Quantum Error Mitigation by Pauli Check Sandwiching

TL;DR

This paper introduces a quantum error mitigation method called Pauli check sandwiching, which uses multiple parity check pairs to detect errors without encoding overhead, improving fidelity in quantum circuits.

Contribution

The paper provides a theoretical foundation for a new error mitigation technique using multiple parity checks, applicable to arbitrary circuits and input states, with an efficient algorithm for check selection.

Findings

Achieves an average fidelity improvement of 34 percentage points with six check layers.

Applicable to a wide range of circuits, including variational algorithms.

No encoding overhead required, compatible with other error mitigation methods.

Abstract

We describe and analyze an error mitigation technique that uses multiple pairs of parity checks to detect the presence of errors. Each pair of checks uses one ancilla qubit to detect a component of the error operator and represents one layer of the technique. We build on the results on extended flag gadgets and put it on a firm theoretical foundation. We prove that this technique can recover the noiseless state under the assumption of noise not affecting the checks. The method does not incur any encoding overhead and instead chooses the checks based on the input circuit. We provide an algorithm for obtaining such checks for an arbitrary target circuit. Since the method applies to any circuit and input state, it can be easily combined with other error mitigation techniques. We evaluate the performance of the proposed methods using extensive numerical simulations on 1,850 random input circuits composed of Clifford gates and non-Clifford single-qubit rotations, a class of circuits encompassing most commonly considered variational algorithm circuits. We observe average improvements in fidelity of 34 percentage points with six layers of checks.