Synthesis of diagonal unitaries

Header: tweedledum/algorithms/synthesis/diagonal_synth.hpp

Algorithm

template<class Circuit>
Circuit tweedledum::diagonal_synth(std::vector<double> const &angles)

Synthesis of diagonal unitary matrices.

This algorithm is based on the work in [SS03]. It takes as input \(2^n - 1\) real angles \(\theta_i\) for \(i = 1, \dots, 2^{n-1}\) and returns a quantum circuit that realizes the \(2^n \times 2^n\) unitary operation

\(U = \mathrm{diag}(1, e^{-\mathrm{i}\theta_1}, e^{-\mathrm{i}\theta_2}, \dots, e^{-\mathrm{i}\theta_{2^{n-1}}}).\)

It uses a fast Hadamard transformation to compute angles for parity terms that are passed to the Gray synthesis algorithm gray_synth.

Return

{CNOT, Rz} network

Parameters

  • angles: Angles for diagonal matrix elements

template<class Circuit>
void tweedledum::diagonal_synth(Circuit &circ, std::vector<io_id> const &qubits, std::vector<double> const &angles)

Gray synthesis for {CNOT, Rz} networks.

This is the in-place variant of diagonal_synth, in which the network is passed as a parameter and can potentially already contain some gates. The parameter qubits provides a qubit mapping to the existing qubits in the network.

Parameters

  • circ: A quantum network

  • qubits: The subset of qubits the linear reversible circuit acts upon

  • angles: Angles for diagonal matrix elements