Scalable Quantum Distribution Error Mitigation via the Circulant Structure of Pauli Noise and the Fast Fourier Transform

This work introduces distribution error mitigation (DEM), which mitigates the output distribution of a quantum circuit and has a rigorous theoretical foundation. If the noise affecting the circuit is a Pauli channel, the ideal and noisy distributions in the standard basis are related by a stochastic matrix. We prove that this matrix has a recursive 2 by 2 block circulant structure. Thus, the noisy distribution can be corrected via a Fast Fourier Transform. Subspace reduction can be used to scale DEM efficiently. The approach is tested with quantum hardware executions including 30-qubit GHZ state preparation, 5-qubit Grover, and 10-qubit quantum phase estimation circuits. DEM dramatically improves the accuracies of all demonstrations. For 30-qubit GHZ state preparation, DEM achieves a fidelity of 97.7% from an initial raw fidelity of 23.2%.