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Towards the Characterization of Logical Errors in Distributed Lattice Surgery

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Pith's one-line read Distributed XX lattice-surgery merges between two surface-code patches keep a fault-tolerance threshold around 0.87 percent even when the shared Bell-pair noise is scaled elevenfold, because the noisy seam contains only O(d) qubits per roun

desk verdict A useful, plausible threshold study for distributed lattice-surgery merges whose quantitative numbers rest on an unvalidated phenomenological noise mapping—worth peer review, with validation requested. read the letter →

arxiv 2607.29186 v1 pith:TUSIYCGX submitted 2026-07-31 quant-ph

Nitish Kumar Chandra , Reza Nejabati , Eneet Kaur This is my paper
classification quant-ph PACS 03.67.Pp
keywords distributedquantumcomputinglatticesurgerysurfacecodeXXmergefault-tolerancethresholdBell-pairnoisephenomenologicalmodelminimum-weightperfectmatching
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that a distributed XX merge between two rotated surface-code patches, hosted on separate processors and connected by noisy Bell pairs, remains fault-tolerant under substantially noisier interconnects. The authors derive effective per-cycle error rates for bulk and seam qubits from circuit-level noise sources, then simulate logical Z errors in the merge's H-shaped spacetime diagram with a minimum-weight perfect matching decoder. They find the threshold degrades only from roughly 0.868 percent at Bell-pair noise scaling k=1 to 0.834 percent at k=11, an absolute drop of about 0.034 percent. The explanation is a scaling argument: the seam contains O(d) qubits per syndrome round while the bulk contains O(d²), so in the large-distance limit the threshold is set by the bulk. If correct, this means modular surface-code architectures can tolerate noisy entanglement links with minimal penalty, easing the rate-fidelity tradeoff for distributed quantum computing.

What carries the argument

The central machinery is a two-tier effective noise model combined with the H-shaped spacetime decoding graph of the merge. The authors map depolarizing noise from local CNOT gates, noisy Bell pairs, readout, and idle steps into four effective phenomenological rates using the 8/15 per-qubit depolarizing counting per CNOT or Bell pair. The seam rates are elevated by the Bell-pair scaling factor k. The H-shaped spacetime diagram, with four disconnected X-type boundaries and two Z-type boundaries, defines the logical-error condition under minimum-weight perfect matching: a decoding failure occurs when the residual error string has odd parity on any of the four X-boundaries. The bulk-versus-seam

What would settle it

Run a full circuit-level simulation of the distributed XX merge with depolarizing noise applied independently to each local CNOT, each shared Bell pair, each readout, and each idle step; extract the per-cycle X/Z error rates on seam and bulk qubits and compare with p_bulk=3ε, q_bulk=4ε, p_seam=ε(k+9)/2, q_seam=ε(k+7). If the measured rates differ materially, or if threshold crossings shift outside the reported band, the central claim does not transfer from the phenomenological model to hardware.

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Extended reading notes

Core claim

The paper claims that the distributed XX merge operation maintains a fault-tolerance threshold close to that of a monolithic memory experiment even when the Bell-pair noise is an order of magnitude larger than local gate noise. Using a phenomenological noise model with distinct bulk and seam error rates—p_bulk=3ε, q_bulk=4ε, p_seam=ε(k+9)/2, q_seam=ε(k+7)—the authors compute logical Z-error rates for distances 5 through 13 and extract thresholds from distance-curve crossings. The threshold decreases monotonically from 0.8683% at k=1 to 0.8339% at k=11. The claimed reason is that the seam's spacetime error volume is asymptotically negligible relative to the bulk, so the bulk-dominated thresho

Load-bearing premise

The load-bearing premise is that the effective per-cycle bulk and seam error rates, obtained by counting independent depolarizing contributions from CNOT gates, Bell pairs, readout, and idle steps, faithfully represent the actual circuit-level noise of the distributed syndrome-extraction circuit—including the treatment of boundary qubits with lower-weight stabilizers as if they had the same seam rates.

Editorial extensions

If this is right

  • Modular or distributed surface-code systems can use entanglement links that are roughly an order of magnitude noisier than local gates while keeping the logical merge threshold above 0.8 percent.
  • Relaxing Bell-pair fidelity targets reduces the need for entanglement distillation, which in turn increases the effective entanglement generation rate and eases a key bottleneck in distributed architectures.
  • The bulk-dominated scaling suggests that larger logical operations built from merge and split primitives should inherit similar tolerance to boundary-localized noise.
  • Thresholds near 0.86 percent at k=1 fall within the range reported for circuit-level surface-code memory, supporting the claim that the effective phenomenological rates capture the dominant noise physics.
  • The results provide concrete design guidance: target local gate fidelities and code distances can be chosen based on bulk noise, while interconnect fidelity requirements can be looser than previously assumed.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The O(d) versus O(d²) seam-to-bulk ratio suggests that other spatially localized noisy regions—such as interfaces to magic-state factories or readout zones—would also be bulk-dominated, so similar threshold robustness may extend beyond the merge operation.
  • A testable extension is to vary the bridge width w beyond 1 and the number of seam rounds: the model predicts threshold degradation should track the seam volume fraction rather than the Bell-pair scaling factor k alone.
  • The effective-rate mapping assumes independent X and Z errors per cycle; if a full circuit-level simulation reveals correlated or feedforward-induced errors, the threshold could shift more than the current model predicts.
  • Comparing the threshold under alternative decoders, such as union-find or belief-propagation variants, would reveal whether the reported resilience is specific to minimum-weight perfect matching or a more general property of the spacetime error model.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper studies logical errors in a distributed XX merge between two rotated surface-code patches hosted on separate QPUs. It introduces a phenomenological noise model with distinct bulk and seam error rates derived from circuit-level depolarizing noise on local CNOTs, noisy Bell pairs, readout, and idle operations. Using MWPM decoding on the H-shaped spacetime syndrome graph for distances d=5,...,13, it estimates thresholds for six Bell-pair noise scaling factors k=1,...,11. The main claim is that the threshold decreases only modestly, from 0.8683% at k=1 to 0.8339% at k=11, because the seam contains O(d) qubits per round while the bulk contains O(d^2), making the asymptotic threshold bulk-dominated. The paper concludes that noisy interconnects can be tolerated with minimal threshold penalty.

Significance. If correct, the result is practically useful: it suggests that distributed lattice surgery can tolerate entanglement fidelities an order of magnitude worse than local gate fidelities without a serious threshold penalty, relaxing distillation requirements. The paper's strengths are the use of a standard MWPM decoder on a nontrivial spacetime geometry, a parameter-free effective noise model with no fitted parameters, explicit threshold extraction, and a clear asymptotic scaling explanation. The central O(d) vs O(d^2) argument is compelling and likely robust. However, because the quantitative thresholds are obtained from an approximate mapping from a circuit-level depolarizing model to independent per-cycle rates, the precise values and the hardware recommendation should be considered preliminary until validated.

major comments (3)
  1. [Appendix, Eqs. (17)-(25); Sec. III-B, Eqs. (12)-(15)] The effective rates are derived by counting marginal single-qubit X/Z error probabilities from two-qubit depolarizing events and then treating X and Z errors as independent per cycle. This discards hook-error correlations in which a single two-qubit fault produces both a data error and a same-round syndrome error. Near threshold at k=11, p_seam ~= 10 epsilon and q_seam ~= 18 epsilon, so these correlations are concentrated exactly where the seam noise is largest and could alter the observed 'modest' reduction. Please either validate the mapping against a full circuit-level simulation (e.g., Stim) of the distributed syndrome-extraction circuit for d=5,7,9,11, or explicitly restrict the claims to the phenomenological model.
  2. [Sec. III-B and final Appendix note] The same effective seam rates are applied to boundary qubits with lower-weight stabilizers, even though the logical failure criterion in Sec. III-C is the parity on four X-type boundaries. These boundary qubits directly determine the logical error measurement. The one-sentence acknowledgement at the end of the Appendix does not quantify the sensitivity. Please either model arch/edge qubits with distinct rates or provide a numerical sensitivity test showing that the threshold is unchanged when boundary rates are varied.
  3. [Sec. IV, first paragraph and Fig. 8] The paper calls epsilon_c 'the fault-tolerance threshold' but the simulations are for logical Z errors only, using X-type checks under a model that ignores X-Z correlations. The comparison to full circuit-level thresholds of the rotated surface code (Refs. [44],[45]) is therefore not apples-to-apples. Please clarify that this is a Z-error threshold under the approximate phenomenological model, not a full depolarizing circuit-level threshold.
minor comments (4)
  1. [References] Several DOI strings appear to be placeholders or malformed (e.g., Refs. [17], [20], [29], [37]: '10.1103/v9ln-c4v2', '10.1103/xqrn-wdw1', '10.1103/sk5y-25b1', '10.1103/ppng-vbqj'). Please verify and correct.
  2. [Fig. 9] The axis label contains 'uni00A0' artifacts (e.g., 'k/uni00A0(Bell...)'). Please fix the typesetting.
  3. [Sec. III-A, Eq. (9)] The requirement h2 = d is stated but not justified or referenced. A brief explanation of why d rounds of the merge stabilizers are needed for fault tolerance would help the reader.
  4. [General] No data/code availability statement is included. Given that the thresholds are simulation results, providing the MWPM graph construction and simulation code would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the central derivation is self-contained and thresholds are measured outputs.

full rationale

The paper's central claim—that distributed XX-merge thresholds degrade only mildly as Bell-pair noise scales from k=1 to k=11—is obtained by defining a phenomenological noise model, deriving effective bulk and seam error rates in Eqs. (12)-(15) from first-order depolarizing-error counting in the Appendix, and then measuring logical error rates and threshold crossings with an MWPM decoder. No fitted parameter is fed back into the model: k is a scanned input, the effective rates are analytical functions of the physical error rates, and the thresholds are simulation outputs. The self-citations [10,11,16,23,47] are contextual background on distributed quantum computing and scheduling; none is load-bearing for the noise mapping, the H-shaped geometry (from Ref. [38]), the scaling argument, or the reported threshold values. The Appendix's closing caveat that boundary qubits are approximated by the same seam rates is a modeling limitation, not a circular reduction. The O(d) vs O(d^2) bulk/seam scaling argument is independent of the authors' prior work and is supported by their own simulations, so the derivation stands on its stated assumptions.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The model is built from standard depolarizing-noise counting and known lattice-surgery fault-tolerance conditions; no new entities are introduced. The main hand-chosen elements are the uniform-noise relation, the Bell-pair scaling factor, and the boundary-qubit approximation, all acknowledged or plainly stated.

free parameters (2)
  • Bell-pair noise scaling factor k = scanned over {1,3,5,7,9,11}
    Chosen by hand to model entangled-link noise elevation; not fitted to data, but the threshold claims are parameterized by it.
  • Simulation geometry h1=h2=d, w=1 = h1=h2=d, bridge width w=1
    Protocol parameters selected by the authors; standard fault-tolerance choices, but they affect the exact threshold numbers.
assumptions (6)
  • domain assumption Two-qubit depolarizing noise model: each CNOT/Bell-pair operation is perfect followed by one of 15 nonidentity Pauli errors with probability ε/15 each.
    Standard circuit-level noise idealization; used in the Appendix to derive effective per-cycle rates.
  • domain assumption Bell-pair error equivalence classes and asymmetric propagation (X errors to the target, Z errors to the control) in the nonlocal CNOT.
    Borrowed from prior distributed-QEC analyses [15,48]; enters the seam error derivations.
  • domain assumption Independent X and Z errors per syndrome-extraction cycle on data and syndrome qubits.
    Phenomenological approximation that ignores correlations, hook errors, and temporal correlations; acknowledged by the authors but not validated.
  • ad hoc to paper Uniform local error rates ε_cx = ε_m = ε_idle = ε and ε_B = k ε.
    Convenient single-parameter noise model chosen by hand; not derived from a specific hardware platform.
  • standard math A merge duration of h2 = d rounds is sufficient for fault tolerance, and the H-shaped spacetime has four disconnected X-boundaries and two Z-boundaries.
    Standard lattice-surgery fault-tolerance condition from Ref. [38]; underlies the decoder success criterion.
  • ad hoc to paper Boundary qubits with lower-weight stabilizers can be assigned the same bulk/seam rates.
    Explicit approximation in the final note of the Appendix; unquantified effect on threshold estimates.

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Pith. "Pith review of Towards the Characterization of Logical Errors in Distributed Lattice Surgery." pith.science (2026). https://pith.science/paper/TUSIYCGX

@misc{pith2026260729186,
  author       = {Pith},
  title        = {Pith review of: Towards the Characterization of Logical Errors in Distributed Lattice Surgery},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TUSIYCGX}},
  note         = {Machine review of arXiv:2607.29186}
}
read the original abstract

Distributed quantum computing offers a scalable alternative to monolithic quantum processors by networking smaller quantum modules through shared entangled pairs. A central challenge in this setting is that inter-module quantum operations are typically noisier than intra-module local gates, which introduces additional noise into the system. In this work, we analyze distributed lattice surgery under heterogeneous noise conditions, focusing in particular on the merge operation as one of its fundamental subroutines. Specifically, we discuss the XX merge operation between two rotated surface-code patches hosted on two different quantum processors. We characterize logical errors in the resulting H-shaped spacetime diagram and estimate thresholds using a minimum-weight perfect matching (MWPM) decoder. We use a phenomenological noise model and derive distinct bulk and seam error rates to approximate a circuit-level noise model that includes contributions from local CNOT gates, noisy entangled pairs, idle errors, and readout errors. Our results provide practical insights into selecting the optimal surface-code distance, establishing target local-gate fidelities, and determining the tolerable entangled-pair fidelity required for logical operations in a distributed architecture.

Figures

Figures reproduced from arXiv: 2607.29186 by the authors.

Figure 2
Figure 2. Entanglement-assisted nonlocal CNOT gate. A shared Bell pair is [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Lattice surgery circuit for a logical CNOT gate. The control ( [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Spacetime diagram of the H-shaped geometry for the merge operation in lattice surgery. The horizontal and vertical axes represent the qubits and syndrome extraction rounds, respectively. Finally, at time 𝑡 = ℎ1 + ℎ2, the split operation occurs along the top seam, shown by the purple dashed line. The interface stabilizers are deactivated, and syndrome extraction is performed on the two independent patches for ℎ3 post… view at source ↗
Figures from the paper (6 more)
Figure 5
Figure 5. Figure 5: Ancilla mediated merge operation between two [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: Visualization of the bridge step joining two rotated surface-code patches during an [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: The 𝑋𝑋 merge operation contains four disconnected 𝑋-type boundaries and two 𝑍-type boundaries. In the figure, the red regions indicate the 𝑋-type boundaries, while the blue regions indicate the visible 𝑍-type boundary. The second 𝑍-type boundary is hidden by the perspe…
Figure 8
Figure 8. Figure 8: Logical error rate versus base physical error rate [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: Logical error threshold 𝜀𝑐 as a function of the Bell pair noise scaling factor 𝑘. Each point represents the mean threshold extracted from linear sign-change interpolation across four adjacent-distance crossing pairs (𝑑𝑖 , 𝑑𝑖+1 ) for 𝑑 ∈ {5, 7, 9, 11, 13}, with error ba…
Figure 10
Figure 10. Figure 10: Schematic of an 𝑋-stabilizer in a distributed architecture, where the two left qubits reside in one QPU and the two right qubits reside in another. The corner circles denote data qubits, the central square represents the ancilla qubit, and the connecting lines indicat…

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Works this paper leans on

50 extracted references · 8 canonical work pages

  1. [44]

    Compare the pair: Rotated versus unrotated surface codes at equal logical error rates,

    A. R. O’Rourke and S. Devitt, “Compare the pair: Rotated versus unrotated surface codes at equal logical error rates, ”Physical Review Research, vol. 7, no. 3, Jul. 2025. [Online]. Available: http://dx.doi.org/10.1103/PhysRevResearch.7.033074

    doi:10.1103/physrevresearch.7.033074 2025

  2. [45]

    Improved decoding of circuit noise and fragile boundaries of tailored surface codes,

    O. Higgott, T. C. Bohdanowicz, A. Kubica, S. T. Flammia, and E. T. Campbell, “Improved decoding of circuit noise and fragile boundaries of tailored surface codes, ”Physical Review X, vol. 13, no. 3, Jul. 2023. [Online]. Available: http://dx.doi.org/10.1103/PhysRevX.13.031007

    doi:10.1103/physrevx.13.031007 2023

  3. [1]

    Quantum computing in the nisq era and beyond,

    J. Preskill, “Quantum computing in the nisq era and beyond, ” Quantum, vol. 2, p. 79, Aug. 2018. [Online]. Available: http: //dx.doi.org/10.22331/q-2018-08-06-79

    doi:10.22331/q-2018-08-06-79 2018

  4. [2]

    Special session: Noisy intermediate-scale quantum (nisq) computers—how they work, how they fail, how to test them?

    S. Brandhofer, S. Devitt, T. Wellens, and I. Polian, “Special session: Noisy intermediate-scale quantum (nisq) computers—how they work, how they fail, how to test them?” in2021 IEEE 39th VLSI Test Symposium (VTS). IEEE, Apr. 2021, p. 1–10. [Online]. Available: http://dx.doi.org/10.1109/VTS50974.2021.9441047

    arXiv 2021

  5. [3]

    From nisq to isq,

    J. M. Arrazola and Xanadu, “From nisq to isq, ” https://pennylane.ai/ blog/2023/06/from-nisq-to-isq/, 2023, accessed: 2026-04-14

    2023

  6. [4]

    Quantum-centric supercomputing for physics research,

    V. R. Pascuzzi and A. Córcoles, “Quantum-centric supercomputing for physics research, ” 2024. [Online]. Available: https://arxiv.org/abs/2408. 11741

    2024

  7. [5]

    Beyond nisq: The megaquop machine,

    J. Preskill, “Beyond nisq: The megaquop machine, ”ACM Transactions on Quantum Computing, vol. 6, no. 3, p. 1–7, Apr. 2025. [Online]. Available: http://dx.doi.org/10.1145/3723153

    doi:10.1145/3723153 2025

  8. [6]

    Mind the gaps: The fraught road to quantum advantage,

    J. Eisert and J. Preskill, “Mind the gaps: The fraught road to quantum advantage, ” 2025. [Online]. Available: https://arxiv.org/abs/2510.19928

    arXiv 2025

Show all 50 references
  1. [7]

    Limitations in quantum computing from resource constraints,

    M. Fellous-Asiani, J. H. Chai, R. S. Whitney, A. Auffèves, and H. K. Ng, “Limitations in quantum computing from resource constraints, ”PRX Quantum, vol. 2, no. 4, Nov. 2021. [Online]. Available: http://dx.doi.org/10.1103/PRXQuantum.2.040335

    2021 doi

  2. [8]

    The complexity of nisq,

    S. Chen, J. Cotler, H.-Y. Huang, and J. Li, “The complexity of nisq, ” Nature Communications, vol. 14, no. 1, Sep. 2023. [Online]. Available: http://dx.doi.org/10.1038/s41467-023-41217-6

    2023 doi

  3. [9]

    Cuomo,Architectures and Circuits for Distributed Quantum Computing

    D. Cuomo,Architectures and Circuits for Distributed Quantum Computing. Springer Nature Switzerland, 2024. [Online]. Available: http://dx.doi.org/10.1007/978-3-031-73808-1

    2024 doi

  4. [10]

    Network operations scheduling for distributed quantum computing,

    N. K. Chandra, E. Kaur, and K. P. Seshadreesan, “Network operations scheduling for distributed quantum computing, ” in2024 IEEE 6th International Conference on Trust, Privacy and Security in Intelligent Systems, and Applications (TPS-ISA). IEEE, Oct. 2024, p. 506–515. [Online]...

    2024

  5. [11]

    Optimized quantum circuit partitioning across multiple quantum processors,

    E. Kaur, S. Pouryousef, H. Shapourian, J. Zhao, M. Kilzer, R. Kompella, and R. Nejabati, “Optimized quantum circuit partitioning across multiple quantum processors, ”IEEE Transactions on Quantum Engineering, vol. 6, p. 1–17, 2025. [Online]. Available: http: //dx.doi.org/10.110...

    2025

  6. [12]

    Distributed quantum computing across an optical network link,

    D. Main, P. Drmota, D. P. Nadlinger, E. M. Ainley, A. Agrawal, B. C. Nichol, R. Srinivas, G. Araneda, and D. M. Lucas, “Distributed quantum computing across an optical network link, ”Nature, vol. 638, no. 8050, p. 383–388, Feb. 2025. [Online]. Available: http://dx.doi.org/10.1...

    2025 doi

  7. [13]

    Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects,

    C. Monroe, R. Raussendorf, A. Ruthven, K. R. Brown, P. Maunz, L.-M. Duan, and J. Kim, “Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects, ” Physical Review A, vol. 89, no. 2, Feb. 2014. [Online]. Available: http://dx.doi.org/10.110...

    2014 doi

  8. [14]

    Topological quantum computing with a very noisy network and local error rates approaching one percent,

    N. H. Nickerson, Y. Li, and S. C. Benjamin, “Topological quantum computing with a very noisy network and local error rates approaching one percent, ”Nature Communications, vol. 4, no. 1, Apr. 2013. [Online]. Available: http://dx.doi.org/10.1038/ncomms2773

    2013 doi

  9. [15]

    Fault- tolerant connection of error-corrected qubits with noisy links,

    J. Ramette, J. Sinclair, N. P. Breuckmann, and V. Vuletić, “Fault- tolerant connection of error-corrected qubits with noisy links, ”npj Quantum Information, vol. 10, no. 1, Jun. 2024. [Online]. Available: http://dx.doi.org/10.1038/s41534-024-00855-4

    2024 doi

  10. [16]

    Multiplexed bilayered realization of fault-tolerant quantum computation over optically networked trapped-ion modules,

    N. K. Chandra, S. Guha, and K. P. Seshadreesan, “Multiplexed bilayered realization of fault-tolerant quantum computation over optically networked trapped-ion modules, ”IEEE Transactions on Quantum Engineering, vol. 7, p. 1–18, 2026. [Online]. Available: http://dx.doi.org/10.11...

    2026

  11. [17]

    Network requirements for distributed quantum computation,

    H. Jacinto, É. Gouzien, and N. Sangouard, “Network requirements for distributed quantum computation, ”Physical Review Research, vol. 8, no. 1, Feb. 2026. [Online]. Available: http://dx.doi.org/10.1103/v9ln-c4v2

    2026 doi

  12. [18]

    Surface codes: Towards practical large-scale quantum computation,

    A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, “Surface codes: Towards practical large-scale quantum computation, ” Physical Review A, vol. 86, no. 3, Sep. 2012. [Online]. Available: http://dx.doi.org/10.1103/PhysRevA.86.032324

    2012 doi

  13. [19]

    Towards fault-tolerant distributed quantum computation (ft-dqc): Taxonomy, recent progress, and challenges,

    H. T. Larasati and B.-S. Choi, “Towards fault-tolerant distributed quantum computation (ft-dqc): Taxonomy, recent progress, and challenges, ”ICT Express, vol. 11, no. 3, p. 417–435, Jun. 2025. [Online]. Available: http://dx.doi.org/10.1016/j.icte.2025.03.007

    2025 doi

  14. [20]

    Optimized noise-resilient surface code teleportation interfaces,

    M. A. Shalby, R. Wang, D. Sedov, and L. P. Pryadko, “Optimized noise-resilient surface code teleportation interfaces, ”Physical Review A, vol. 112, no. 2, Aug. 2025. [Online]. Available: http://dx.doi.org/10.1103/ xqrn-wdw1

    2025

  15. [21]

    Quantum error correction for quantum memories,

    B. M. Terhal, “Quantum error correction for quantum memories, ” Reviews of Modern Physics, vol. 87, no. 2, p. 307–346, Apr. 2015. [Online]. Available: http://dx.doi.org/10.1103/RevModPhys.87.307

    2015 doi

  16. [22]

    Early fault- tolerant quantum computing,

    A. Katabarwa, K. Gratsea, A. Caesura, and P. D. Johnson, “Early fault- tolerant quantum computing, ”PRX Quantum, vol. 5, no. 2, Jun. 2024. [Online]. Available: http://dx.doi.org/10.1103/PRXQuantum.5.020101

    2024 doi

  17. [23]

    Distributed realization of color codes for quantum error correction,

    N. K. Chandra, D. Tipper, R. Nejabati, E. Kaur, and K. P. Seshadreesan, “Distributed realization of color codes for quantum error correction, ” in2025 IEEE International Conference on Quantum Computing and Engineering (QCE). IEEE, Aug. 2025, p. 2482–2492. [Online]. Available: ...

    2025

  18. [24]

    A game of surface codes: Large-scale quantum computing with lattice surgery,

    D. Litinski, “A game of surface codes: Large-scale quantum computing with lattice surgery, ”Quantum, vol. 3, p. 128, Mar. 2019. [Online]. Available: http://dx.doi.org/10.22331/q-2019-03-05-128

    2019 doi

  19. [25]

    Dependency-aware compilation for surface code quantum architectures,

    A. Molavi, A. Xu, S. Tannu, and A. Albarghouthi, “Dependency-aware compilation for surface code quantum architectures, ”Proceedings of the ACM on Programming Languages, vol. 9, no. OOPSLA1, p. 57–84, Apr

  20. [26]

    Transversal logical clifford gates on the rotated surface code with reconfigurable neutral atom arrays,

    Z.-H. Chen, M.-C. Chen, C.-Y. Lu, and J.-W. Pan, “Transversal logical clifford gates on the rotated surface code with reconfigurable neutral atom arrays, ”Phys. Rev. Lett., pp. –, Jan 2026. [Online]. Available: https://link.aps.org/doi/10.1103/m7tq-9v3g

    2026 doi

  21. [27]

    Surface code quantum computing by lattice surgery,

    D. Horsman, A. G. Fowler, S. Devitt, and R. V. Meter, “Surface code quantum computing by lattice surgery, ”New Journal of Physics, vol. 14, no. 12, p. 123011, Dec. 2012. [Online]. Available: http://dx.doi.org/10.1088/1367-2630/14/12/123011

    2012 doi

  22. [28]

    Code deformation and lattice surgery are gauge fixing,

    C. Vuillot, L. Lao, B. Criger, C. García Almudéver, K. Bertels, and B. M. Terhal, “Code deformation and lattice surgery are gauge fixing, ” New Journal of Physics, vol. 21, no. 3, p. 033028, Mar. 2019. [Online]. Available: http://dx.doi.org/10.1088/1367-2630/ab0199

    2019 doi

  23. [29]

    Decoding across transversal clifford gates in the surface code,

    M. Serra-Peralta, M. H. Shaw, and B. M. Terhal, “Decoding across transversal clifford gates in the surface code, ”PRX Quantum, vol. 7, no. 1, Feb. 2026. [Online]. Available: http://dx.doi.org/10.1103/sk5y-25b1

    2026 doi

  24. [30]

    Restrictions on transversal encoded quantum gate sets,

    B. Eastin and E. Knill, “Restrictions on transversal encoded quantum gate sets, ”Physical Review Letters, vol. 102, no. 11, Mar. 2009. [Online]. Available: http://dx.doi.org/10.1103/PhysRevLett.102.110502

    2009 doi

  25. [31]

    Entangling logical qubits with lattice surgery,

    A. Erhard, H. Poulsen Nautrup, M. Meth, L. Postler, R. Stricker, M. Stadler, V. Negnevitsky, M. Ringbauer, P. Schindler, H. J. Briegel, R. Blatt, N. Friis, and T. Monz, “Entangling logical qubits with lattice surgery, ”Nature, vol. 589, no. 7841, p. 220–224, Jan. 2021. [Online...

    2021 doi

  26. [32]

    Lattice surgery-based surface code architecture using remote logical cnot operation,

    J. Lee, Y. Kang, J. Ha, and J. Heo, “Lattice surgery-based surface code architecture using remote logical cnot operation, ”Quantum Information Processing, vol. 21, no. 6, Jun. 2022. [Online]. Available: http://dx.doi.org/10.1007/s11128-022-03556-z

    2022 doi

  27. [33]

    Co-designed superconducting architecture for lattice surgery of surface codes with quantum interface routing card,

    C. Guinn, S. Stein, E. Tureci, G. Avis, C. Liu, S. Krastanov, A. A. Houck, and A. Li, “Co-designed superconducting architecture for lattice surgery of surface codes with quantum interface routing card, ” 2023. [Online]. Available: https://arxiv.org/abs/2312.01246

    2023 arXiv

  28. [34]

    Lattice surgery aware resource analysis for the mapping and scheduling of quantum circuits for scalable modular architectures,

    B. Keskin, C. Afradi, S. Lovis, M. Palesi, P. Escofet, C. G. Almudever, and E. Charbon, “Lattice surgery aware resource analysis for the mapping and scheduling of quantum circuits for scalable modular architectures, ” 2025. [Online]. Available: https://arxiv.org/abs/2511.21885

    2025

  29. [35]

    Remote entanglement in lattice surgery: To distill, or not to distill,

    S. Liu, J. Stack, K. Sun, R. Van Beeumen, I. Monga, K. Klymko, K. R. Brown, and E. Saglamyurek, “Remote entanglement in lattice surgery: To distill, or not to distill, ” 2026. [Online]. Available: https://arxiv.org/abs/2603.06513

    2026 arXiv

  30. [36]

    Entanglement boosting: Low-volume logical bell pair preparation for distributed fault-tolerant quantum computation,

    S. Sunami, Y. Hirano, T. Hinokuma, and H. Yamasaki, “Entanglement boosting: Low-volume logical bell pair preparation for distributed fault-tolerant quantum computation, ” 2025. [Online]. Available: https://arxiv.org/abs/2511.10729

    2025 arXiv

  31. [37]

    Lattice surgery-based logical state teleportation via noisy links,

    Á’. Márton, L. Colmenarez, L. Bödeker, and M. Müller, “Lattice surgery-based logical state teleportation via noisy links, ”Physical Review Research, vol. 7, no. 3, Sep. 2025. [Online]. Available: http://dx.doi.org/10.1103/ppng-vbqj

    2025 doi

  32. [38]

    Characterization of errors in a cnot between surface code patches,

    B. Domokos, Á. Márton, and J. K. Asbóth, “Characterization of errors in a cnot between surface code patches, ”Quantum, vol. 8, p. 1577, Dec

  33. [39]

    Low-distance surface codes under realistic quantum noise,

    Y. Tomita and K. M. Svore, “Low-distance surface codes under realistic quantum noise, ”Physical Review A, vol. 90, no. 6, Dec. 2014. [Online]. Available: http://dx.doi.org/10.1103/PhysRevA.90.062320

    2014 doi

  34. [40]

    Topological quantum memory,

    E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, “Topological quantum memory, ”Journal of Mathematical Physics, vol. 43, no. 9, p. 4452–4505, Sep. 2002. [Online]. Available: http://dx.doi.org/10.1063/1.1499754

    2002 doi

  35. [41]

    Pymatching: A python package for decoding quantum codes with minimum-weight perfect matching,

    O. Higgott, “Pymatching: A python package for decoding quantum codes with minimum-weight perfect matching, ”ACM Transactions on Quantum Computing, vol. 3, no. 3, p. 1–16, Jun. 2022. [Online]. Available: http://dx.doi.org/10.1145/3505637

    2022 doi

  36. [42]

    Introducing lattice surgery,

    K. Kottmann, “Introducing lattice surgery, ” https://pennylane.ai/qml/ demos/tutorial_lattice_surgery, 12 2025, accessed: 2026-04-14

    2025

  37. [43]

    Proof of finite surface code threshold for matching,

    A. G. Fowler, “Proof of finite surface code threshold for matching, ” Physical Review Letters, vol. 109, no. 18, Nov. 2012. [Online]. Available: http://dx.doi.org/10.1103/PhysRevLett.109.180502

    2012 doi

  38. [46]

    Confinement-higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory,

    C. Wang, J. Harrington, and J. Preskill, “Confinement-higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory, ”Annals of Physics, vol. 303, no. 1, p. 31–58, Jan. 2003. [Online]. Available: http://dx.doi.org/10.1016/s0003-4916(02)00019-2

    2003 doi

  39. [47]

    Benchmarking quantum data center architectures: A performance and scalability perspective,

    S. Pouryousef, E. Kaur, H. Shapourian, D. Towsley, R. Kompella, and R. Nejabati, “Benchmarking quantum data center architectures: A performance and scalability perspective, ” 2026. [Online]. Available: https://arxiv.org/abs/2601.01353

    2026

  40. [48]

    Fault-tolerant optical interconnects for neutral-atom arrays,

    J. Sinclair, J. Ramette, B. Grinkemeyer, D. Bluvstein, M. D. Lukin, and V. Vuletić, “Fault-tolerant optical interconnects for neutral-atom arrays, ” Physical Review Research, vol. 7, no. 1, Mar. 2025. [Online]. Available: http://dx.doi.org/10.1103/PhysRevResearch.7.013313

    2025 doi

  41. [2024]

    Available: http://dx.doi.org/10.22331/q-2024-12-27-1577

    [Online]. Available: http://dx.doi.org/10.22331/q-2024-12-27-1577

    2024 doi

  42. [2025]

    Available: http://dx.doi.org/10.1145/3720416

    [Online]. Available: http://dx.doi.org/10.1145/3720416

    doi

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.