Quantum error correction with gauge symmetries

Abstract Quantum simulations of lattice gauge theories (LGTs) are often formulated on an enlarged Hilbert space containing both physical and unphysical sectors in order to retain a local Hamiltonian. We provide simple fault-tolerant procedures that exploit such redundancy by combining a phase flip error correction code with the Gauss’ law constraint to correct one-qubit errors for a $${{\mathbb{Z}}}_{2}$$ Z 2 or truncated U(1) LGT in 1+1 and 2+1 dimensions with a link flux cutoff of 1. Unlike existing work on detecting violations of Gauss’ law, our circuits are fault tolerant and the overall error correction scheme outperforms a naïve application of the [5, 1, 3] code. The constructions outlined can be extended to LGT systems with larger cutoffs and may be of use in understanding how to hybridize error correction and quantum simulation for LGTs in higher space-time dimensions and with different symmetry groups.

Authors

Abhishek Rajput; Alessandro Roggero; Nathan Wiebe

Published

Apr 25, 2023

Journal or venue

npj Quantum Information

DOI

10.1038/s41534-023-00706-8

Paper type

journal article

Source

Crossref