arxiv: 2604.06149 · v1 · submitted 2026-04-07 · 🪐 quant-ph · hep-lat· hep-th

Recognition: 2 theorem links

· Lean Theorem

Error Correction in Lattice Quantum Electrodynamics with Quantum Reference Frames

Elias Rothlin , Carla Ferradini , Lin-Qing Chen

Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:40 UTC · model grok-4.3

classification 🪐 quant-ph hep-lathep-th

keywords quantum error correctionlattice quantum electrodynamicsquantum reference framesgauge symmetryAbelian gauge theorieserror-correcting codesspanning trees

0 comments

The pith

Gauge symmetry in lattice QED encodes information that supports explicit quantum error correction through quantum reference frames.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that the apparent redundancy of gauge symmetry in lattice quantum electrodynamics can instead serve as a resource for protecting quantum information against noise. It constructs quantum reference frames from spanning trees on the lattice for the gauge sector and from the matter fields for the fermionic sector. These frames turn generically degenerate syndromes from constraint measurements into distinguishable families of errors, for which group-theoretical recovery maps can then be written down. The result gives two concrete error-correcting structures, one purely gauge and one that includes fermions, both outside the usual stabilizer-code setting. A reader would care because this suggests gauge theories carry their own built-in encoding mechanism that could be harnessed for fault-tolerant quantum simulation or computation.

Core claim

For Abelian gauge groups the authors construct explicit recovery operations via group-theoretical methods once quantum reference frames resolve the degeneracy of gauge-violating error syndromes. Applied to lattice QED this produces a pure-gauge code whose logical information is encoded in the physical degrees of freedom selected by a spanning-tree reference frame, and a second code that additionally incorporates the fermionic matter field as its reference frame. The gauge symmetry thereby supplies a concrete encoding structure that supports error correction beyond stabilizer formalism.

What carries the argument

Quantum reference frames built from spanning trees of the lattice (for gauge fields) and from the matter field (for fermions), which select physical degrees of freedom and lift the degeneracy of constraint-syndrome measurements to permit explicit recovery.

If this is right

Explicit group-theoretical recovery maps exist for any Abelian gauge theory once a suitable quantum reference frame is chosen.
Lattice QED admits at least two distinct error-correcting encodings, one using only gauge degrees of freedom and one that includes fermions.
Constraint measurements in gauge theories yield syndromes whose degeneracy is lifted by reference-frame information, turning them into correctable error families.
The same construction applies to both ideal and non-ideal reference frames, showing robustness of the encoding.
Gauge symmetry supplies an intrinsic encoding structure that is not limited to stabilizer codes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same reference-frame technique might extend to non-Abelian gauge theories if suitable spanning-tree analogs can be defined.
Quantum simulators of lattice gauge theories could incorporate these encodings as a form of hardware-level error suppression.
The approach links gauge redundancy directly to quantum reference-frame ideas used in quantum gravity and quantum foundations, suggesting a broader information-theoretic role for gauge symmetry.

Load-bearing premise

Quantum reference frames based on spanning trees and matter fields can resolve the generic degeneracy in syndromes of gauge-violating errors to single out families of correctable errors.

What would settle it

An explicit computation on a small lattice showing that the proposed spanning-tree or fermionic reference frame leaves at least one pair of distinct gauge-violating errors with identical syndromes and no group-theoretical recovery map that corrects both.

Figures

Figures reproduced from arXiv: 2604.06149 by Carla Ferradini, Elias Rothlin, Lin-Qing Chen.

**Figure 1.** Figure 1: Under the gauge symmetry, Hkin decomposes into a direct sum of charge sectors Hq, where Hphys corresponds to the trivial representation. (1) An error E maps a physical state |ψ⟩ ∈ Hphys to the error state E|ψ⟩ which may have support spread across every charge sector. (2) A measurement collapses the state to one of the charge sectors, ΠqE|ψ⟩ ∈ Hq, and (3) applying an operator A † q recovers the original sta… view at source ↗

**Figure 2.** Figure 2: The electric flux on the lattice (here represented in 2 dimensions, with links oriented upwards/to the right) is [PITH_FULL_IMAGE:figures/full_fig_p031_2.png] view at source ↗

**Figure 3.** Figure 3: An error U m l acting on the strong-coupling ground state creates m units of electric flux on l = [v, v′ ] (middle, oriented upwards). A measurement of the constraints results in Cv = m and Cv′ = −m (marked in red) and 0 elsewhere, and the error is corrected with (U m l ) † . 5.3 Lattice QED with Fermionic Matter as a QECC Including staggered fermions into the model, the kinematical space contains both qua… view at source ↗

**Figure 4.** Figure 4: The fermionic field QRF lives on the sites of the lattice (marked in blue). We assume that the top left site is even. [PITH_FULL_IMAGE:figures/full_fig_p036_4.png] view at source ↗

**Figure 5.** Figure 5: To illustrate Theorem 5.4, we consider two different errors. (Top) A gauge-violating error excites the strongcoupling vacuum to |0⟩v|0⟩l|0⟩v′ ⊗ |ϕ⟩rest, where we take v to be an even site. Now, a coarse-grained measurement yields rv′ = 1 and 0 elsewhere, and the error is corrected with Xv′ . (Bottom) A different gauge-violating error excites the strong-coupling vacuum to |0⟩v|m⟩l|1⟩v′ ⊗ |ϕ⟩rest (where v i… view at source ↗

**Figure 6.** Figure 6: Physical states correspond to a coherent average over the [PITH_FULL_IMAGE:figures/full_fig_p050_6.png] view at source ↗

**Figure 7.** Figure 7: On the sites v, v ′ , the matter field operators have a phase degree of freedom (red arrow), which we picture to be indicated with respect to a reference frame (green arrow). The angle θl of the link l measures the relative angle between the reference frames on v and v ′ . Locally rotating the frames on v, v′ by λv, λv′ changes the phase of the field by −λv, −λv′ and the angle on l by λv′ − λv. C.3 Stagger… view at source ↗

**Figure 8.** Figure 8: In an infinite lattice, we can split the tree into subtrees by cutting all links attached to a vertex [PITH_FULL_IMAGE:figures/full_fig_p062_8.png] view at source ↗

read the original abstract

Is gauge symmetry merely a redundancy in our description, or does it carry a deeper information-theoretic significance? Quantum error-correcting codes (QECCs) show that redundancy can serve as a resource for protecting information against noise. In this work, we ask whether gauge theories can be understood in similar terms, and make this idea concrete in lattice quantum electrodynamics (QED), building on and extending earlier works that established a bridge between gauge systems, stabilizer codes, and quantum reference frames (QRFs). For Abelian gauge groups, we show that explicit recovery operations can be constructed using group-theoretical methods for error sets determined by both ideal and non-ideal QRFs. Applied to lattice QED, this yields two QECC structures: one in the pure-gauge sector and one including fermions. We construct a gauge-field QRF based on spanning trees of the lattice and a fermionic field QRF from the matter field, thereby making explicit how physical information is encoded. While the syndromes of gauge-violating errors associated with constraint measurements are generically degenerate, QRFs resolve this degeneracy and single out families of correctable errors. This establishes lattice QED as a QECC beyond the stabilizer setting and shows concretely how gauge symmetry provides an encoding structure that supports error correction.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives concrete QRF constructions that turn gauge constraints in lattice QED into an error-correcting code for both pure-gauge and fermionic cases, but the step that resolves degenerate syndromes into unique correctable errors is the one that still needs explicit verification.

read the letter

The core move here is to treat the gauge redundancy in lattice QED as an encoding protected by quantum reference frames. They build a gauge-field QRF from spanning trees on the lattice and a fermionic QRF from the matter degrees of freedom, then use group-theoretic recovery maps for gauge-violating errors. This is applied separately to the pure-gauge sector and the sector with fermions, and they handle both ideal and non-ideal QRF states. That extension to explicit lattice QED with matter is the clearest new piece relative to earlier gauge-stabilizer-QRF work. It does a clean job showing how the physical states sit inside a larger space where the gauge constraints act like stabilizers, and it spells out how the QRFs are supposed to pick out which error occurred when the syndrome is degenerate. The constructions look reproducible in principle because they stay within group theory and lattice geometry rather than fitting parameters. The soft spot is exactly the one the stress test flags. The abstract states that QRFs resolve the generic degeneracy in constraint-measurement syndromes and single out families of correctable errors, but the letter does not show the explicit labeling map or the check that the recovery leaves the logical operators invariant once fermions are included or once the QRF is only approximate. If that labeling fails to be faithful for some error classes, the recovery will not map every errored state back into the gauge-invariant subspace without disturbing the encoded information. That is the load-bearing claim, and it is presented as solved but not walked through in enough detail to judge from the abstract alone. This paper is for people already working on quantum simulation of gauge theories or on information-theoretic reformulations of symmetries. A reader who wants a concrete bridge between QEC and lattice QED will get value from the constructions even if they later need to fill in the recovery details themselves. It is worth sending to referees; the idea is grounded enough and the new lattice-specific pieces are worth checking in detail rather than desk-rejecting.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that lattice quantum electrodynamics (QED) can be interpreted as a quantum error-correcting code (QECC) beyond the stabilizer formalism by constructing quantum reference frames (QRFs): a gauge-field QRF based on spanning trees of the lattice and a fermionic QRF from the matter field. These QRFs are said to resolve the generic degeneracy of syndromes arising from gauge-violating constraint measurements, thereby identifying families of correctable errors for which explicit group-theoretical recovery operations can be defined, both in the pure-gauge sector and when fermions are included.

Significance. If the explicit QRF constructions and the associated recovery maps are rigorously established, the work would offer a concrete information-theoretic role for gauge symmetry as an encoding resource in lattice gauge theories. This could inform the design of fault-tolerant protocols for quantum simulation of QED and related models, extending the gauge-stabilizer bridge from prior literature to non-stabilizer settings with explicit error families.

major comments (2)

[Abstract and gauge QRF construction section] Abstract and the section introducing the gauge-field QRF: the central assertion that spanning-tree QRFs resolve generic syndrome degeneracy to single out uniquely identifiable families of correctable errors (allowing group-theoretical recovery that preserves the code space and logical operators) is load-bearing for the QECC claim, yet the manuscript provides no explicit verification that the QRF state furnishes a faithful distinguishing label, particularly for non-ideal QRFs or when the error set is not stabilizer-like.
[Fermionic QRF and full lattice QED section] The fermionic QRF construction and its application to the matter-inclusive sector: the claim that the matter-field QRF similarly resolves degeneracies for gauge-violating errors including fermions requires an explicit demonstration that the resulting recovery operators map errored states back into the gauge-invariant subspace without disturbing logical information; this step is not shown to hold when the QRF is non-ideal or when fermionic statistics affect the constraint measurements.

minor comments (2)

The notation distinguishing ideal versus non-ideal QRF states and the precise definition of the error families could be clarified with additional diagrams or a summary table.
A brief comparison table relating the new QRF-based recovery to standard stabilizer recovery in lattice gauge theories would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting these important points regarding the rigor of the QRF constructions. We address each major comment below and indicate the revisions we will make to strengthen the explicit verifications while preserving the core claims.

read point-by-point responses

Referee: [Abstract and gauge QRF construction section] Abstract and the section introducing the gauge-field QRF: the central assertion that spanning-tree QRFs resolve generic syndrome degeneracy to single out uniquely identifiable families of correctable errors (allowing group-theoretical recovery that preserves the code space and logical operators) is load-bearing for the QECC claim, yet the manuscript provides no explicit verification that the QRF state furnishes a faithful distinguishing label, particularly for non-ideal QRFs or when the error set is not stabilizer-like.

Authors: We agree that an explicit verification of the distinguishing power of the spanning-tree QRF state would strengthen the presentation. The manuscript constructs the gauge QRF via spanning trees in the relevant section and uses group representation theory to define the recovery maps for the identified error families. To address the referee's concern, we will add an explicit calculation (including a small-lattice example) showing that the QRF state provides a faithful label for both ideal and non-ideal cases within the considered error sets, confirming that the group-theoretical recovery preserves the code space and logical operators. We will also clarify the abstract accordingly. This is a partial revision as the foundational construction is present but requires this additional verification step. revision: partial
Referee: [Fermionic QRF and full lattice QED section] The fermionic QRF construction and its application to the matter-inclusive sector: the claim that the matter-field QRF similarly resolves degeneracies for gauge-violating errors including fermions requires an explicit demonstration that the resulting recovery operators map errored states back into the gauge-invariant subspace without disturbing logical information; this step is not shown to hold when the QRF is non-ideal or when fermionic statistics affect the constraint measurements.

Authors: We thank the referee for this comment. The fermionic QRF is constructed from the matter fields, and the recovery operators are defined to act consistently with the gauge constraints. In the revised manuscript we will include an explicit demonstration that these operators map states back to the gauge-invariant subspace while leaving logical information invariant. This will cover the effect of fermionic statistics on the constraint measurements (by showing that the anticommutation relations are preserved under the QRF-based recovery) and will extend the analysis to non-ideal QRFs in parallel with the gauge-sector treatment. We view this as a necessary clarification and will expand the relevant section accordingly. revision: yes

Circularity Check

0 steps flagged

No significant circularity; new lattice QRF constructions are independent of prior inputs

full rationale

The derivation introduces explicit new elements—spanning-tree gauge QRFs and matter-field QRFs—applied to lattice QED, with group-theoretical recovery maps for both ideal and non-ideal cases. While the abstract references earlier works establishing the general gauge-QRF-stabilizer bridge, the central claims (resolution of degenerate syndromes into correctable families and explicit QECC structures) rest on these fresh constructions rather than redefining inputs or fitting parameters. No equation or step reduces by construction to a prior result or self-citation; the work remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 2 invented entities

The central claim rests on the domain assumption that gauge symmetry functions as an information-encoding resource and that QRFs can be constructed to resolve error degeneracy; no free parameters or new invented entities with external evidence are introduced beyond the QRF constructions themselves.

axioms (2)

domain assumption For Abelian gauge groups, group-theoretical methods suffice to construct explicit recovery operations for error sets determined by QRFs.
Invoked in the abstract to establish recovery for ideal and non-ideal cases.
domain assumption Quantum reference frames resolve the degeneracy of syndromes associated with gauge-violating errors.
Key premise allowing identification of correctable error families.

invented entities (2)

Gauge-field quantum reference frame based on spanning trees of the lattice no independent evidence
purpose: To encode physical information in the pure-gauge sector and enable error correction
New construction applied to lattice QED in the paper.
Fermionic field quantum reference frame from the matter field no independent evidence
purpose: To extend the QECC structure to include fermions
Constructed to handle the matter-inclusive sector.

pith-pipeline@v0.9.0 · 5531 in / 1460 out tokens · 49078 ms · 2026-05-10T18:40:48.971823+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We construct a gauge-field QRF based on spanning trees... syndromes of gauge-violating errors... QRFs resolve this degeneracy... explicit recovery operations... group-theoretical methods
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Theorem 3.1 (Correctable gauge-fixing operators)... Knill-Laflamme... Proposition 3.3... charge measurements... A_q = 1/√|G| ∫ χ_q(g) P_g^R

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

106 extracted references · 96 canonical work pages · 3 internal anchors

[1]

Dirac.Lectures on Quantum Mechanics

P. Dirac.Lectures on Quantum Mechanics. Belfer Graduate School of Science. Monographs series. Belfer Graduate School of Science, Yeshiva University, 1964

1964
[2]

Henneaux and C

M. Henneaux and C. Teitelboim.Quantization of Gauge Systems. Princeton: Princeton University Press, 2020.isbn: 9780691213866.doi:10.1515/9780691213866

work page doi:10.1515/9780691213866 2020
[4]

A change of perspective: switching quantum reference frames via a perspective-neutral framework

A. Vanrietvelde, P. A. Höhn, F. Giacomini, and E. Castro-Ruiz. “A change of perspective: switching quantum reference frames via a perspective-neutral framework”. In:Quantum4 (2020), p. 225.doi: 10.22331/q-2020-01-27-225

work page doi:10.22331/q-2020-01-27-225 2020
[5]

de la Hamette, T

A.-C. de la Hamette, T. D. Galley, P. A. Höhn, L. Loveridge, and M. P. Mueller. “Perspective-neutral approach to quantum frame covariance for general symmetry groups”. In:arXiv:2110.13824 [quant- ph](2021).doi:10.48550/arXiv.2110.13824

work page doi:10.48550/arxiv.2110.13824 2021
[6]

Quantum reference frame transformations as symmetries and the paradox of the third particle

M. Krumm, P. A. Höhn, and M. P. Müller. “Quantum reference frame transformations as symmetries and the paradox of the third particle”. In:Quantum5 (2021), p. 530.doi:10.22331/q-2021-08- 27-530. 41

work page doi:10.22331/q-2021-08- 2021
[7]

Internal quantum reference frames for finite Abelian groups

P. A. Höhn, M. Krumm, and M. P. Müller. “Internal quantum reference frames for finite Abelian groups”. In:Journal of Mathematical Physics63.11 (2022).doi:10.1063/5.0088485

work page doi:10.1063/5.0088485 2022
[8]

High precision analytical description of the allowed beta spectrum shape

S. D. Bartlett, T. Rudolph, and R. W. Spekkens. “Reference frames, superselection rules, and quantum information”. In:Reviews of Modern Physics79.2 (2007), pp. 555–609.doi:10.1103/revmodphys. 79.555

work page doi:10.1103/revmodphys 2007
[9]

The resource theory of quantum reference frames: manipulations and monotones

G. Gour and R. W. Spekkens. “The resource theory of quantum reference frames: manipulations and monotones”. In:New Journal of Physics10.3 (2008), p. 033023.doi:10.1088/1367-2630/10/ 3/033023

work page doi:10.1088/1367-2630/10/ 2008
[10]

High-threshold uni- versal quantum computation on the surface code,

G. Gour, I. Marvian, and R. W. Spekkens. “Measuring the quality of a quantum reference frame: The relative entropy of frameness”. In:Physical Review A80.1 (2009).doi:10.1103/physreva.80. 012307

work page doi:10.1103/physreva.80 2009
[11]

Relative subsystems and quantum reference frame transforma- tions

E. Castro-Ruiz and O. Oreshkov. “Relative subsystems and quantum reference frame transforma- tions”. In:Commun. Phys.8.1 (2025), p. 187.doi:10.1038/s42005-025-02036-x

work page doi:10.1038/s42005-025-02036-x 2025
[12]

Approximating relational observables by absolute quan- tities: a quantum accuracy-size trade-off

T. Miyadera, L. Loveridge, and P. Busch. “Approximating relational observables by absolute quan- tities: a quantum accuracy-size trade-off”. In:Journal of Physics A: Mathematical and Theoretical 49.18 (2016), p. 185301.doi:10.1088/1751-8113/49/18/185301

work page doi:10.1088/1751-8113/49/18/185301 2016
[13]

Relative Quantum Time

L. Loveridge, T. Miyadera, and P. Busch. “Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics”. In:Foundations of Physics48.2 (2018), pp. 135–198.doi:10.1007/s10701- 018-0138-3

work page doi:10.1007/s10701- 2018
[14]

Real-space RG, error correction and Petz map

K. Furuya, N. Lashkari, and S. Ouseph. “Real-space RG, error correction and Petz map”. In:Journal of High Energy Physics2022.1 (2022).doi:10.1007/jhep01(2022)170

work page doi:10.1007/jhep01(2022)170 2022
[15]

Renormalization group and approximate error correction

K. Furuya, N. Lashkari, and M. Moosa. “Renormalization group and approximate error correction”. In:Physical Review D106.10 (2022).doi:10.1103/physrevd.106.105007

work page doi:10.1103/physrevd.106.105007 2022
[16]

Bulk locality and quantum error correction in AdS/CFT

A. Almheiri, X. Dong, and D. Harlow. “Bulk locality and quantum error correction in AdS/CFT”. In: Journal of High Energy Physics2015.4 (2015).doi:10.1007/jhep04(2015)163

work page doi:10.1007/jhep04(2015)163 2015
[17]

Pastawski, B

F. Pastawski, B. Yoshida, D. Harlow, and J. Preskill. “Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence”. In:Journal of High Energy Physics2015.6 (2015). doi:10.1007/jhep06(2015)149

work page doi:10.1007/jhep06(2015)149 2015
[18]

Code Properties from Holographic Geometries

F. Pastawski and J. Preskill. “Code Properties from Holographic Geometries”. In:Phys. Rev. X7 (2017), p. 021022.doi:10.1103/PhysRevX.7.021022

work page doi:10.1103/physrevx.7.021022 2017
[19]

The Ryu–Takayanagi Formula from Quantum Error Correction

D. Harlow. “The Ryu–Takayanagi Formula from Quantum Error Correction”. In:Communications in Mathematical Physics354.3 (2017), 865–912.doi:10.1007/s00220-017-2904-z

work page doi:10.1007/s00220-017-2904-z 2017
[20]

Holographic spacetime, black holes and quantum error correcting codes: a review

T. Kibe, P. Mandayam, and A. Mukhopadhyay. “Holographic spacetime, black holes and quantum error correcting codes: a review”. In:The European Physical Journal C82.5 (2022), p. 463.doi:10. 1140/epjc/s10052-022-10382-1

2022
[21]

Superselection Rules, Quantum Er- ror Correction, and Quantum Chromodynamics

N. Bao, C. Cao, A. Chatwin-Davies, G. Cheng, and G. Zhu. “Superselection Rules, Quantum Er- ror Correction, and Quantum Chromodynamics”. In:arXiv:2306.17230 [quant-ph](2023).doi:10. 48550/arXiv.2306.17230

work page arXiv 2023
[22]

Rothlin.Bridging Quantum Error Correction, Gauge Theories and Quantum Reference Frames

E. Rothlin.Bridging Quantum Error Correction, Gauge Theories and Quantum Reference Frames. en. Student Paper. Zurich, 2024.doi:10.3929/ethz-b-000708367. 42

work page doi:10.3929/ethz-b-000708367 2024
[23]

A correspondence between quantum error correcting codes and quantum reference frames,

S. Carrozza, A. Chatwin-Davies, P. A. Höhn, and F. M. Mele. “A correspondence between quantum error correcting codes and quantum reference frames”. In:arXiv:2412.15317 [quant-ph](2024).doi: 10.48550/arXiv.2412.15317

work page doi:10.48550/arxiv.2412.15317 2024
[24]

Stabilizer Codes and Quantum Error Correction

D. Gottesman. “Stabilizer Codes and Quantum Error Correction”. In:arXiv:quant-ph/9705052(1997). doi:10.48550/arXiv.quant-ph/9705052

work page internal anchor Pith review doi:10.48550/arxiv.quant-ph/9705052 1997
[25]

Oracles for Gauss’s law on digital quantum computers

J. R. Stryker. “Oracles for Gauss’s law on digital quantum computers”. In:Phys. Rev. A99 (2019), p. 042301.doi:10.1103/PhysRevA.99.042301

work page doi:10.1103/physreva.99.042301 2019
[26]

Quantum error correction with gauge symmetries

A. Rajput, A. Roggero, and N. Wiebe. “Quantum error correction with gauge symmetries”. In:npj Quantum Information9.1 (2023), p. 41.doi:10.1038/s41534-023-00706-8

work page doi:10.1038/s41534-023-00706-8 2023
[27]

Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes

L. Spagnoli, A. Roggero, and N. Wiebe. “Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes”. In:Quantum10 (2026), p. 1968.doi:10.22331/q-2026-01-16-1968

work page doi:10.22331/q-2026-01-16-1968 2026
[28]

Quantum error thresholds for gauge-redundant digitiza- tions of lattice field theories

M. Carena, H. Lamm, Y.-Y. Li, and W. Liu. “Quantum error thresholds for gauge-redundant digitiza- tions of lattice field theories”. In:arXiv:2402.16780 [hep-lat](2024).doi:10.48550/arXiv.2402. 16780

work page doi:10.48550/arxiv.2402 2024
[29]

Robustness of Gauge Digitization to Quantum Noise

E. J. Gustafson and H. Lamm. “Robustness of Gauge Digitization to Quantum Noise”. In: arXiv:2301.10207 [hep-lat](2023).doi:10.48550/arXiv.2301.10207

work page doi:10.48550/arxiv.2301.10207 2023
[30]

Yao, (2025), arXiv:2511.13721 [quant-ph]

X. Yao. “Quantum Error Correction Codes for Truncated SU(2) Lattice Gauge Theories”. In: arXiv:2511.13721 [quant-ph](2025).doi:10.48550/arXiv.2511.13721

work page doi:10.48550/arxiv.2511.13721 2025
[31]

Pato and N

B. Pato and N. Klco. “Trade-offs in Gauss’s law error correction for lattice gauge theory quantum simulations”. In:arXiv:2602.22121 [quant-ph](2026).doi:10.48550/arXiv.2602.22121

work page doi:10.48550/arxiv.2602.22121 2026
[32]

Spagnoli, A

L. Spagnoli, A. Roggero, and N. Wiebe.Qudit stabiliser codes forZ N lattice gauge theories with matter. 2026.doi:10.48550/arXiv.2602.20661

work page doi:10.48550/arxiv.2602.20661 2026
[33]

Exploring the Connection between Gauge Theory and Quantum Error Correction via Quantum Reference Frames

E. Rothlin. “Exploring the Connection between Gauge Theory and Quantum Error Correction via Quantum Reference Frames”. Master’s thesis. ETH Zurich, July 18, 2025.doi:10.3929/ethz-c- 000784853

work page doi:10.3929/ethz-c- 2025
[34]

Gauss law codes and vacuum codes from lattice gauge theories

J. P. Lacambra, A. Chatwin-Davies, M. Honda, and P. Höhn. “Gauss law codes and vacuum codes from lattice gauge theories”.Forthcoming
[35]

Trinity of relational quantum dynamics

P. A. Höhn, A. R. H. Smith, and M. P. E. Lock. “Trinity of relational quantum dynamics”. In:Phys. Rev. D104 (2021), p. 066001.doi:10.1103/PhysRevD.104.066001

work page doi:10.1103/physrevd.104.066001 2021
[36]

Hamiltonian formulation of Wilson’s lattice gauge theories

J. Kogut and L. Susskind. “Hamiltonian formulation of Wilson’s lattice gauge theories”. In:Phys. Rev. D11 (1975), pp. 395–408.doi:10.1103/PhysRevD.11.395

work page doi:10.1103/physrevd.11.395 1975
[38]

Gattringer and C.B

C. Gattringer and C. B. Lang.Quantum chromodynamics on the lattice. Vol. 788. Berlin: Springer, 2010.isbn: 978-3-642-01849-7, 978-3-642-01850-3.doi:10.1007/978-3-642-01850-3

work page doi:10.1007/978-3-642-01850-3 2010
[39]

Contour Gauge: Compendium of Results in Theory and Applications

I. V. Anikin. “Contour Gauge: Compendium of Results in Theory and Applications”. In:Physics of Particles and Nuclei56.1 (2025), pp. 12–42.doi:10.1134/S106377962470120X

work page doi:10.1134/s106377962470120x 2025
[40]

Charge Superselection Rule

Y. Aharonov and L. Susskind. “Charge Superselection Rule”. In:Phys. Rev.155 (1967), pp. 1428–1431. doi:10.1103/PhysRev.155.1428. 43

work page doi:10.1103/physrev.155.1428 1967
[41]

Observability of the Sign Change of Spinors under2πRotations

Y. Aharonov and L. Susskind. “Observability of the Sign Change of Spinors under2πRotations”. In:Phys. Rev.158 (1967), pp. 1237–1238.doi:10.1103/PhysRev.158.1237

work page doi:10.1103/physrev.158.1237 1967
[42]

Quantum frames of reference

Y. Aharonov and T. Kaufherr. “Quantum frames of reference”. In:Phys. Rev. D30 (1984), pp. 368– 385.doi:10.1103/PhysRevD.30.368

work page doi:10.1103/physrevd.30.368 1984
[43]

Operational Quantum Reference Frame Transforma- tions

T. Carette, J. Glowacki, and L. Loveridge. “Operational Quantum Reference Frame Transforma- tions”. In:Quantum9 (2025), p. 1680.doi:10.22331/q-2025-03-27-1680

work page doi:10.22331/q-2025-03-27-1680 2025
[44]

Quantum mechanics and the covariance of physical laws in quantum reference frames

F. Giacomini, E. Castro-Ruiz, and Č. Brukner. “Quantum mechanics and the covariance of physical laws in quantum reference frames”. In:Nature Communications10.1 (2019), p. 494.doi:10.1038/ s41467-018-08155-0

2019
[45]

Quantum reference frames for general sym- metry groups

A.-C. de la Hamette and T. D. Galley. “Quantum reference frames for general symmetry groups”. In:Quantum4 (2020), p. 367.doi:10.22331/q-2020-11-30-367

work page doi:10.22331/q-2020-11-30-367 2020
[46]

The perspectives of non-ideal quantum reference frames,

S. C. Garmier, L. Hausmann, and E. Castro-Ruiz. “The Perspectives of Non-Ideal Quantum Reference Frames”. In:arXiv:2512.19343 [quant-ph](2025).doi:10.48550/arXiv.2512.19343

work page doi:10.48550/arxiv.2512.19343 2025
[47]

De Vuyst, P

J. De Vuyst, P. A. Hoehn, and A. Tsobanjan. “On the relation between perspective-neutral, algebraic, and effective quantum reference frames”. In:arXiv:2507.14131 [quant-ph](2025).doi:10.48550/ arXiv.2507.14131

work page arXiv 2025
[49]

Quantum reference frames in arbitrary charge sectors: Accessibility of global properties from internal perspectives,

A.-C. de la Hamette, V. Kabel, and Časlav Brukner. “Accessibility of Global Properties from Internal Quantum Reference Frame Perspectives”. In:arXiv:2510.09100 [quant-ph](2026).doi:10.48550/ arXiv.2510.09100

work page arXiv 2026
[50]

What can we do in a symmetry-constrained perspective? the importance of the total charge’s status in quantum reference frame frameworks,

G. Doat and A. Vanrietvelde. “What can we do in a symmetry-constrained perspective? The im- portance of the total charge’s status in quantum reference frame frameworks”. In:arXiv:2510.13607 [quant-ph](2025).doi:10.48550/arXiv.2510.13607

work page doi:10.48550/arxiv.2510.13607 2025
[51]

Superselection rules and quantum protocols

A. Kitaev, D. Mayers, and J. Preskill. “Superselection rules and quantum protocols”. In:Physical Review A69.5 (2004).doi:10.1103/physreva.69.052326

work page doi:10.1103/physreva.69.052326 2004
[52]

Degradation of a quantum reference frame

S. D. Bartlett, T. Rudolph, R. W. Spekkens, and P. S. Turner. “Degradation of a quantum reference frame”. In:New Journal of Physics8.4 (2006), pp. 58–58.doi:10.1088/1367-2630/8/4/058

work page doi:10.1088/1367-2630/8/4/058 2006
[53]

Changing quantum reference frames

M. C. Palmer, F. Girelli, and S. D. Bartlett. “Changing quantum reference frames”. In:Physical Review A89.5 (2014).doi:10.1103/physreva.89.052121

work page doi:10.1103/physreva.89.052121 2014
[54]

Uncertainty relations relative to phase-space quantum refer- ence frames

M. Jorquera Riera and L. Loveridge. “Uncertainty relations relative to phase-space quantum refer- ence frames”. In:Phys. Rev. A111 (2025), p. L060201.doi:10.1103/PhysRevA.111.L060201

work page doi:10.1103/physreva.111.l060201 2025
[56]

control bars

G. Araujo-Regado, P. A. Höhn, and F. Sartini. “Relational entanglement entropies and quantum reference frames in gauge theories”. In:arXiv:2506.23459 [hep-th](2025).doi:10.48550/arXiv. 2506.23459

work page internal anchor Pith review doi:10.48550/arxiv 2025
[57]

Einstein’s Equivalence principle for superpositions of gravitational fields,

F. Giacomini and Č. Brukner. “Einstein’s Equivalence principle for superpositions of gravitational fields and quantum reference frames”. In:arXiv:2012.13754 [quant-ph](2020).doi:10 . 48550 / arXiv.2012.13754. 44

work page arXiv 2012
[58]

Quantum reference frames for an indefinite metric

A.-C. de la Hamette, V. Kabel, E. Castro-Ruiz, and Č. Brukner. “Quantum reference frames for an indefinite metric”. In:Commun. Phys.6.1 (2023), p. 231.doi:10.1038/s42005-023-01344-4

work page doi:10.1038/s42005-023-01344-4 2023
[59]

Quantum reference frames at the boundary of spacetime

V. Kabel, Č. Brukner, and W. Wieland. “Quantum reference frames at the boundary of spacetime”. In:Physical Review D108.10 (2023).doi:10.1103/physrevd.108.106022

work page doi:10.1103/physrevd.108.106022 2023
[60]

Kabel, A.-C

V. Kabel, A.-C. de la Hamette, L. Apadula, C. Cepollaro, H. Gomes, J. Butterfield, and Č. Brukner. “Quantum coordinates, localisation of events, and the quantum hole argument”. In:Commun. Phys. 8.1 (2025), p. 185.doi:10.1038/s42005-025-02084-3

work page doi:10.1038/s42005-025-02084-3 2025
[61]

Localization and anomalous reference frames in gravity

L. Freidel and J. Kirklin. “Localization and anomalous reference frames in gravity”. In: arXiv:2510.26589 [hep-th](2025).doi:10.48550/arXiv.2510.26589

work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2510.26589 2025
[62]

Sum of Entanglement and Subsystem Coherence Is Invariant under Quantum Reference Frame Transformations

C. Cepollaro, A. Akil, P. Cieśliński, A.-C. de la Hamette, and v. Brukner. “Sum of Entanglement and Subsystem Coherence Is Invariant under Quantum Reference Frame Transformations”. In:Phys. Rev. Lett.135 (2025), p. 010201.doi:10.1103/h6b3-y4vt

work page doi:10.1103/h6b3-y4vt 2025
[63]

Gravitational entropy is observer-dependent

J. De Vuyst, S. Eccles, P. A. Höhn, and J. Kirklin. “Gravitational entropy is observer-dependent”. In: Journal of High Energy Physics07 (2025), p. 146.doi:10.1007/JHEP07(2025)146

work page doi:10.1007/jhep07(2025)146 2025
[64]

Observer-Dependent Entropy and Diagonal Rényi Invariants in Quantum Reference Frames

A.-C. de la Hamette. “Observer-Dependent Entropy and Diagonal Rényi Invariants in Quantum Reference Frames”. In:arXiv:2603.23598 [quant-ph](2026).doi:10.48550/arXiv.2603.23598

work page doi:10.48550/arxiv.2603.23598 2026
[65]

Quantum Relativity of Subsys- tems

S. Ali Ahmad, T. D. Galley, P. A. Höhn, M. P. Lock, and A. R. Smith. “Quantum Relativity of Subsys- tems”. In:Physical Review Letters128.17 (2022).doi:10.1103/physrevlett.128.170401

work page doi:10.1103/physrevlett.128.170401 2022
[66]

Quantum Frame Relativity of Subsystems, Correlations and Thermodynamics,

P. A. Höhn, I. Kotecha, and F. M. Mele. “Quantum Frame Relativity of Subsystems, Correlations and Thermodynamics”. In:arXiv:2308.09131 [quant-ph](2023).doi:10.48550/arXiv.2308.09131

work page doi:10.48550/arxiv.2308.09131 2023
[67]

Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems

E. Castro-Ruiz, F. Giacomini, A. Belenchia, and Č. Brukner. “Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems”. In:Nature Commun.11.1 (2020), p. 2672.doi:10.1038/s41467-020-16013-1

work page doi:10.1038/s41467-020-16013-1 2020
[68]

Events and their localisation are relative to a lab,

V. Vilasini, L.-Q. Chen, L. Ye, and R. Renner. “Events and their Localisation are Relative to a Lab”. In:arXiv:2505.21797 [quant-ph](2025).doi:10.48550/arXiv.2505.21797

work page doi:10.48550/arxiv.2505.21797 2025
[69]

An algebra of observables for de Sitter space

V. Chandrasekaran, R. Longo, G. Penington, and E. Witten. “An algebra of observables for de Sitter space”. In:Journal of High Energy Physics02 (2023), p. 082.doi:10.1007/JHEP02(2023)082

work page doi:10.1007/jhep02(2023)082 2023
[70]

Quantum Reference Frames, Measurement Schemes and the Type of Local Algebras in Quantum Field Theory

C. J. Fewster, D. W. Janssen, L. D. Loveridge, K. Rejzner, and J. Waldron. “Quantum Reference Frames, Measurement Schemes and the Type of Local Algebras in Quantum Field Theory”. In:Communica- tions in Mathematical Physics406.1 (2024).doi:10.1007/s00220-024-05180-7

work page doi:10.1007/s00220-024-05180-7 2024
[71]

Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy

J. De Vuyst, S. Eccles, P. A. Höhn, and J. Kirklin. “Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy”. In:Journal of High Energy Physics(2025). doi:10.1007/JHEP07(2025)063

work page doi:10.1007/jhep07(2025)063 2025
[72]

Evolution without evolution: Dynamics described by stationary observables

D. N. Page and W. K. Wootters. “Evolution without evolution: Dynamics described by stationary observables”. In:Phys. Rev. D27 (1983), pp. 2885–2892.doi:10.1103/PhysRevD.27.2885

work page doi:10.1103/physrevd.27.2885 1983
[73]

M. A. Nielsen and I. L. Chuang.Quantum Computation and Quantum Information. Cambridge Uni- versity Press, 2012.isbn: 978-0-521-63503-5.doi:10.1017/cbo9780511976667

work page doi:10.1017/cbo9780511976667 2012
[74]

Preskill.Lecture Notes: Quantum Computation, Chapter 7

J. Preskill.Lecture Notes: Quantum Computation, Chapter 7. 1999

1999
[75]

Theory of quantum error-correcting codes

E. Knill and R. Laflamme. “Theory of quantum error-correcting codes”. In:Phys. Rev. A55 (1997), pp. 900–911.doi:10.1103/PhysRevA.55.900. 45

work page doi:10.1103/physreva.55.900 1997
[76]

Theory of Quantum Error Correction for General Noise

E. Knill, R. Laflamme, and L. Viola. “Theory of Quantum Error Correction for General Noise”. In: Phys. Rev. Lett.84 (2000), pp. 2525–2528.doi:10.1103/PhysRevLett.84.2525

work page doi:10.1103/physrevlett.84.2525 2000
[77]

Generalization of Quantum Error Correction via the Heisen- berg Picture

C. Bény, A. Kempf, and D. W. Kribs. “Generalization of Quantum Error Correction via the Heisen- berg Picture”. In:Phys. Rev. Lett.98 (2007), p. 100502.doi:10.1103/PhysRevLett.98.100502

work page doi:10.1103/physrevlett.98.100502 2007
[78]

Fulton and J

W. Fulton and J. Harris.Representation Theory. Graduate Texts in Mathematics. New York: Springer, 2004.doi:10.1007/978-1-4612-0979-9

work page doi:10.1007/978-1-4612-0979-9 2004
[79]

An introduction to lattice gauge theory and spin systems

J. B. Kogut. “An introduction to lattice gauge theory and spin systems”. In:Rev. Mod. Phys.51 (1979), pp. 659–713.doi:10.1103/RevModPhys.51.659

work page doi:10.1103/revmodphys.51.659 1979
[80]

Tinto and J

L. Susskind. “Lattice fermions”. In:Phys. Rev. D16 (1977), pp. 3031–3039.doi:10.1103/PhysRevD. 16.3031

work page doi:10.1103/physrevd 1977
[81]

Lattice fermions: Species doubling, chiral invariance and the triangle anomaly

L. H. Karsten and J. Smith. “Lattice fermions: Species doubling, chiral invariance and the triangle anomaly”. In:Nuclear Physics B183.1 (1981), pp. 103–140.doi:10.1016/0550-3213(81)90549- 6

work page doi:10.1016/0550-3213(81)90549- 1981
[82]

Symmetries and Anomalies of Hamiltonian Staggered Fermions,

S. Catterall, A. Pradhan, and A. Samlodia. “Symmetries and Anomalies of Hamiltonian Staggered Fermions”. In:arXiv:2501.10862 [hep-lat](2025).doi:10.48550/arXiv.2501.10862

work page doi:10.48550/arxiv.2501.10862 2025
[83]

Gauge fixing, the transfer matrix, and confinement on a lattice

M. Creutz. “Gauge fixing, the transfer matrix, and confinement on a lattice”. In:Phys. Rev. D15 (1977), pp. 1128–1136.doi:10.1103/PhysRevD.15.1128

work page doi:10.1103/physrevd.15.1128 1977
[84]

Toward a Many-Body Treatment of Hamiltonian Lattice SU(N) Gauge Theory

N. Ligterink, N. Walet, and R. Bishop. “Toward a Many-Body Treatment of Hamiltonian Lattice SU(N) Gauge Theory”. In:Annals of Physics284.2 (2000), pp. 215–262.doi:10.1006/aphy.2000. 6070

work page doi:10.1006/aphy.2000 2000

Showing first 80 references.