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Quantum Error Correction with Gauge Symmetries

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arxiv 2112.05186 v2 pith:KUI2MCZM submitted 2021-12-09 quant-ph hep-lat

Abhishek Rajput , Alessandro Roggero , Nathan Wiebe This is my paper · ORCID
classification quant-phhep-lat
keywords correctionerrorquantumcodedimensionsgaugegausslgts
verification ladder T0 review T1 audit T2 compute T3 formal
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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 $\mathbb{Z}_2$ 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 na\"{i}ve 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.

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Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Binary Gauss Stabilizers for Abelian Lattice Gauge Theories

    quant-ph 2026-07 conditional novelty 7.0 of 10

    Binary Gauss stabilizers provide a non-Pauli stabilizer description of the physical subspace of Z_{2^η} lattice gauge theories, enabling bit-flip error correction and gauge fixing from gauge constraints alone.

  2. Local Thermalization of SU(2) Lattice Gauge Fields on Quantum Computers

    hep-lat 2026-03 unverdicted novelty 7.0 of 10

    Quantum hardware simulation of SU(2) lattice gauge thermalization matches classical extrapolations up to 101 plaquettes after error mitigation, establishing feasibility for chaotic quantum field systems.

  3. Confinement as Decoding: Higher Form Codes and Lattice Yang-Mills Theory

    hep-th 2026-08 conditional novelty 6.0 of 10

    Decoding a higher-form quantum code with Wilson-line noise is the same computation as comparing center-twisted Yang-Mills partition functions; the paper works out this dictionary and its strong-coupling consequences.

  4. Realizing Error Suppression in Partially Fault-Tolerant Quantum Simulations with IBM Quantum Computers

    quant-ph 2026-07 conditional novelty 6.0 of 10

    Partially fault-tolerant [[4,2,2]] Iceberg-code simulations on ibm_boston improve local Ising observables over unencoded baselines by a few percent in 1D and over 200% in 2D at late times via Observable-Ranked Postselection.

  5. Quantum Error Correction Codes for Truncated SU(2) Lattice Gauge Theories

    quant-ph 2025-11 conditional novelty 6.0 of 10

    Gauss's law constraints in jmax=1/2 SU(2) lattice gauge theory are converted into stabilizer codes that correct single-qubit errors using about 9N or 12N physical qubits per N plaquettes.

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