cirq.quantum_shannon_decomposition

Decomposes n-qubit unitary 1-q, 2-q and GlobalPhase gates, preserving global phase.

cirq.quantum_shannon_decomposition(
    qubits: 'List[cirq.Qid]', u: np.ndarray, atol: float = 1e-08
) -> Iterable['cirq.Operation']

The gates used are CX/YPow/ZPow/CNOT/GlobalPhase/CZ/PhasedXZGate/PhasedXPowGate.

The algorithm is described in Shende et al.: Synthesis of Quantum Logic Circuits. Tech. rep. 2006, https://arxiv.org/abs/quant-ph/0406176

qubits List of qubits in order of significance
u Numpy array for unitary matrix representing gate to be decomposed
atol Absolute tolerance of floating point checks.

(Base Case)

  1. _single_qubit_decomposition OR (Recursive Case)
  2. _msb_demuxer
  3. _multiplexed_cossin
  4. _msb_demuxer

A single 2-qubit or 1-qubit operations from OP TREE composed from the set { CNOT, rz, ry, ZPowGate }

ValueError If the u matrix is non-unitary
ValueError If the u matrix is not of shape (2^n,2^n)