Simulating Quantum Pauli Noise with Three Independently Controlled Pauli Gates

A quantum Pauli noise is a nonunitary process that alters the state of a qubit by random application of the four Pauli operators. We investigate a four-qubit quantum circuit, consisting of a pipeline of three independently controlled Pauli gates, for simulating the general class of qubit Pauli noises. The circuit with a fixed architecture is controllable by three separable quantum states from three auxiliary qubits in order to adjust the parameters of the targeted Pauli noise on the principal qubit. Important Pauli noises such as bit flip, phase flip, bit phase flip, and depolarizing noise are readily simulated, along with an infinite subset of other Pauli noises. However, the quantum circuit with its simple and fixed architecture cannot simulate all conceivable Pauli noises, and a characterization is proposed, in the parameter space of the Pauli noises, denoting those that are simulable by the circuit and those that are not. The circuit is a useful tool to contribute to controlled simulation, on current or future quantum processors, of nonunitary processes of noise and decoherence.