Quantum algorithms with local particle number conservation: noise effects and error correction

TL;DR

This paper investigates how local particle number conservation in quantum circuits affects noise resilience and error correction, providing formulas and benchmarks for symmetry robustness and proposing resource-efficient error mitigation strategies.

Contribution

It offers an exact formula for symmetry preservation probability under noise and explores error correction methods tailored for symmetry-conserving quantum algorithms.

Findings

Exact formula for symmetry preservation probability under depolarizing noise

Benchmarking of XY-QAOA's symmetry robustness under noise

Proposal of resource-efficient error correction for symmetry-breaking errors

Abstract

Quantum circuits with local particle number conservation (LPNC) restrict the quantum computation to a subspace of the Hilbert space of the qubit register. In a noiseless or fault-tolerant quantum computation, such quantities are preserved. In the presence of noise, however, the evolution's symmetry could be broken and non-valid states could be sampled at the end of the computation. On the other hand, the restriction to a subspace in the ideal case suggest the possibility of more resource efficient error mitigation techniques for circuits preserving symmetries that are not possible for general circuits. Here, we analyze the probability of staying in such symmetry-preserved subspaces under noise, providing an exact formula for local depolarizing noise. We apply our findings to benchmark, under depolarizing noise, the symmetry robustness of XY-QAOA, which has local particle number conserving symmetries, and is a special case of the Quantum Alternating Operator Ansatz. We also analyze the influence of the choice of encoding the problem on the symmetry robustness of the algorithm and discuss a simple adaption of the bit flip code to correct for symmetry-breaking errors with reduced resources.