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.

Error-correcting codes for fermionic quantum simulation

“…After N gauge constraints (stabilizer conditions) are imposed, the gaugeinvariant subspace (code space) has dimension 2 N , which matches the dimension of the logical fermions. It has been shown that gauge constraints can be utilized for error correction [54], and code distances can be studied for these stabilizer codes. Ref.…”