Quantum algorithms with local particle-number conservation: Noise effects and error correction
Streif M, Leib M, Wudarski F, Rieffel E, Wang Z (2021)
Publication Type: Journal article
Publication year: 2021
Journal
Book Volume: 103
Article Number: 042412
Journal Issue: 4
DOI: 10.1103/PhysRevA.103.042412
Abstract
Quantum circuits with local particle-number conservation 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 nonvalid states could be sampled at the end of the computation. On the other hand, the restriction to a subspace in the ideal case suggests 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 the XY quantum alternating operator Ansatz, 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.
Authors with CRIS profile
Involved external institutions
Volkswagen AG
Germany (DE)
National Aeronautics and Space Administration (NASA)
United States (USA) (US)
Germany (DE)
National Aeronautics and Space Administration (NASA)
United States (USA) (US)
How to cite
APA:
Streif, M., Leib, M., Wudarski, F., Rieffel, E., & Wang, Z. (2021). Quantum algorithms with local particle-number conservation: Noise effects and error correction. Physical Review A, 103(4). https://dx.doi.org/10.1103/PhysRevA.103.042412
MLA:
Streif, Michael, et al. "Quantum algorithms with local particle-number conservation: Noise effects and error correction." Physical Review A 103.4 (2021).
BibTeX: Download