Generates exact quantum circuits for exponentiating diagonal operators. Supports symbolics.
For example, here is a circuit for with
Supply a function that maps i → Hi,i and the program will output QASM code for the circuit implementing ei H up to a global phase. The circuit will always be composed exclusively of phase shift and CNOT gates.
Note that this method will use 2n-3 fundamental gates in the worst case, so will not provide an efficient quantum circuit in general. Reference [2] details how to approximate the exponentiation to arbitrary precision and produce an efficient quantum circuit, but this project was designed to exactly replicate the desired operator.
The gates(n, fn) function takes as input the number of qubits n and a function f(x) that takes x = 0 ... 2n-1 to the corresponding diagonal element of the desired Hamiltonian. The output for the Hamiltonian above is
('R', -225*t/4, 0)
('CNOT', 0, 1)
('R', 135*t/4, 1)
('CNOT', 0, 1)
('R', -153*t/4, 1)
('CNOT', 1, 2)
('R', 51*t/4, 2)
('CNOT', 0, 2)
('R', -45*t/4, 2)
('CNOT', 1, 2)
('R', 75*t/4, 2)
('CNOT', 0, 2)
('R', -85*t/4, 2)
where ('R', θ, q) represents a phase shift of θ on qubit q, and ('CNOT', qc, qt) is a CNOT with control qc and target qt. Further, the function print_qasm(n, gates) takes in the number of qubits and the list of gates and converts it to QASM code. The circuit can then be visualised with a program such as qasm2circ.
[1] J. L. Shanks, 1969, IEEE Transactions on Computers 18-5, 457
[2] Jonathan Welch et al, 2014, New J. Phys. 16, 033040