8I9I10I11')\n",
      "((-0.25+0j), 'I0Y1Z2Z3Z4Z5Z6Y7I8I9I10I11')\n",
      "((-0.25+0j), 'I0X1Z2Z3Z4Z5Z6X7I8I9I10I11')\n",
      "(-0.25j, 'I0X1Z2Z3Z4Z5Z6Y7I8I9I10I11')\n",
      "(0.25j, 'I0I1Y2Z3Z4Z5Z6Z7X8I9I10I11')\n",
      "((-0.25+0j), 'I0I1Y2Z3Z4Z5Z6Z7Y8I9I10I11')\n",
      "((-0.25+0j), 'I0I1X2Z3Z4Z5Z6Z7X8I9I10I11')\n",
      "(-0.25j, 'I0I1X2Z3Z4Z5Z6Z7Y8I9I10I11')\n",
      "(0.25j, 'I0I1I2Y3Z4Z5Z6Z7Z8X9I10I11')\n",
      "((-0.25+0j), 'I0I1I2Y3Z4Z5Z6Z7Z8Y9I10I11')\n",
      "((-0.25+0j), 'I0I1I2X3Z4Z5Z6Z7Z8X9I10I11')\n",
      "(-0.25j, 'I0I1I2X3Z4Z5Z6Z7Z8Y9I10I11')\n",
      "(0.25j, 'I0I1I2I3Y4Z5Z6Z7Z8Z9X10I11')\n",
      "((-0.25+0j), 'I0I1I2I3Y4Z5Z6Z7Z8Z9Y10I11')\n",
      "((-0.25+0j), 'I0I1I2I3X4Z5Z6Z7Z8Z9X10I11')\n",
      "(-0.25j, 'I0I1I2I3X4Z5Z6Z7Z8Z9Y10I11')\n",
      "(0.25j, 'I0I1I2I3I4Y5Z6Z7Z8Z9Z10X11')\n",
      "((-0.25+0j), 'I0I1I2I3I4Y5Z6Z7Z8Z9Z10Y11')\n",
      "((-0.25+0j), 'I0I1I2I3I4X5Z6Z7Z8Z9Z10X11')\n",
      "(-0.25j, 'I0I1I2I3I4X5Z6Z7Z8Z9Z10Y11')\n",
      "((3+0j), 'I0I1I2I3I4I5I6I7I8I9I10I11')\n",
      "((-0.5+0j), 'I0Z1I2I3I4I5I6I7I8I9I10I11')\n",
      "((-0.5+0j), 'Z0I1I2I3I4I5I6I7I8I9I10I11')\n",
      "((0.5+0j), 'Z0Z1I2I3I4I5I6I7I8I9I10I11')\n",
      "((-0.5+0j), 'I0I1I2Z3I4I5I6I7I8I9I10I11')\n",
      "((-0.5+0j), 'I0I1Z2I3I4I5I6I7I8I9I10I11')\n",
      "((0.5+0j), 'I0I1Z2Z3I4I5I6I7I8I9I10I11')\n",
      "((-0.5+0j), 'I0I1I2I3I4Z5I6I7I8I9I10I11')\n",
      "((-0.5+0j), 'I0I1I2I3Z4I5I6I7I8I9I10I11')\n",
      "((0.5+0j), 'I0I1I2I3Z4Z5I6I7I8I9I10I11')\n",
      "((-0.5+0j), 'I0I1I2I3I4I5I6Z7I8I9I10I11')\n",
      "((-0.5+0j), 'I0I1I2I3I4I5Z6I7I8I9I10I11')\n",
      "((0.5+0j), 'I0I1I2I3I4I5Z6Z7I8I9I10I11')\n",
      "((-0.5+0j), 'I0I1I2I3I4I5I6I7I8Z9I10I11')\n",
      "((-0.5+0j), 'I0I1I2I3I4I5I6I7Z8I9I10I11')\n",
      "((0.5+0j), 'I0I1I2I3I4I5I6I7Z8Z9I10I11')\n",
      "((-0.5+0j), 'I0I1I2I3I4I5I6I7I8I9I10Z11')\n",
      "((-0.5+0j), 'I0I1I2I3I4I5I6I7I8I9Z10I11')\n",
      "((0.5+0j), 'I0I1I2I3I4I5I6I7I8I9Z10Z11')\n"
     ]
    }
   ],
   "source": [
    "# generate a Hamiltonian with 2 sites\n",
    "ops,coeffs,nqubits=constructSymbolicHubbard2(3,2,1.0,2.0)\n",
    "number_op = constructNumberOperator(nqubits)\n",
    "print(ops)\n",
    "print(coeffs)\n",
    "print(nqubits)\n",
    "\n",
    "# generate symbolic hamiltonian (ham) and its matrix form (hamo)\n",
    "ham = getJWHamiltonian(coeffs, ops, nqubits)\n",
    "hamo=getHamiltonianObject(ham)\n",
    "\n",
    "#print(hamo)\n",
    "print(\"Symbolic Hamiltonian:\")\n",
    "for x in ham:\n",
    "    print(x.printTerm())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T10:43:48.986401",
     "start_time": "2016-12-14T10:37:25.414808"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-3.12310563 -1.22965392e-15j -2.56155281 -1.69195862e-08j] [ 4.  3.]\n"
     ]
    }
   ],
   "source": [
    "eigenvals,eigenvecs=hamo.eigenstates(eigvals=2)\n",
    "print(eigenvals,expect(number_op,eigenvecs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T10:49:08.433054",
     "start_time": "2016-12-14T10:49:08.424256"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 4.  3.]\n"
     ]
    }
   ],
   "source": [
    "print(expect(number_op,eigenvecs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example with different values of N and M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T10:49:10.316806",
     "start_time": "2016-12-14T10:49:10.307487"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.01        0.09142857  0.17285714  0.25428571  0.33571429  0.41714286\n",
      "  0.49857143  0.58        0.66142857  0.74285714  0.82428571  0.90571429\n",
      "  0.98714286  1.06857143  1.15        1.23142857  1.31285714  1.39428571\n",
      "  1.47571429  1.55714286  1.63857143  1.72        1.80142857  1.88285714\n",
      "  1.96428571  2.04571429  2.12714286  2.20857143  2.29        2.37142857\n",
      "  2.45285714  2.53428571  2.61571429  2.69714286  2.77857143  2.86\n",
      "  2.94142857  3.02285714  3.10428571  3.18571429  3.26714286  3.34857143\n",
      "  3.43        3.51142857  3.59285714  3.67428571  3.75571429  3.83714286\n",
      "  3.91857143  4.        ] [ 2.]\n"
     ]
    }
   ],
   "source": [
    "N=50\n",
    "M=1\n",
    "ts=np.linspace(0.01,4,N)\n",
    "Us=np.linspace(2,4,M)\n",
    "print(ts,Us)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T10:50:15.591037",
     "start_time": "2016-12-14T10:49:11.271131"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time for transformation: 0.003206014633178711\n",
      "length of products: 16\n",
      "Time for simplification: 0.00014519691467285156\n",
      "length of products3: 9\n",
      "Time for transformation: 0.010890960693359375\n",
      "length of products: 48\n",
      "Time for simplification: 0.002844095230102539\n",
      "length of products3: 45\n",
      "t and U combination: 0.01 2.0\n",
      "Energy:  -0.0141918704738\n",
      "-0.0141918704738 2\n",
      "-0.01 2\n",
      "\n",
      "Time for transformation: 0.011836051940917969\n",
      "length of products: 48\n",
      "Time for simplification: 0.002051830291748047\n",
      "length of products3: 45\n",
      "t and U combination: 0.0914285714286 2.0\n",
      "Energy:  -0.133277357585\n",
      "-0.133277357585 2\n",
      "-0.0914285714286 1\n",
      "\n",
      "Time for transformation: 0.01014089584350586\n",
      "length of products: 48\n",
      "Time for simplification: 0.0029609203338623047\n",
      "length of products3: 45\n",
      "t and U combination: 0.172857142857 2.0\n",
      "Energy:  -0.258047283912\n",
      "-0.258047283912 2\n",
      "-0.172857142857 2\n",
      "\n",
      "Time for transformation: 0.010755062103271484\n",
      "length of products: 48\n",
      "Time for simplification: 0.002040863037109375\n",
      "length of products3: 45\n",
      "t and U combination: 0.254285714286 2.0\n",
      "Energy:  -0.387713342521\n",
      "-0.387713342521 2\n",
      "-0.254285714286 2\n",
      "\n",
      "Time for transformation: 0.009578943252563477\n",
      "length of products: 48\n",
      "Time for simplification: 0.002282857894897461\n",
      "length of products3: 45\n",
      "t and U combination: 0.335714285714 2.0\n",
      "Energy:  -0.521566995807\n",
      "-0.521566995807 1\n",
      "-0.335714285714 2\n",
      "\n",
      "Time for transformation: 0.010154008865356445\n",
      "length of products: 48\n",
      "Time for simplification: 0.002056121826171875\n",
      "length of products3: 45\n",
      "t and U combination: 0.417142857143 2.0\n",
      "Energy:  -0.658989204415\n",
      "-0.658989204415 2\n",
      "-0.428399915392 3\n",
      "\n",
      "Time for transformation: 0.009936094284057617\n",
      "length of products: 48\n",
      "Time for simplification: 0.0020079612731933594\n",
      "length of products3: 45\n",
      "t and U combination: 0.498571428571 2.0\n",
      "Energy:  -0.79944922034\n",
      "-0.79944922034 2\n",
      "-0.532533150102 2\n",
      "\n",
      "Time for transformation: 0.013643026351928711\n",
      "length of products: 48\n",
      "Time for simplification: 0.002171039581298828\n",
      "length of products3: 45\n",
      "t and U combination: 0.58 2.0\n",
      "Energy:  -0.942497417993\n",
      "-0.942497417993 1\n",
      "-0.643887168328 3\n",
      "\n",
      "Time for transformation: 0.013485193252563477\n",
      "length of products: 48\n",
      "Time for simplification: 0.002081155776977539\n",
      "length of products3: 45\n",
      "t and U combination: 0.661428571429 2.0\n",
      "Energy:  -1.08775556847\n",
      "-1.08775556847 2\n",
      "-0.761965302384 2\n",
      "\n",
      "Time for transformation: 0.030466079711914062\n",
      "length of products: 48\n",
      "Time for simplification: 0.00321197509765625\n",
      "length of products3: 45\n",
      "t and U combination: 0.742857142857 2.0\n",
      "Energy:  -1.23490661112\n",
      "-1.23490661112 2\n",
      "-0.886066728966 3\n",
      "\n",
      "Time for transformation: 0.00896310806274414\n",
      "length of products: 48\n",
      "Time for simplification: 0.0027320384979248047\n",
      "length of products3: 45\n",
      "t and U combination: 0.824285714286 2.0\n",
      "Energy:  -1.38368501595\n",
      "-1.38368501595 1\n",
      "-1.01541406094 3\n",
      "\n",
      "Time for transformation: 0.010928869247436523\n",
      "length of products: 48\n",
      "Time for simplification: 0.002939939498901367\n",
      "length of products3: 45\n",
      "t and U combination: 0.905714285714 2.0\n",
      "Energy:  -1.53386822457\n",
      "-1.53386822457 2\n",
      "-1.14924688971 3\n",
      "\n",
      "Time for transformation: 0.013602018356323242\n",
      "length of products: 48\n",
      "Time for simplification: 0.002685070037841797\n",
      "length of products3: 45\n",
      "t and U combination: 0.987142857143 2.0\n",
      "Energy:  -1.68526930962\n",
      "-1.68526930962 2\n",
      "-1.28687469958 3\n",
      "\n",
      "Time for transformation: 0.009554862976074219\n",
      "length of products: 48\n",
      "Time for simplification: 0.002285003662109375\n",
      "length of products3: 45\n",
      "t and U combination: 1.06857142857 2.0\n",
      "Energy:  -1.83773081199\n",
      "-1.83773081199 1\n",
      "-1.42769807634 3\n",
      "\n",
      "Time for transformation: 0.01673293113708496\n",
      "length of products: 48\n",
      "Time for simplification: 0.005856037139892578\n",
      "length of products3: 45\n",
      "t and U combination: 1.15 2.0\n",
      "Energy:  -1.99111963379\n",
      "-1.99111963379 2\n",
      "-1.5712104542 2\n",
      "\n",
      "Time for transformation: 0.009284019470214844\n",
      "length of products: 48\n",
      "Time for simplification: 0.002187013626098633\n",
      "length of products3: 45\n",
      "t and U combination: 1.23142857143 2.0\n",
      "Energy:  -2.14532283823\n",
      "-2.14532283823 2\n",
      "-1.71699012674 3\n",
      "\n",
      "Time for transformation: 0.013273954391479492\n",
      "length of products: 48\n",
      "Time for simplification: 0.002074003219604492\n",
      "length of products3: 45\n",
      "t and U combination: 1.31285714286 2.0\n",
      "Energy:  -2.3002442091\n",
      "-2.3002442091 1\n",
      "-1.86468861754 2\n",
      "\n",
      "Time for transformation: 0.0208740234375\n",
      "length of products: 48\n",
      "Time for simplification: 0.0036940574645996094\n",
      "length of products3: 45\n",
      "t and U combination: 1.39428571429 2.0\n",
      "Energy:  -2.45580143698\n",
      "-2.45580143698 2\n",
      "-2.01401866201 3\n",
      "\n",
      "Time for transformation: 0.011729001998901367\n",
      "length of products: 48\n",
      "Time for simplification: 0.0026760101318359375\n",
      "length of products3: 45\n",
      "t and U combination: 1.47571428571 2.0\n",
      "Energy:  -2.61192381732\n",
      "-2.61192381732 1\n",
      "-2.16474327378 3\n",
      "\n",
      "Time for transformation: 0.009696006774902344\n",
      "length of products: 48\n",
      "Time for simplification: 0.0028519630432128906\n",
      "length of products3: 45\n",
      "t and U combination: 1.55714285714 2.0\n",
      "Energy:  -2.7685503648\n",
      "-2.7685503648 2\n",
      "-2.3166663995 3\n",
      "\n",
      "Time for transformation: 0.009788036346435547\n",
      "length of products: 48\n",
      "Time for simplification: 0.002301931381225586\n",
      "length of products3: 45\n",
      "t and U combination: 1.63857142857 2.0\n",
      "Energy:  -2.92562826516\n",
      "-2.92562826516 2\n",
      "-2.46962519439 3\n",
      "\n",
      "Time for transformation: 0.010445833206176758\n",
      "length of products: 48\n",
      "Time for simplification: 0.0020182132720947266\n",
      "length of products3: 45\n",
      "t and U combination: 1.72 2.0\n",
      "Energy:  -3.0831116005\n",
      "-3.0831116005 2\n",
      "-2.62348375316 2\n",
      "\n",
      "Time for transformation: 0.016616106033325195\n",
      "length of products: 48\n",
      "Time for simplification: 0.0025720596313476562\n",
      "length of products3: 45\n",
      "t and U combination: 1.80142857143 2.0\n",
      "Energy:  -3.24096029642\n",
      "-3.24096029642 2\n",
      "-2.77812806961 3\n",
      "\n",
      "Time for transformation: 0.015211105346679688\n",
      "length of products: 48\n",
      "Time for simplification: 0.0034799575805664062\n",
      "length of products3: 45\n",
      "t and U combination: 1.88285714286 2.0\n",
      "Energy:  -3.3991392493\n",
      "-3.3991392493 2\n",
      "-2.9334620007 2\n",
      "\n",
      "Time for transformation: 0.023591995239257812\n",
      "length of products: 48\n",
      "Time for simplification: 0.004782915115356445\n",
      "length of products3: 45\n",
      "t and U combination: 1.96428571429 2.0\n",
      "Energy:  -3.55761760029\n",
      "-3.55761760029 2\n",
      "-3.0894040366 3\n",
      "\n",
      "Time for transformation: 0.018078088760375977\n",
      "length of products: 48\n",
      "Time for simplification: 0.00496983528137207\n",
      "length of products3: 45\n",
      "t and U combination: 2.04571428571 2.0\n",
      "Energy:  -3.71636812917\n",
      "-3.71636812917 2\n",
      "-3.24588471203 3\n",
      "\n",
      "Time for transformation: 0.010832071304321289\n",
      "length of products: 48\n",
      "Time for simplification: 0.003590822219848633\n",
      "length of products3: 45\n",
      "t and U combination: 2.12714285714 2.0\n",
      "Energy:  -3.87536674626\n",
      "-3.87536674626 2\n",
      "-3.40284452519 3\n",
      "\n",
      "Time for transformation: 0.009323835372924805\n",
      "length of products: 48\n",
      "Time for simplification: 0.0029299259185791016\n",
      "length of products3: 45\n",
      "t and U combination: 2.20857142857 2.0\n",
      "Energy:  -4.03459206499\n",
      "-4.03459206499 2\n",
      "-3.56023225848 3\n",
      "\n",
      "Time for transformation: 0.009454011917114258\n",
      "length of products: 48\n",
      "Time for simplification: 0.002020120620727539\n",
      "length of products3: 45\n",
      "t and U combination: 2.29 2.0\n",
      "Energy:  -4.19402504106\n",
      "-4.19402504106 2\n",
      "-3.71800361736 3\n",
      "\n",
      "Time for transformation: 0.012492179870605469\n",
      "length of products: 48\n",
      "Time for simplification: 0.0021419525146484375\n",
      "length of products3: 45\n",
      "t and U combination: 2.37142857143 2.0\n",
      "Energy:  -4.35364866655\n",
      "-4.35364866655 2\n",
      "-3.87612012198 3\n",
      "\n",
      "Time for transformation: 0.009755849838256836\n",
      "length of products: 48\n",
      "Time for simplification: 0.0025169849395751953\n",
      "length of products3: 45\n",
      "t and U combination: 2.45285714286 2.0\n",
      "Energy:  -4.51344770984\n",
      "-4.51344770984 2\n",
      "-4.0345482001 3\n",
      "\n",
      "Time for transformation: 0.009432077407836914\n",
      "length of products: 48\n",
      "Time for simplification: 0.0021178722381591797\n",
      "length of products3: 45\n",
      "t and U combination: 2.53428571429 2.0\n",
      "Energy:  -4.67340849362\n",
      "-4.67340849362 1\n",
      "-4.19325844134 3\n",
      "\n",
      "Time for transformation: 0.008999109268188477\n",
      "length of products: 48\n",
      "Time for simplification: 0.0021140575408935547\n",
      "length of products3: 45\n",
      "t and U combination: 2.61571428571 2.0\n",
      "Energy:  -4.83351870476\n",
      "-4.83351870476 2\n",
      "-4.35222498081 3\n",
      "\n",
      "Time for transformation: 0.01916813850402832\n",
      "length of products: 48\n",
      "Time for simplification: 0.0035560131072998047\n",
      "length of products3: 45\n",
      "t and U combination: 2.69714285714 2.0\n",
      "Energy:  -4.99376723098\n",
      "-4.99376723098 1\n",
      "-4.51142498737 3\n",
      "\n",
      "Time for transformation: 0.03178000450134277\n",
      "length of products: 48\n",
      "Time for simplification: 0.004868984222412109\n",
      "length of products3: 45\n",
      "t and U combination: 2.77857142857 2.0\n",
      "Energy:  -5.15414402008\n",
      "-5.15414402008 2\n",
      "-4.67083823681 3\n",
      "\n",
      "Time for transformation: 0.010012149810791016\n",
      "length of products: 48\n",
      "Time for simplification: 0.002146005630493164\n",
      "length of products3: 45\n",
      "t and U combination: 2.86 2.0\n",
      "Energy:  -5.31463995822\n",
      "-5.31463995822 2\n",
      "-4.83044675405 3\n",
      "\n",
      "Time for transformation: 0.012020111083984375\n",
      "length of products: 48\n",
      "Time for simplification: 0.0032050609588623047\n",
      "length of products3: 45\n",
      "t and U combination: 2.94142857143 2.0\n",
      "Energy:  -5.47524676431\n",
      "-5.47524676431 2\n",
      "-4.99023451206 2\n",
      "\n",
      "Time for transformation: 0.009119033813476562\n",
      "length of products: 48\n",
      "Time for simplification: 0.0034689903259277344\n",
      "length of products3: 45\n",
      "t and U combination: 3.02285714286 2.0\n",
      "Energy:  -5.63595689824\n",
      "-5.63595689824 2\n",
      "-5.15018717736 3\n",
      "\n",
      "Time for transformation: 0.013772010803222656\n",
      "length of products: 48\n",
      "Time for simplification: 0.0021479129791259766\n",
      "length of products3: 45\n",
      "t and U combination: 3.10428571429 2.0\n",
      "Energy:  -5.79676348078\n",
      "-5.79676348078 2\n",
      "-5.31029189392 3\n",
      "\n",
      "Time for transformation: 0.012644052505493164\n",
      "length of products: 48\n",
      "Time for simplification: 0.0019829273223876953\n",
      "length of products3: 45\n",
      "t and U combination: 3.18571428571 2.0\n",
      "Energy:  -5.95766022354\n",
      "-5.95766022354 2\n",
      "-5.4705370991 3\n",
      "\n",
      "Time for transformation: 0.009957075119018555\n",
      "length of products: 48\n",
      "Time for simplification: 0.0020160675048828125\n",
      "length of products3: 45\n",
      "t and U combination: 3.26714285714 2.0\n",
      "Energy:  -6.11864136754\n",
      "-6.11864136754 2\n",
      "-5.63091236618 3\n",
      "\n",
      "Time for transformation: 0.009773015975952148\n",
      "length of products: 48\n",
      "Time for simplification: 0.0019941329956054688\n",
      "length of products3: 45\n",
      "t and U combination: 3.34857142857 2.0\n",
      "Energy:  -6.27970162924\n",
      "-6.27970162924 2\n",
      "-5.79140826914 3\n",
      "\n",
      "Time for transformation: 0.009716987609863281\n",
      "length of products: 48\n",
      "Time for simplification: 0.002031087875366211\n",
      "length of products3: 45\n",
      "t and U combination: 3.43 2.0\n",
      "Energy:  -6.44083615293\n",
      "-6.44083615293 2\n",
      "-5.95201626621 3\n",
      "\n",
      "Time for transformation: 0.008913040161132812\n",
      "length of products: 48\n",
      "Time for simplification: 0.0020170211791992188\n",
      "length of products3: 45\n",
      "t and U combination: 3.51142857143 2.0\n",
      "Energy:  -6.60204046868\n",
      "-6.60204046868 2\n",
      "-6.11272859913 3\n",
      "\n",
      "Time for transformation: 0.01002192497253418\n",
      "length of products: 48\n",
      "Time for simplification: 0.0019750595092773438\n",
      "length of products3: 45\n",
      "t and U combination: 3.59285714286 2.0\n",
      "Energy:  -6.76331045516\n",
      "-6.76331045516 2\n",
      "-6.27353820588 2\n",
      "\n",
      "Time for transformation: 0.008980035781860352\n",
      "length of products: 48\n",
      "Time for simplification: 0.002000093460083008\n",
      "length of products3: 45\n",
      "t and U combination: 3.67428571429 2.0\n",
      "Energy:  -6.92464230654\n",
      "-6.92464230654 1\n",
      "-6.43443864467 3\n",
      "\n",
      "Time for transformation: 0.018218040466308594\n",
      "length of products: 48\n",
      "Time for simplification: 0.001990795135498047\n",
      "length of products3: 45\n",
      "t and U combination: 3.75571428571 2.0\n",
      "Energy:  -7.08603250317\n",
      "-7.08603250317 2\n",
      "-6.59542402768 2\n",
      "\n",
      "Time for transformation: 0.009596824645996094\n",
      "length of products: 48\n",
      "Time for simplification: 0.0019919872283935547\n",
      "length of products3: 45\n",
      "t and U combination: 3.83714285714 2.0\n",
      "Energy:  -7.24747778536\n",
      "-7.24747778536 2\n",
      "-6.75648896301 3\n",
      "\n",
      "Time for transformation: 0.009604930877685547\n",
      "length of products: 48\n",
      "Time for simplification: 0.002145051956176758\n",
      "length of products3: 45\n",
      "t and U combination: 3.91857142857 2.0\n",
      "Energy:  -7.40897513\n",
      "-7.40897513 2\n",
      "-6.9176285038 3\n",
      "\n",
      "Time for transformation: 0.008781909942626953\n",
      "length of products: 48\n",
      "Time for simplification: 0.0020101070404052734\n",
      "length of products3: 45\n",
      "t and U combination: 4.0 2.0\n",
      "Energy:  -7.57052172966\n",
      "-7.57052172966 2\n",
      "-7.07883810342 3\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jrf/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:17: ComplexWarning: Casting complex values to real discards the imaginary part\n"
     ]
    }
   ],
   "source": [
    "number_op = constructNumberOperator(8)\n",
    "energyMatrix = np.zeros((N,M))\n",
    "nFockMatrix = np.zeros((N,M))\n",
    "stdMatrix = np.zeros((N,M))\n",
    "numbers = np.zeros((N,M))\n",
    "states = []\n",
    "\n",
    "for n in range(0,N):\n",
    "    for m in range(0,M):\n",
    "        ops,coeffs,nqubits=constructSymbolicHubbard2(4,1,ts[n],Us[m])\n",
    "        ham = getJWHamiltonian(coeffs, ops, nqubits)\n",
    "        hamo=getHamiltonianObject(ham)\n",
    "        eigenvals,eigenvecs=hamo.eigenstates()\n",
    "        val, vector =  hamo.groundstate()\n",
    "        \n",
    "        entries, n_fock, std_state = getFockStateNumber(vector)\n",
    "        energyMatrix[n,m]=val\n",
    "        nFockMatrix[n,m] = n_fock\n",
    "        stdMatrix[n,m] = std_state\n",
    "        numbers[n,m]=int(expect(number_op,vector))\n",
    "        states.append(vector)\n",
    "        \n",
    "        print('t and U combination:',ts[n],Us[m])\n",
    "        print('Energy: ',val.real)\n",
    "        for p in range(0,2):\n",
    "            number = int(expect(number_op,eigenvecs[p]))\n",
    "            print(eigenvals[p].real,number)\n",
    "        print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T10:52:10.334778",
     "start_time": "2016-12-14T10:52:03.396646"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10df10400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10df246d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x111238d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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amnJNSUFEiso//gHPPhtqEE89FdZpSiTgjDPC4n3HHRdWgpXWUVIQkaK2cWPo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\nQUlBRER2+P8TgFJvKNzr8wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1107dbda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10df380b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ts/2.0,energyMatrix)\n",
    "plt.show()\n",
    "plt.plot(ts/2.0,numbers)\n",
    "plt.show()\n",
    "plt.plot(ts/2.0,nFockMatrix)\n",
    "plt.show()\n",
    "plt.plot(ts/2.0,stdMatrix)\n",
    "plt.show()\n",
    "\n",
    "fidelities4=[]\n",
    "for n in range(0,len(states)-1):\n",
    "    fidelities4.append(fidelity(states[n],states[n+1]))\n",
    "plt.plot(ts[1:]/2.0,fidelities4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-12-14T10:52:14.027330",
     "start_time": "2016-12-14T10:52:12.606113"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x110639550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1106cb4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1107e97b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2S3ttetrLUqkiSvYBHbgmnpD6/gZJ2yX9pMU2l0ra5NwWV+dVw8cCTgbOcl4Cw8A+km4F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\ngB4TBegxUYAeEwXoMVGAHvP/eOemQ4WSwtwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110a34a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#print(energyMatrix)\n",
    "plt.imshow(energyMatrix)\n",
    "plt.colorbar()\n",
    "plt.show()\n",
    "#print(energyMatrix)\n",
    "plt.imshow(numbers)\n",
    "plt.colorbar()\n",
    "plt.show()\n",
    "#print(energyMatrix)\n",
    "plt.imshow(nFockMatrix)\n",
    "plt.colorbar()\n",
    "plt.show()\n",
    "#print(energyMatrix)\n",
    "plt.imshow(stdMatrix)\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.4/dist-packages/ipykernel/__main__.py:14: ComplexWarning: Casting complex values to real discards the imaginary part\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.01 3 -0.010199980694763416 -0.0101999806948\n",
      "0.0914285714286 3 -0.10800947955122907 -0.108009479551\n",
      "0.172857142857 3 -0.23093009508748372 -0.230930095087\n",
      "0.254285714286 3 -0.3761791640122718 -0.376179164012\n",
      "0.335714285714 3 -0.5402126591026436 -0.540212659103\n",
      "0.417142857143 3 -0.7194610406634098 -0.719461040663\n",
      "0.498571428571 3 -0.910766126318117 -0.910766126318\n",
      "0.58 3 -1.1115351859403857 -1.11153518594\n",
      "0.661428571429 3 -1.3197262039375715 -1.31972620394\n",
      "0.742857142857 3 -1.5337638925846582 -1.53376389258\n",
      "0.824285714286 3 -1.75244229706432 -1.75244229706\n",
      "0.905714285714 3 -1.974838132219754 -1.97483813222\n",
      "0.987142857143 3 -2.200241156285451 -2.20024115629\n",
      "1.06857142857 3 -2.4281009700781397 -2.42810097008\n",
      "1.15 3 -2.6579872554379222 -2.65798725544\n",
      "1.23142857143 3 -2.8895605301650544 -2.88956053017\n",
      "1.31285714286 3 -3.1225502774559386 -3.12255027746\n",
      "1.39428571429 3 -3.3567392408835737 -3.35673924088\n",
      "1.47571428571 3 -3.5919509294732923 -3.59195092947\n",
      "1.55714285714 3 -3.828041136921422 -3.82804113692\n",
      "1.63857142857 3 -4.852638997093733 -4.85263899709\n",
      "1.72 3 -4.302401473887191 -4.30240147389\n",
      "1.80142857143 3 -5.478122649926714 -5.47812264993\n",
      "1.88285714286 3 -5.792458939675628 -5.79245893968\n",
      "1.96428571429 3 -5.018132484435688 -5.01813248444\n",
      "2.04571428571 3 -5.25757710281116 -5.25757710281\n",
      "2.12714285714 3 -5.497377054452387 -5.49737705445\n",
      "2.20857142857 3 -5.737495290212702 -5.73749529021\n",
      "2.29 3 -7.375798632649913 -7.37579863265\n",
      "2.37142857143 3 -6.218561215374642 -6.21856121537\n",
      "2.45285714286 3 -8.013197821487644 -8.01319782149\n",
      "2.53428571429 3 -6.700562549717505 -6.70056254972\n",
      "2.61571428571 3 -6.941861688471601 -6.94186168847\n",
      "2.69714285714 3 -7.183336292331132 -7.18333629233\n",
      "2.77857142857 3 -7.424971831981576 -7.42497183198\n",
      "2.86 3 -7.666754786899007 -7.6667547869\n",
      "2.94142857143 3 -7.908673217932389 -7.90867321793\n",
      "3.02285714286 3 -10.255718865001722 -10.255718865\n",
      "3.10428571429 3 -8.392875406344064 -8.39287540634\n",
      "3.18571428571 3 -10.898852978589423 -10.8988529786\n",
      "3.26714285714 3 -8.877505161569722 -8.87750516157\n",
      "3.34857142857 3 -11.542779987724764 -11.5427799877\n",
      "3.43 3 -9.362503222304374 -9.3625032223\n",
      "3.51142857143 3 -9.605124537188349 -9.60512453719\n",
      "3.59285714286 3 -9.847820370978507 -9.84782037098\n",
      "3.67428571429 3 -10.09058553351148 -10.0905855335\n",
      "3.75571428571 3 -13.155402889223824 -13.1554028892\n",
      "3.83714285714 3 -10.576307059769004 -10.5763070598\n",
      "3.91857142857 3 -10.819255558653115 -10.8192555587\n",
      "4.0 3 -11.062257843358859 -11.0622578434\n"
     ]
    }
   ],
   "source": [
    "number_op = constructNumberOperator(8)\n",
    "energyMatrix = np.zeros((N,M))\n",
    "nFockMatrix = np.zeros((N,M))\n",
    "stdMatrix = np.zeros((N,M))\n",
    "states=[]\n",
    "for n in range(0,N):\n",
    "    for m in range(0,M):\n",
    "        ops,coeffs,nqubits=constructSymbolicHubbard2(2,2,ts[n],Us[m])\n",
    "        ham = getJWHamiltonian(coeffs, ops, nqubits)\n",
    "        hamo=getHamiltonianObject(ham)\n",
    "        eigenvals,eigenvecs=hamo.eigenstates()\n",
    "        eigenvals2,eigenvecs2=pickSubspace(3,eigenvals,eigenvecs)\n",
    "        arg = np.argmin(eigenvals2)\n",
    "        energyMatrix[n,m]=eigenvals2[arg]\n",
    "        entries, n_fock, std_state = getFockStateNumber(eigenvecs2[arg])\n",
    "        states.append(eigenvecs2[arg])\n",
    "        nFockMatrix[n,m] = n_fock\n",
    "        stdMatrix[n,m] = std_state\n",
    "        print(ts[n],int(expect(number_op,eigenvecs2[arg])),expect(hamo,eigenvecs2[arg]).real,eigenvals2[arg].real)\n",
    "        #rho = eigenvecs2[arg]*eigenvecs2[arg].dag()\n",
    "        #plt.bar(np.arange(0, 256)-.5, rho.diag())\n",
    "        #plt.title(\"Distribution of states\")\n",
    "        #plt.show()\n",
    "        #energyMatrix3[n,m]=min(eigenvals3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7faaca002d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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6vl1UbhMo8JCA3gNizHSqBgG7koEqJReNJFEnW7mucqla0dGmyqX8WSmuUljp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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7faaca0b1208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9t7/Ntc1ngA8BzVOuI1V1j//5EeDIGNdLPO9+8Xre/Pyj+fT19/HDe/aOujux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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7faaca0279e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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sGTJUpzWVpvO4Vq2gUa3E29xHY9QqhJqhcAdkuW03hfvCZqgCXmXIPDV3L5rA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\nbvK9uFp0ySV05XNVzMMebaI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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7faaca162908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ts/2.0,energyMatrix)\n",
    "plt.show()\n",
    "plt.plot(ts/2.0,nFockMatrix)\n",
    "plt.show()\n",
    "plt.plot(ts/2.0,stdMatrix)\n",
    "plt.show()\n",
    "\n",
    "fidelities4=[]\n",
    "for n in range(0,len(states)-1):\n",
    "    fidelities4.append(fidelity(states[n],states[n+1]))\n",
    "plt.plot(ts[1:]/2.0,fidelities4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.3"
  },
  "latex_envs": {
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 0
  },
  "toc": {
   "toc_cell": false,
   "toc_number_sections": true,
   "toc_threshold": 6,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}