qp.labs.estimator_beta.mcx_one_dirty_aux_resource_decomp

mcx_one_dirty_aux_resource_decomp(num_ctrl_wires, num_zero_ctrl)

Returns a list representing the resources of the operator.

Parameters:

• num_ctrl_wires (int) – the number of qubits the operation is controlled on

• num_zero_ctrl (int) – the number of control qubits, that are controlled when in the \(|0\rangle\) state

Resources:

The resources are obtained based on the unary iteration technique described in Khattar and Gidney, (2024). Specifically, the resources are defined as the following rules:

• If there are no control qubits, treat the operation as a X gate.

• If there is only one control qubit, treat the resources as a CNOT gate.

• If there are two control qubits, treat the resources as a Toffoli gate.

• If there are three or more control qubits (\(n\)), the resources are obtained based on the conditionally clean technique described in Khattar and Gidney, (2024). Specifically, it requires \(1\) dirty qubit, and produces \(4n - 8\) Toffoli gates.

Returns:

A list of GateCount objects, where each object represents a specific quantum gate and the number of times it appears in the decomposition.

Return type:

list[GateCount]

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