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 Z2 or truncated U(1) LGT in 1+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.

Robustness of Gauge Digitization to Quantum Noise

“…Future focus to matter fields should be made. Finally, threshold error rates for error correction using gauge-transformation stabilizers as in [98] should be determined for comparison with general QEC. Together, our results reduce the resources needed for quantum advantage in LFT simulations.…”

Snowmass White Paper: Quantum Computing Systems and Software for High-energy Physics Research

“…There have been several successful HEP problem implementations, generally focusing on how to truncate gauge degrees of freedom while simultaneously satisfying gauge constraints efficiently [42,119]. This has paved the way, similarly to fermionic mappings, for methods of how to actually embed HEP simulations natively in error detection and correction schemes [41,120]. These methods have so far proven to be very specific to the target mod-els and its symmetries.…”

Improved Hamiltonians for Quantum Simulations

“…Furthermore, performing scale setting classically can reduce quantum resources [57][58][59]. Lattice field theory specific error correction or mitigation could also potentially decrease quantum costs [60,61].…”