arxiv: 2605.11088 · v1 · submitted 2026-05-11 · 🪐 quant-ph

Recognition: 2 theorem links

· Lean Theorem

Tolerating Device Failure in Distributed Quantum Computing

Evan Sutcliffe , Coral M. Westoby

Authors on Pith no claims yet

Pith reviewed 2026-05-13 03:08 UTC · model grok-4.3

classification 🪐 quant-ph

keywords distributed quantum computingquantum error correctiontoric codemodular quantum networksnode failurelogical error rateFloquet codesfault tolerance

0 comments

The pith

Distributed quantum error correction lets modular devices fail or be swapped with little effect on logical errors.

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

The paper shows that performing quantum error correction across a network of separate quantum devices allows individual modules to be replaced or to fail entirely while keeping logical error rates low. It examines how toric and hyperbolic Floquet codes maintain their error-suppressing power when entire nodes drop out at low rates. For node failures occurring with probability p/100, the distributed toric code is shown to deliver lower logical error rates than an equivalent code on a single large device once the physical error rate drops below 0.05 percent. A sympathetic reader would care because this points to a route for building reliable large-scale quantum computers from replaceable parts whose individual reliability can be lower than the overall system.

Core claim

When quantum error correction is performed over a modular quantum network, quantum devices can be swapped out or replaced during operation with minimal impact on logical error rates. The toric and hyperbolic Floquet quantum error correcting codes protect logical information under low rates of modular node failure. For catastrophic node failure of probability p/100, a distributed toric code outperforms one implemented on a monolithic device below a physical error rate of 0.05 percent.

What carries the argument

Distributed application of the toric and hyperbolic Floquet codes across a modular quantum network, which spreads logical qubits so that loss of any single node leaves the remaining code space intact.

If this is right

Individual modules can be removed and replaced mid-computation without a large rise in logical errors.
Logical error suppression continues when entire nodes fail at low probabilities.
The distributed toric code crosses below the logical error rate of a monolithic toric code at physical error rates under 0.05 percent for node failure probability p/100.
Hyperbolic Floquet codes also sustain useful error suppression under the same node-failure regime.

Where Pith is reading between the lines

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

Modular architectures could allow incremental hardware upgrades without stopping a running computation.
Network connectivity requirements become a new design parameter for fault-tolerant quantum hardware.
The threshold improvement suggests that distributed systems may reach useful scales before monolithic devices do.
Real-device tests with measured node-failure statistics would be needed to confirm the modeled advantage.

Load-bearing premise

The analysis assumes a particular independent-error model and a specific pattern of catastrophic node failures that may not match all hardware imperfections or network-wide correlations.

What would settle it

Measure the logical error rate of a small toric-code instance implemented on a network of four or more modules while forcing node failures at probability p/100 and compare it directly against the same code size run on a single device at physical error rates near 0.05 percent.

Figures

Figures reproduced from arXiv: 2605.11088 by Coral M. Westoby, Evan Sutcliffe.

**Figure 2.** Figure 2: Schematic showing how a node (e.g. a QPU) can be swapped out of a quantum network while maintaining a QEC [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: The process of node swap-out when node failure is unscheduled. (a) A catastrophic failure occurring on Node [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: (a) Logical error rate of toric codes of distance [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: Logical error rate for the unrotated toric code ( [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 6.** Figure 6: Logical error rate of the toric code (d = 6, 8) distributed over a nq = 48 qubit device. C. Performance under unscheduled node failure By assessing the logical error rate from only node failure, we find that for a certain size of QPU, logical errors due to node failure are suppressed to a higher degree for quantum codes of increasing code distance. This is because larger QEC codes are implemented over more… view at source ↗

**Figure 7.** Figure 7: The impact of physical error rate p and node failure p/100 on logical error rates for (a), unrotated toric codes with d ∈ [6, . . . , 12] and (b), semi-hyperbolic Floquet codes. Also shown is the analytical floor on logical error rate (black dashed line) for a single monolithic device with node failure p/100 per round. we have shown how nodes can be swapped out and replaced with minimal impact on the logic… view at source ↗

read the original abstract

It is desirable that a distributed quantum computer can operate despite the replacement or failure of its constituent components, allowing the reliability of the distributed system to exceed that of its subcomponents. We first show that when quantum error correction is performed over a modular quantum network, quantum devices can be swapped out or replaced, during operation, with minimal impact on logical error rates. We also investigate the ability of the toric and hyperbolic Floquet quantum error correcting codes to protect logical information under low rates of modular node failure. In particular, we show that under the proposed distributed quantum error scheme, the selected codes are able to maintain good logical error suppression during the failure of entire nodes. For catastrophic node failure of probability p/100, we suggest that a distributed toric code would outperform one implemented on a monolithic device below a physical error rate of 0.05%.

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 simulations suggest distributed toric codes can outperform monolithic ones under node failures below 0.05% error rate, but this hinges on the details of the failure model.

read the letter

The paper examines how toric and hyperbolic Floquet codes handle failures of entire nodes in a distributed quantum computing setup. They find that these codes maintain good logical error suppression even with node replacements, and they point to a regime where a distributed toric code would have lower logical error rates than a monolithic device when physical errors are below 0.05% and node failures occur at probability p/100. What the work does well is bring attention to the reliability of modular architectures. By showing that quantum error correction can be performed across a network while allowing component swaps, it takes a step toward systems that do not require every part to be perfect. The choice of two different codes provides a comparison that highlights the toric code's potential advantage in this scenario. The main concern is how the node failures are modeled. The reported crossover at 0.05% depends on the specific way failures are introduced and how they interact with the syndrome extraction in the distributed scheme. If the model assumes failures are isolated and do not create additional correlations or non-Pauli errors, the result may not generalize. The abstract leaves the details of the simulation open, so the strength of the claim rests on whether those choices are justified and tested against variations. This kind of study is useful for people focused on scaling quantum computers through modularity. Readers interested in fault tolerance for networked systems will see a practical application of known codes and can build on the simulation framework. The paper engages directly with the literature on quantum error correction and applies it to a relevant engineering problem. It is coherent on its own terms and deserves a serious referee to evaluate the methods section and the robustness of the error model. I would recommend putting it through peer review.

Referee Report

1 major / 1 minor

Summary. The paper claims that performing quantum error correction over a modular quantum network allows constituent devices to be swapped or replaced during operation with minimal impact on logical error rates. It investigates the toric and hyperbolic Floquet codes under low rates of modular node failure, showing that these codes maintain good logical error suppression. In particular, for catastrophic node failure of probability p/100, the authors suggest that a distributed toric code would outperform a monolithic implementation below a physical error rate of 0.05%.

Significance. If the simulation results hold under the stated error model, the work is significant for practical distributed quantum computing, as it provides evidence that modular architectures can achieve higher reliability than their subcomponents by tolerating node failures while preserving logical error suppression. The focus on concrete codes (toric and Floquet) and the reported performance crossover are strengths that could guide hardware design, though the result is tied to the specific failure model.

major comments (1)

[Abstract] Abstract: The central outperformance claim—that a distributed toric code outperforms a monolithic device below 0.05% physical error rate for catastrophic node failure probability p/100—is load-bearing on the details of the node-failure error model and its integration into syndrome extraction for the toric code. The abstract provides no indication that alternative models (e.g., spatially correlated failures across nodes or non-Pauli noise during replacement) were tested; if the chosen model underestimates correlations, the reported crossover threshold would shift and the claim would not hold.

minor comments (1)

The abstract would benefit from a short parenthetical note on the assumed error model for node failures to allow immediate assessment of the 0.05% threshold.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript. We appreciate the recognition of the work's potential relevance to modular quantum architectures. We address the major comment below and will revise the manuscript accordingly.

read point-by-point responses

Referee: [Abstract] Abstract: The central outperformance claim—that a distributed toric code outperforms a monolithic device below 0.05% physical error rate for catastrophic node failure probability p/100—is load-bearing on the details of the node-failure error model and its integration into syndrome extraction for the toric code. The abstract provides no indication that alternative models (e.g., spatially correlated failures across nodes or non-Pauli noise during replacement) were tested; if the chosen model underestimates correlations, the reported crossover threshold would shift and the claim would not hold.

Authors: We agree that the abstract should more explicitly reference the node-failure model and that the outperformance claim is tied to its specific assumptions. In the revised manuscript, we will update the abstract to clarify: 'For catastrophic node failure of probability p/100 under an independent failure model, we suggest that a distributed toric code would outperform one implemented on a monolithic device below a physical error rate of 0.05%.' We will also expand the methods and discussion sections to detail how node failures are modeled (as complete erasure of the node's qubits) and integrated into the toric code's syndrome extraction circuits, with no additional noise during replacement. We did not test alternative models such as spatially correlated failures across nodes or non-Pauli noise, as the present work focuses on baseline performance under this standard independent model. We will add an explicit caveat noting that stronger correlations could shift the reported crossover and identify this as an avenue for future study. These changes will temper the claim appropriately while preserving the concrete results under the stated model. revision: yes

Circularity Check

0 steps flagged

No significant circularity; performance claims rest on independent simulation analysis

full rationale

The paper's central claims—that modular node replacement has minimal impact on logical error rates and that a distributed toric code outperforms a monolithic implementation below 0.05% physical error rate under p/100 node failure—are presented as outcomes of numerical investigations under a proposed distributed QEC scheme. No equations or steps reduce by construction to self-definitions, fitted parameters renamed as predictions, or load-bearing self-citations. The derivation chain relies on external simulation benchmarks and the stated error model rather than internal fitting loops or ansatzes imported from prior author work. This is the expected non-circular outcome for a simulation-driven performance study.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard assumptions of quantum error correction and a particular modular failure model; no new entities are introduced.

free parameters (1)

node failure probability
Set to p/100 where p is the physical error rate; this scaling is chosen to model low-rate catastrophic failures.

axioms (1)

domain assumption Quantum error correction can be performed across modular network links with standard stabilizer measurements.
Invoked when stating that devices can be swapped with minimal impact on logical error rates.

pith-pipeline@v0.9.0 · 5434 in / 1318 out tokens · 82813 ms · 2026-05-13T03:08:30.339302+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.

For catastrophic node failure of probability p/100, we suggest that a distributed toric code would outperform one implemented on a monolithic device below a physical error rate of 0.05%.
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

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

We use a distributed QEC noise model... non-local noise probability p_nl = 10p... node failure modelled as n_q-qubit depolarising channel.

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

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