Update bitwise operation

itsubaki · Jan 8, 2025 · 462a421 · 462a421
1 parent b0f902a
commit 462a421
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Showing 4 changed files with 55 additions and 108 deletions.
diff --git a/quantum/density/matrix.go b/quantum/density/matrix.go
@@ -87,24 +87,22 @@ func (m *Matrix) SquareTrace() float64 {
 // PartialTrace returns the partial trace of the density matrix.
 func (m *Matrix) PartialTrace(index ...int) *Matrix {
 	n := m.NumberOfBit()
-	f := fmt.Sprintf("%s%s%s", "%0", strconv.Itoa(n), "s")
+	p, q := m.Dimension()
+
 	d := number.Pow(2, n-1)
 	out := matrix.Zero(d, d)
-
-	p, q := m.Dimension()
 	for i := range p {
-		k, kr := take(fmt.Sprintf(f, strconv.FormatInt(int64(i), 2)), index)
+		k, kr := take(fmt.Sprintf("%0*b", n, i), index)
 
 		for j := range q {
-			l, lr := take(fmt.Sprintf(f, strconv.FormatInt(int64(j), 2)), index)
+			l, lr := take(fmt.Sprintf("%0*b", n, j), index)
 
 			if k != l {
 				continue
 			}
 
 			r := number.Must(strconv.ParseInt(kr, 2, 0))
 			c := number.Must(strconv.ParseInt(lr, 2, 0))
-
 			out[r][c] = out[r][c] + m.m[i][j]
 
 			// fmt.Printf("[%v][%v] = [%v][%v] + [%v][%v]\n", r, c, r, c, i, j)
@@ -136,28 +134,24 @@ func (m *Matrix) Depolarizing(p float64) (*Matrix, error) {
 	n := m.NumberOfBit()
 	i := gate.I(n).Mul(complex(p/2, 0))
 	r := m.m.Mul(complex(1-p, 0))
-
 	return &Matrix{i.Add(r)}, nil
 }
 
 func take(binary string, index []int) (string, string) {
-	var out, remain string
-	for i, v := range binary {
-		found := false
-		for _, j := range index {
-			if i == j {
-				out = out + string(v)
-				found = true
-				break
-			}
-		}
+	idx := make(map[int]struct{})
+	for _, i := range index {
+		idx[i] = struct{}{}
+	}
 
-		if found {
+	var out, remain []rune
+	for i, v := range binary {
+		if _, ok := idx[i]; ok {
+			out = append(out, v)
 			continue
 		}
 
-		remain = remain + string(v)
+		remain = append(remain, v)
 	}
 
-	return out, remain
+	return string(out), string(remain)
 }
diff --git a/quantum/gate/gate.go b/quantum/gate/gate.go
@@ -137,52 +137,30 @@ func RZ(theta float64) matrix.Matrix {
 
 // Controlled returns a controlled-u gate.
 func Controlled(u matrix.Matrix, n int, c []int, t int) matrix.Matrix {
-	g := I(n)
-
-	for i := range g {
-		row := []rune(fmt.Sprintf("%0*b", n, i))
-
-		active := true
-		for _, j := range c {
-			if row[j] == '0' {
-				active = false
-				break
-			}
-		}
+	var mask int
+	for _, bit := range c {
+		mask |= (1 << (n - 1 - bit))
+	}
 
-		if !active {
+	s := (1 << n)
+	g := I(n)
+	for i := 0; i < s; i++ {
+		if (i & mask) != mask {
 			continue
 		}
 
-		for j := range g[i] {
-			col := []rune(fmt.Sprintf("%0*b", n, j))
-
-			active := true
-			for _, k := range c {
-				if col[k] == '0' {
-					active = false
-					break
-				}
-			}
-
-			if !active {
+		for j := 0; j < s; j++ {
+			if (j & mask) != mask {
 				continue
 			}
 
-			same := true
-			for i := range row {
-				if i != t && row[i] != col[i] {
-					same = false
-					break
-				}
-			}
-
-			if !same {
+			// modify only the target qubit
+			if (i & ^(1 << (n - 1 - t))) != (j & ^(1 << (n - 1 - t))) {
 				continue
 			}
 
-			r := number.Must(strconv.Atoi(string(row[t])))
-			c := number.Must(strconv.Atoi(string(col[t])))
+			c := (j >> (n - 1 - t)) & 1
+			r := (i >> (n - 1 - t)) & 1
 			g[j][i] = u[c][r]
 		}
 	}
@@ -236,21 +214,14 @@ func Toffoli(n, c0, c1, t int) matrix.Matrix {
 
 // ControlledZ returns a controlled-z gate.
 func ControlledZ(n int, c []int, t int) matrix.Matrix {
-	g := I(n)
-	d, _ := g.Dimension()
-
-	for i := range d {
-		bits := []rune(fmt.Sprintf("%0*b", n, i))
-
-		apply := true
-		for _, j := range c {
-			if bits[j] == '0' {
-				apply = false
-				break
-			}
-		}
+	var mask int
+	for _, bit := range c {
+		mask |= (1 << (n - 1 - bit))
+	}
 
-		if apply && bits[t] == '1' {
+	g := I(n)
+	for i := 0; i < (1 << n); i++ {
+		if (i&mask) == mask && (i&(1<<(n-1-t))) != 0 {
 			g[i][i] = -1 * g[i][i]
 		}
 	}
@@ -265,21 +236,14 @@ func CZ(n, c, t int) matrix.Matrix {
 
 // ControlledS returns a controlled-s gate.
 func ControlledS(n int, c []int, t int) matrix.Matrix {
-	g := I(n)
-	d, _ := g.Dimension()
-
-	for i := range d {
-		bits := []rune(fmt.Sprintf("%0*b", n, i))
-
-		apply := true
-		for _, j := range c {
-			if bits[j] == '0' {
-				apply = false
-				break
-			}
-		}
+	var mask int
+	for _, bit := range c {
+		mask |= (1 << (n - 1 - bit))
+	}
 
-		if apply && bits[t] == '1' {
+	g := I(n)
+	for i := 0; i < (1 << n); i++ {
+		if (i&mask) == mask && (i&(1<<(n-1-t))) != 0 {
 			g[i][i] = 1i * g[i][i]
 		}
 	}
@@ -297,22 +261,14 @@ func ControlledR(theta float64, n int, c []int, t int) matrix.Matrix {
 	// exp(i * theta)
 	e := cmplx.Exp(complex(0, theta))
 
-	g := I(n)
-	d, _ := g.Dimension()
-
-	for i := range d {
-		bits := []rune(fmt.Sprintf("%0*b", n, i))
-
-		// Apply R(k)
-		apply := true
-		for _, j := range c {
-			if bits[j] == '0' {
-				apply = false
-				break
-			}
-		}
+	var mask int
+	for _, bit := range c {
+		mask |= (1 << (n - 1 - bit))
+	}
 
-		if apply && bits[t] == '1' {
+	g := I(n)
+	for i := 0; i < (1 << n); i++ {
+		if (i&mask) == mask && (i&(1<<(n-1-t))) != 0 {
 			g[i][i] = e * g[i][i]
 		}
 	}

diff --git a/quantum/gate/gate_test.go b/quantum/gate/gate_test.go
@@ -101,9 +101,8 @@ func ExampleControlledModExp2() {
 	n, a, j, N := 5, 7, 0, 15
 	g := gate.ControlledModExp2(n, a, j, N, 0, []int{1, 2, 3, 4})
 
-	f := fmt.Sprintf("%s%s%s", "%0", strconv.Itoa(n), "s")
 	for i, r := range g.Transpose() {
-		bin := fmt.Sprintf(f, strconv.FormatInt(int64(i), 2))
+		bin := fmt.Sprintf("%0*b", n, i)
 		if bin[:1] == "0" { // control qubit is |0>
 			continue
 		}
@@ -120,7 +119,7 @@ func ExampleControlledModExp2() {
 			}
 
 			// decimal number representation of a^2^j * k mod N
-			a2jkmodNs := fmt.Sprintf(f, strconv.FormatInt(int64(ii), 2)[1:])
+			a2jkmodNs := fmt.Sprintf("%0*s", n, strconv.FormatInt(int64(ii), 2)[1:])
 			a2jkmodN := number.Must(strconv.ParseInt(a2jkmodNs, 2, 64))
 			got := (int64(number.ModExp2(a, j, N)) * k) % int64(N)
 

diff --git a/quantum/qubit/qubit.go b/quantum/qubit/qubit.go
@@ -156,13 +156,11 @@ func (q *Qubit) Probability() []float64 {
 // Measure returns a measured qubit.
 func (q *Qubit) Measure(index int) *Qubit {
 	n := q.NumberOfBit()
-	f := fmt.Sprintf("%s%s%s", "%0", strconv.Itoa(n), "s")
 
 	zidx, oidx := make([]int, 0), make([]int, 0)
 	zprop := make([]float64, 0)
 	for i, p := range q.Probability() {
-		bits := []rune(fmt.Sprintf(f, strconv.FormatInt(int64(i), 2)))
-
+		bits := []rune(fmt.Sprintf("%0*b", n, i))
 		if bits[index] == '0' {
 			zidx, zprop = append(zidx, i), append(zprop, p)
 			continue
@@ -228,19 +226,19 @@ func (q *Qubit) State(index ...[]int) []State {
 
 		index = append(index, idx)
 	}
-	f := fmt.Sprintf("%s%s%s", "%0", strconv.Itoa(q.NumberOfBit()), "s")
 
+	n := q.NumberOfBit()
 	state := make([]State, 0)
 	for i, a := range q.Amplitude() {
 		amp := round(a)
 		if amp == 0 {
 			continue
 		}
 
-		b := fmt.Sprintf(f, strconv.FormatInt(int64(i), 2))
+		bit := fmt.Sprintf("%0*b", n, i)
 		var bin []string
 		for _, idx := range index {
-			bin = append(bin, take(b, idx))
+			bin = append(bin, take(bit, idx))
 		}
 
 		state = append(state, NewState(amp, bin...))