qiskit.synthesis.synth_stabilizer_layers

synth_stabilizer_layers(stab, cz_synth_func=<function _default_cz_synth_func>, cz_func_reverse_qubits=False, validate=False)

Synthesis of a stabilizer state into layers.

It provides a similar decomposition to the synthesis described in Lemma 8 of Bravyi and Maslov, without the initial Hadamard-free sub-circuit which do not affect the stabilizer state.

For example, a 5-qubit stabilizer state is decomposed into the following layers:

     ┌─────┐┌─────┐┌─────┐┌─────┐┌────────┐
q_0: ┤0    ├┤0    ├┤0    ├┤0    ├┤0       ├
     │     ││     ││     ││     ││        │
q_1: ┤1    ├┤1    ├┤1    ├┤1    ├┤1       ├
     │     ││     ││     ││     ││        │
q_2: ┤2 H2 ├┤2 S1 ├┤2 CZ ├┤2 H1 ├┤2 Pauli ├
     │     ││     ││     ││     ││        │
q_3: ┤3    ├┤3    ├┤3    ├┤3    ├┤3       ├
     │     ││     ││     ││     ││        │
q_4: ┤4    ├┤4    ├┤4    ├┤4    ├┤4       ├
     └─────┘└─────┘└─────┘└─────┘└────────┘

Parameters

• stab (StabilizerState) – a stabilizer state.
• cz_synth_func (Callable) – a function to decompose the CZ sub-circuit. It gets as input a boolean symmetric matrix, and outputs a QuantumCircuit.
• validate (Boolean) – if True, validates the synthesis process.
• cz_func_reverse_qubits (Boolean) – True only if cz_synth_func is synth_cz_depth_line_mr, since this function returns a circuit that reverts the order of qubits.

Returns

a circuit implementation of the stabilizer state.

Return type

QuantumCircuit

Raises

QiskitError – if the input is not a StabilizerState.

Reference:

1. S. Bravyi, D. Maslov, Hadamard-free circuits expose the structure of the Clifford group, arXiv:2003.09412 [quant-ph]