diff --git a/documentation/source/reference/Miscellaneous Functions/Phase polynomial tools.rst b/documentation/source/reference/Miscellaneous Functions/Phase polynomial tools.rst index d7ab3e07..dcfea314 100644 --- a/documentation/source/reference/Miscellaneous Functions/Phase polynomial tools.rst +++ b/documentation/source/reference/Miscellaneous Functions/Phase polynomial tools.rst @@ -16,7 +16,7 @@ The application of general diagonal Hamiltonian functions can be achieved in the - The :ref:`first method ` consists of computing the Hamiltonian on all outcome labels of the input QuantumVariables, and subsequently applying the classically computed phases using logic synthesis. While this facilitates a convenient application of arbitray diagonal Hamiltonian functions, it does not scale to large systems as all phases have to be computed classically. -- The second method is based on evaluating the Hamiltonian on its input QuantumVariables in superposition into an auxiliary variable of type QuantumFloat, subsequently applying the phases on the auxiliary variable, and finally uncomputing the auxiliary variable. This approch requires additional qubits and performing arithmetic on the quantum computer. Therefore, on the one hand it introduces an additional burden on simulators, and on the other hand is not suitable for NISQ devices. +- The second method is based on evaluating the Hamiltonian on its input QuantumVariables in superposition into an auxiliary variable of type QuantumFloat, subsequently applying the phases on the auxiliary variable, and finally uncomputing the auxiliary variable. This approch requires additional qubits and performing arithmetic on the quantum computer. Therefore, it introduces an additional burden on simulators, and moreover it is not suitable for NISQ devices. In the special case where the Hamiltonian function is given by a polynomial, its application can be achieved by employing (multi-) controlled phase gates accordingly. The following functions facilitate convenient application of such diagonal Hamiltonians that are given by polynomials.