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A workflow-level runtime model splits hybrid quantum-classical jobs into compute and communication, and shows most current applications are compute-bound.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

T0 review · deepseek-v4-flash

2026-08-01 23:23 UTC pith:4A7T5V3H

load-bearing objection A useful framework for QPU-HPC integration decisions whose headline co-location claim is broader than the evidence supports. the 3 major comments →

arxiv 2607.15426 v1 pith:4A7T5V3H submitted 2026-07-16 quant-ph

Performance Model for Hybrid Quantum-Classical Workflows

classification quant-ph
keywords hybrid quantum-classical workflowscommunication-to-computation ratioreal-time feasibility constraintquantum error correctionco-locationreaction timefault-tolerant quantum computationruntime performance model
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper introduces a common way to reason about hybrid quantum-classical workflows by splitting each repeated quantum-classical exchange into three wall-clock pieces: quantum compute, classical compute, and communication. It then defines a single unitless diagnostic—the communication-to-computation ratio Rcc—that tells whether a workflow is communication-bound or compute-bound, and a separate feasibility constraint that tells whether real-time classical processing can keep up with the physical quantum device at all. Applied to representative workflows, the model argues that today's compute-intensive applications (subspace diagonalization, generative quantum eigensolvers) are deeply compute-bound and gain almost nothing from co-locating a QPU with an HPC facility, while latency-sensitive single-shot workflows need tight integration and fault-tolerant error correction requires it outright. The point of the framework is to turn integration decisions—remote access, co-location, or on-node co-design—into a measurable quantity rather than a matter of opinion.

Core claim

On the paper's terms: every hybrid workflow can be modeled as repeated compute cycles costing T_Q + T_C + T_comm. The application-level diagnostic is Rcc = T_comm/(T_Q + T_C): Rcc >> 1 means communication-bound; Rcc << 1 means compute-bound. The real-time diagnostic is whether classical step time plus communication step time fits within the physical qubit timescale; if not, execution fails outright. Surveying representative workflows, the paper finds none are simultaneously compute-intensive and highly communication-bound today, so heavy compute absorbs communication overhead, while real-time error correction remains strictly latency-limited; once the real-time constraint is met, reaction ti

What carries the argument

The central object is the compute-cycle decomposition and its two derived diagnostics. Each compute cycle—the smallest repeated unit containing a blocking classical-quantum exchange—has time T_cycle = T_C + T_Q + T_comm, with T_comm = F(L + V/B) for exchange frequency F, latency L, volume V, and bandwidth B. The application-level diagnostic is Rcc = T_comm/(T_Q + T_C), which plays a role analogous to arithmetic intensity in classical performance analysis. The real-time-level diagnostic is the feasibility inequality T_C,step + T_comm,step <= tau_phys, where tau_phys is a device-imposed timescale such as qubit coherence time; failure means failure of execution, not mere slowdown.

Load-bearing premise

The paper's headline implication—that co-location offers limited performance advantage today—rests on the assumption that the workflow families and order-of-magnitude parameters it surveys adequately represent the current landscape, and in particular that no workflow is simultaneously compute-intensive and highly communication-bound; the paper says this absence is 'almost by construction' rather than proven.

What would settle it

Demonstrate one real hybrid workload whose per-cycle classical compute is hours-scale or large (say T_C + T_Q > 1000 s) yet whose algorithm forces a blocking exchange frequency F >= 10^4 per cycle at current remote latency (L ~ 100 ms). Such a workflow would have T_comm ~ 1000 s and Rcc ~ 1, directly contradicting the paper's claim that compute-intensive workflows are not communication-bound; alternatively, a measurement showing that a representative SQD or GQE instance already achieves Rcc >= 0.1 under the parameters the paper assigns would falsify the numerical claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • SQD and GQE, the representative HPC-scale workflows, have Rcc between 10^-4 and 10^-1 even at remote latency, so moving them into co-located or tightly integrated facilities will not reduce runtime; their bottleneck is quantum shot budget and classical diagonalization, not communication.
  • QE-MCMC, with one round-trip per accept/reject step and tiny per-step compute, has Rcc around 10^3 at remote latency, so it needs low-latency integration—but not HPC-class classical resources.
  • Under fault tolerance, real-time decoder reaction time becomes a continuous performance variable: doubling it increases the estimated runtime to factor a 2048-bit RSA integer by 60-100%, because slower decoding means more idle error accumulation and higher code distances.
  • Hardware evolution that shrinks quantum compute time—faster throughput or parallel shot distribution across multiple QPUs—raises Rcc for workflows like GQE and can move them into a communication-bound regime, so co-location decisions are not permanent.
  • Dynamic circuits are application-level when executed on fault-tolerant logical qubits but real-time level when executed on physical qubits: the same feed-forward can be performance-neutral or feasibility-critical depending on where it is implemented.

Where Pith is reading between the lines

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

  • The model's basic structure (T_C, T_Q, T_comm plus Rcc) is general enough that a workflow library analogous to roofline charts could be built for parameterized circuit families; the paper sketches one classification table but does not exhaust the space.
  • A testable consequence the paper leaves implicit: if a workflow exists with per-cycle classical compute over ~1 second and exchange frequency above ~1000 per cycle, Rcc would cross unity at current latency, and co-location would become material. The absence of such a workflow is presented as 'almost by construction' rather than demonstrated.
  • Quantum memory, which the paper discusses qualitatively, would restructure exactly the metrics the model tracks—reducing C_Q per cycle by amortizing state preparation and lowering F by eliminating re-initialization round trips—so the same formalism could quantify the value of quantum memory before it is built.
  • The model suggests a procurement rule that the community can test: for a candidate hybrid application, compute Rcc under remote and co-located parameters before choosing an integration tier; applications with Rcc below ~0.01 are safe to run remotely, while error-correction workloads must be evaluated by the feasibility inequality instead.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper introduces a runtime model for hybrid quantum-classical workflows that decomposes each repeated compute cycle into classical compute time T_C = C_C/τ_C, quantum compute time T_Q = C_Q/τ_Q, and communication time T_comm = F(L+V/B). It defines the communication-to-computation ratio Rcc = T_comm/(T_Q+T_C) as an application-level diagnostic, and a real-time feasibility constraint T_C,step + T_comm,step ≤ τ_phys. The model is applied to three application-level workflows (SQD, GQE, QE-MCMC) and to real-time level tasks (QEC, Pauli-based computation, Shor factoring). The paper's central claim is that, among the analyzed application workflows, none is simultaneously compute-intensive and highly communication-bound, so co-location of QPUs with HPC infrastructure offers limited performance advantage for most application-level workloads today, while tight integration remains essential for real-time tasks.

Significance. The model provides a useful shared vocabulary for reasoning about hybrid integration, and it is definitional rather than fitted: no constants are calibrated to data, and the SQD estimate in Section 3.1 reproduces the reported runtime within order-of-magnitude. The Rcc diagnostic cleanly separates application-level performance from real-time feasibility, and the scenario analysis for GQE (Table 5) gives concrete, falsifiable crossover conditions. The resource estimates for reaction-time effects on Shor factoring (Table 8) are based on state-of-the-art compilation and illustrate a genuine performance cascade. If the broad Section 4 conclusion is supported, the paper would be valuable for procurement and integration decisions. However, the generalization from three representative workflows to 'most application-level workloads' is an induction over an unproven sample; the manuscript itself lists high-Rcc families in Table B5 without application-level analysis.

major comments (3)
  1. [Section 4, Eq. (5)] The transition from 'across the application-level workflows analyzed in this work' to 'most application-level workloads in the current landscape' is not justified by the analysis. Eq. (5) imposes no structural bound preventing simultaneous large T_C and large F: a workflow with T_C ~ 10^3 s and F ~ 10^5 blocking exchanges per cycle would have Rcc > 1 even with negligible data volume. The statement that the absence is 'almost by construction' is therefore an empirical regularity, not a consequence of the model. Table B5 itself lists Quantum Metropolis Sampling and LAQCC as high-Rcc families, but no application-level profile is provided for them. Please either supply a concrete scaling argument bounding F relative to T_C, analyze representatives of these families, or confine the headline claim to the workflows actually profiled.
  2. [Section 3.1, QE-MCMC, Table 6] There is a factor-of-ten arithmetic inconsistency. With T_Q ~ 10^-5 s, T_C negligible, F = 1, and the latency tiers in Table 3 (L = 100 ms, 10 µs, 100 ns; V/B negligible), Eq. (5) gives Rcc ≈ 10^4, 1, and 10^-2 for remote, co-located, and on-chip tiers, respectively. The text and Table 6 report ~10^3, ~10^-1, and ~10^-3. The stated values would follow from per-cycle quantum time ~10^-4 s, which is consistent with the 2–48 layer range at τ_Q ~ 10^5 layers/s. Please reconcile the reported T_Q value with the Rcc estimates.
  3. [Section 2, Eq. (5); Section 4] Because F is acknowledged to be a workflow-implementation metric, the conclusion that workflows 'fall into two categories' is sensitive to implementation choices. For GQE, per-term measurement with F = 150 already gives Rcc ~ 10^-1 at remote parameters, within an order of magnitude of the communication-bound threshold, and faster QPU throughput or multi-QPU shot parallelism could push it higher. The paper would be strengthened by an explicit statement of which implementation version each Rcc value refers to, and by a sensitivity scan over (T_Q+T_C, F) showing how robust the compute-bound classification is across plausible parameter ranges.
minor comments (4)
  1. [Section 3.1, SQD, Eq. (7)] Equation (7) estimates T_Q ~ 10^3 s using d ~ 10^2, s ~ 10^6, τ_Q ~ 10^5, while the subsequent reconstruction from the experimental parameters gives T_Q ≈ 2400 s. Both are order-of-magnitude consistent, but the discrepancy between the idealized d·s model and the reported shot count/circuit-layer count should be clarified in a footnote.
  2. [Section 2, Eq. (6); Appendix C.4, Eq. (C1)] The main-text feasibility condition T_C,step + T_comm,step ≤ τ_phys omits the quantum step time T_Q,step, while Eq. (C1) in the SQSP-MaF analysis explicitly includes it. Please clarify whether T_Q,step is intended to be absorbed into τ_phys or should be added to the left-hand side in the main-text statement.
  3. [Table A3] The description of Rcc score 2 as 'Latency has minor impact (<10% runtime)' is inconsistent with the definition Rcc = T_comm/(T_Q+T_C): the runtime overhead fraction is Rcc/(1+Rcc), so Rcc = 0.1 gives ~9% overhead, but Rcc = 0.01 gives ~1%. The score boundaries should be translated to overhead percentages consistently.
  4. [Table B5 / C.4] The radar chart in Figure A1 and Table A4 give SQSP-MaF an application-level Rcc of 4, while the text notes that the binding constraint is at the real-time level. The caption should state more explicitly that the discrete Rcc score refers only to the idealized application-level regime and does not capture the feasibility constraint.

Circularity Check

0 steps flagged

No significant circularity: the runtime model is a set of explicit definitions, the workflow metrics come from independent experimental reports, and the Section 4 generalization is an acknowledged inductive claim rather than a derived result.

full rationale

The paper's derivation chain is transparent and definitional rather than circular. Equations (1)-(6) explicitly define T_cycle = T_C + T_Q + T_comm, R_cc = T_comm/(T_Q + T_C), and the real-time feasibility constraint T_C,step + T_comm,step <= tau_phys; these are named definitions, not hidden identifications. The R_cc values in Tables 3, 5, and 6 are computed from reported experimental inputs (e.g., SQD from [36], GQE from [9], QE-MCMC from [33]) using stated order-of-magnitude parameters, with no constants fitted to force the conclusions. Table 5 is explicitly an 'illustrative example of such an analysis' under stated hardware-evolution assumptions, not a fitted prediction labeled as discovery. The central Section 4 claim that no analyzed workflow is simultaneously compute-intensive and communication-bound is a generalization over a non-exhaustive sample; the paper itself flags the limitation with 'almost by construction' and by calling Table B5 a 'non-exhaustive classification.' That is an empirical-induction / correctness-risk issue, not a circular reduction. The model also transparently adapts the classical communication-to-computation ratio [34] and roofline ideas [25] to the hybrid setting, acknowledging the antecedents rather than renaming them as a first-principles derivation. The QEC and reaction-time content rests on external references [50,51,52]; the few self-citations (e.g., [8]) are not load-bearing for the paper's central claims. No step in the derivation reduces by construction to its own inputs, so the circularity score is 0.

Axiom & Free-Parameter Ledger

10 free parameters · 7 axioms · 0 invented entities

The central claims rest on a small set of domain assumptions and hand-chosen order-of-magnitude parameters; no constants are fitted to data and no new physical entities are postulated. The model is a definitional framework, so the main risk is not circularity but representativeness and parameter uncertainty.

free parameters (10)
  • tau_Q (quantum throughput) = 1e5 layers/s (superconducting); 1e3-1e7 across modalities (Table B6)
    Chosen by hand from reported hardware ranges; enters Eq. 3 to convert C_Q to T_Q and directly sets Rcc.
  • s (shot budget) = 1e6 (SQD/GQE), 1e8 (utility-scale GQE)
    Taken from reported experiments/resource analyses; dominates C_Q ~ d*s and therefore T_Q and Rcc.
  • d (logical circuit depth) = ~1e2 (SQD/utility GQE), ~10 (small GQE)
    Order-of-magnitude depth estimates used to compute C_Q and T_Q.
  • L (round-trip latency tiers) = 100 ms / 10 us / 100 ns (remote/co-located/tight)
    Representative latency values for integration tiers; controls T_comm and Rcc.
  • B (bandwidth tiers) = 1 Gbps / 100 Gbps / 500 Gbps
    Representative bandwidth values for integration tiers; enters T_comm = F(L + V/B).
  • F (communication frequency) = 1 (batched) to 150 (per-term GQE)
    Workflow-implementation choice that changes Rcc by orders of magnitude; the paper treats it as tunable via batching.
  • V (data volume per exchange) = 100 MB (SQD), ~600 kB (GQE batched), ~10 B (QE-MCMC)
    Order-of-magnitude payload estimates from reported experiments and algorithm structure.
  • tau_phys (physical timescale for real-time level) = 10-100 us (superconducting), 1-10 s (ion)
    Coherence/feed-forward deadline in Eq. 6; determines real-time feasibility.
  • Reaction time tau_r = 10 us / 20 us scenarios
    Chosen for the factoring resource estimates in Table 8; demonstrates reaction-time sensitivity.
  • P (number of QPUs in future scenarios) = 1, 100, 1000
    Scenario inputs in Table 5 for shot-level parallelism; not fitted, but the projected Rcc values are direct functions of these assumptions.
axioms (7)
  • domain assumption T_cycle = T_C + T_Q + T_comm (Eq. 1), with T_C = C_C/tau_C, T_Q = C_Q/tau_Q, T_comm = F(L+V/B)
    The entire framework rests on separability of quantum compute, classical compute, and communication; if any overlap (e.g., absorbing decoding into T_Q) is chosen differently, the decomposition changes.
  • domain assumption Application-level analysis is valid whenever correctness does not require classical processing within device-imposed coherence times
    Used in Section 2 to assign SQD/GQE/QE-MCMC to application level and QEC/dynamic circuits without fault tolerance to real-time level.
  • domain assumption Real-time feasibility requires T_C,step + T_comm,step <= tau_phys (Eq. 6)
    Standard real-time scheduling condition borrowed from [14]; the paper restates it for hybrid workflows and treats violation as correctness failure.
  • domain assumption C_Q is proportional to d*s and tau_Q is measured in CLOPS
    Used to express T_Q in Eq. 7; the paper notes more refined models are possible but does not use them centrally.
  • ad hoc to paper The workflow families in Table B5 and their representative members (SQD, GQE, QE-MCMC) are representative of the space of hybrid workflows
    The generalization from three examples to 'most application-level workloads' in Section 4 depends on this classification; no proof or exhaustive survey is given.
  • domain assumption Reported or estimated experimental values from [36], [9], [33], [42] are valid inputs
    The order-of-magnitude runtimes and shot budgets are taken from cited prior experiments and resource analyses without independent re-verification.
  • domain assumption Latency/bandwidth values for integration tiers are representative of current real systems
    The Rcc conclusions depend on these tier values (Table 3 and text); they are presented as illustrative rather than measured for a specific system.

pith-pipeline@v1.3.0-alltime-deepseek · 23291 in / 15273 out tokens · 152964 ms · 2026-08-01T23:23:52.596893+00:00 · methodology

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read the original abstract

Hybrid quantum-classical workflows are expected to underpin practical quantum computing applications, yet the quantum and HPC communities lack a shared framework for reasoning about where and when their integration requirements matter most. Such a framework must separate two distinct levels of analysis: the application level, where communication overhead affects runtime performance, and the real-time level, where it determines feasibility. To address this, we introduce a runtime model that decomposes workflow execution into quantum compute, classical compute, and communication costs. At the application level, a communication-to-computation ratio from this decomposition quantifies whether a workflow is communication-bound or compute-bound; at the real-time level, a feasibility constraint determines whether timing requirements can be met at all, with the reaction time setting the logical clock speed of fault-tolerant computation once they are. Application of this model to representative workflows demonstrates that co-location of quantum processors with HPC infrastructure offers negligible performance benefit for compute-intensive applications today, while tight integration remains crucial for real-time tasks such as quantum error correction needed for large scale quantum computations. However, we discuss how even at the application level these assessments may shift with hardware evolution, illustrating how the model can identify specific crossover conditions, and how, under fault tolerance, the reaction time can set application-level performance.

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Reference graph

Works this paper leans on

83 extracted references · 5 canonical work pages · cited by 1 Pith paper

  1. [1]

    W., Siegel, A

    Draeger, E. W., Siegel, A. & Gottlieb, S. The scientific impact of the exascale computing project.Computing in Science and Engi- neering26(2) (2024). URL https://www. osti.gov/biblio/2476896. https://doi.org/10. 1109/mcse.2024.3437608

  2. [2]

    E.et al.Aurora: Archi- tecting argonne’s first exascale supercom- puter for accelerated scientific discovery (2025)

    Allcock, W. E.et al.Aurora: Archi- tecting argonne’s first exascale supercom- puter for accelerated scientific discovery (2025). URL https://arxiv.org/abs/2509. 08207. 2509.08207

  3. [3]

    D.et al.GPU computing.Pro- ceedings of the IEEE96(5), 879–899 (2008)

    Owens, J. D.et al.GPU computing.Pro- ceedings of the IEEE96(5), 879–899 (2008)

  4. [4]

    & Skadron, K

    Nickolls, J., Buck, I., Garland, M. & Skadron, K. Scalable parallel programming with CUDA.Queue6(2), 40–53 (2008) 13

  5. [5]

    & Vetter, J

    Mittal, S. & Vetter, J. S. A survey of CPU- GPU heterogeneous computing techniques. ACM Computing Surveys (CSUR)47(4), 1–35 (2015)

  6. [6]

    URL https://arxiv

    Sommers, D.et al.Open-source highly paral- lel electromagnetic simulations for supercon- ducting circuits (2025). URL https://arxiv. org/abs/2511.01220. 2511.01220

  7. [7]

    T., Krishnan, P., Krishnaswamy, D., Usman, M

    Nguyen, H. T., Krishnan, P., Krishnaswamy, D., Usman, M. & Buyya, R. Quantum cloud computing: A review, open problems, and future directions (2024). URL https://arxiv. org/abs/2404.11420. 2404.11420

  8. [8]

    H., Patti, T

    Alexeev, Y., Farag, M. H., Patti, T. L., Wolf, M. E.et al.Artificial intelligence for quantum computing.Nature Communications(2025). https://doi.org/10.1038/s41467-025-65836-3

  9. [9]

    URL https://doi.org/ 10.48550/arXiv.2401.09253

    Nakajiet al.The generative quantum eigen- solver (gqe) and its application for ground state search (2024). URL https://doi.org/ 10.48550/arXiv.2401.09253. quant-ph/2401. 09253

  10. [10]

    & Kadowaki, T

    Minami, S., Nakaji, K., Suzuki, Y., Aspuru- Guzik, A. & Kadowaki, T. Generative quan- tum combinatorial optimization by means of a novel conditional generative quantum eigensolver.arXiv preprint arXiv:2501.16986 (2025)

  11. [11]

    URL https://arxiv.org/abs/2506

    Zhao, L.et al.Quantum-classical auxiliary field quantum monte carlo with matchgate shadows on trapped ion quantum comput- ers (2025). URL https://arxiv.org/abs/2506. 22408. 2506.22408

  12. [12]

    Future Generation Computer Systems 174, 107980 (2026)

    Shehata, A.et al.Bridging paradigms: Designing for hpc-quantum convergence. Future Generation Computer Systems 174, 107980 (2026). URL https://www. sciencedirect.com/science/article/pii/ S0167739X25002754. https://doi.org/https: //doi.org/10.1016/j.future.2025.107980

  13. [13]

    URL https://arxiv.org/abs/2603

    Seelam, S.et al.Reference architec- ture of a quantum-centric supercomputer (2026). URL https://arxiv.org/abs/2603. 10970. 2603.10970

  14. [14]

    Stankovic, J. A. Misconceptions about real- time computing: A serious problem for next- generation systems.Computer21(10), 10–19 (1988). https://doi.org/10.1109/2.7053

  15. [15]

    URL https://arxiv.org/abs/2508

    Honda, D.et al.Advantages of co- locating quantum-hpc platforms: A sur- vey for near-future industrial applications (2025). URL https://arxiv.org/abs/2508. 04171. 2508.04171

  16. [16]

    A., Khazraee, M., Agostini, E.et al.Platform architecture for tight coupling of high-performance com- puting with quantum processors.arXiv preprint(2025)

    Caldwell, S. A., Khazraee, M., Agostini, E.et al.Platform architecture for tight coupling of high-performance com- puting with quantum processors.arXiv preprint(2025). https://doi.org/10.48550/ arXiv.2510.25213, arXiv:2510.25213 [quant- ph]

  17. [17]

    URL https: //arxiv.org/abs/2411.10406

    Mohseni, M.et al.How to build a quan- tum supercomputer: Scaling from hundreds to millions of qubits (2025). URL https: //arxiv.org/abs/2411.10406. 2411.10406

  18. [18]

    & Jattana, M

    D¨ obler, P. & Jattana, M. S. A survey on integrating quantum computers into high performance computing systems (2025). URL https://arxiv.org/abs/2507.03540. 2507. 03540

  19. [19]

    https://doi.org/10.1016/ j.future.2024.06.058

    Beck, T.et al.Integrating quantum com- puting resources into scientific hpc ecosys- tems.Future Generation Computer Systems 161, 11–25 (2024). https://doi.org/10.1016/ j.future.2024.06.058

  20. [20]

    Rallis, K.et al.Hardware-level interfaces for hybrid quantum-classical computing systems 1–6 (2025)

  21. [21]

    URL https://arxiv.org/abs/2506.10052

    Sitdikov, I.et al.Quantum resources in resource management systems.arXiv preprint arXiv:2506.10052(2025). URL https://arxiv.org/abs/2506.10052. https:// doi.org/10.48550/arXiv.2506.10052

  22. [22]

    URL http://arxiv.org/abs/ 2512.19653

    Zimbor´ as, Z.et al.The EU quantum flag- ship’s key performance indicators for quan- tum computing. URL http://arxiv.org/abs/ 2512.19653. 2512.19653 14

  23. [23]

    URL https://arxiv.org/abs/ 2511.10633

    Khalid, A.et al.Impacts of decoder latency on utility-scale quantum computer architec- tures (2025). URL https://arxiv.org/abs/ 2511.10633. 2511.10633

  24. [24]

    URL https:// doi.org/10.1145/173284.155333

    Culler, D.et al.Logp: towards a realistic model of parallel computation.SIGPLAN Not.28(7), 1–12 (1993). URL https:// doi.org/10.1145/173284.155333. https://doi. org/10.1145/173284.155333

  25. [25]

    & Patterson, D

    Williams, S., Waterman, A. & Patterson, D. Roofline: An insightful visual performance model for multicore architectures.Commun. ACM52(4), 65–76 (2009). URL https: //doi.org/10.1145/1498765.1498785. https: //doi.org/10.1145/1498765.1498785

  26. [26]

    URL https://arxiv.org/abs/2110

    Wack, A.et al.Quality, speed, and scale: three key attributes to measure the per- formance of near-term quantum computers (2021). URL https://arxiv.org/abs/2110. 14108. arXiv:2110.14108 [quant-ph]

  27. [27]

    W., Bishop, L

    Cross, A. W., Bishop, L. S., Sheldon, S., Nation, P. D. & Gambetta, J. M. Validating quantum computers using randomized model circuits.Physical Review A100(3), 032328 (2019)

  28. [28]

    Azure quantum resource estimator

    Microsoft. Azure quantum resource estimator. https://learn. microsoft.com/en-us/azure/quantum/ learn-how-the-resource-estimator-works. Accessed: 2026-05-26

  29. [29]

    URL https://arxiv.org/abs/2409

    Babbush, R.et al.Expressing and ana- lyzing quantum algorithms with qualtran (2024). URL https://arxiv.org/abs/2409. 04643. 2409.04643

  30. [30]

    & Liu, J

    Tremba, M., Hovland, P. & Liu, J. Is cir- cuit depth accurate for comparing quantum circuit runtimes? (2025). URL https://arxiv. org/abs/2505.16908. 2505.16908

  31. [31]

    Hockney, R. W. The communication chal- lenge for mpp: Intel paragon and meiko cs-2.Parallel Comput.20(3), 389–398 (1994). URL https://doi.org/10.1016/ S0167-8191(06)80021-9. https://doi.org/10. 1016/S0167-8191(06)80021-9

  32. [32]

    & O’Flynn, M

    Lastovetsky, A., Rychkov, V. & O’Flynn, M. Revisiting communication performance mod- els for computational clusters 1–11 (2009). URL https://ieeexplore.ieee.org/document/ 5160918. https://doi.org/10.1109/IPDPS. 2009.5160918

  33. [33]

    Layden, D.et al.Quantum-enhanced markov chain monte carlo.Nature619(7969), 282– 287 (2023)

  34. [34]

    Crovella, Bianchini, LeBlanc, Markatos & Wisniewski. Using communication-to- computation ratio in parallel program design and performance prediction.Proceed- ings of the 1992 Fourth IEEE Sympo- sium on Parallel and Distributed Processing 238–245 (1992). URL https://doi.org/10. 1109/SPDP.1992.242738. https://doi.org/ 10.1109/SPDP.1992.242738

  35. [35]

    URL https://arxiv

    Kanno, K.et al.Quantum-selected configu- ration interaction: classical diagonalization of hamiltonians in subspaces selected by quan- tum computers (2023). URL https://arxiv. org/abs/2302.11320. 2302.11320

  36. [36]

    URL https://www.science.org/doi/abs/10.1126/ sciadv.adu9991

    Robledo-Moreno, J.et al.Chemistry beyond the scale of exact diagonalization on a quantum-centric supercomputer.Science Advances11(25), eadu9991 (2025). URL https://www.science.org/doi/abs/10.1126/ sciadv.adu9991

  37. [37]

    URL https://arxiv.org/abs/ 2511.00224

    Shirakawa, T.et al.Closed-loop calcula- tions of electronic structure on a quantum processor and a classical supercomputer at full scale (2025). URL https://arxiv.org/abs/ 2511.00224. 2511.00224

  38. [38]

    URL https://arxiv.org/abs/2504

    Tyagin, I.et al.QAOA-GPT: Efficient gen- eration of adaptive and regular quantum approximate optimization algorithm circuits (2025). URL https://arxiv.org/abs/2504. 16350. 2504.16350

  39. [39]

    M., Hohenstein, E

    Oumarou, O., Scheurer, M., Parrish, R. M., Hohenstein, E. G. & Gogolin, C. Accelerating quantum computations of chemistry through regularized compressed double factorization 8, 1371. URL https://quantum-journal. org/papers/q-2024-06-13-1371/. https:// 15 doi.org/10.22331/q-2024-06-13-1371

  40. [40]

    URL https://pubs.acs.org/doi/10.1021/acs

    Rocca, D.et al.Reducing the run- time of fault-tolerant quantum simulations in chemistry through symmetry-compressed double factorization20(11), 4639–4653. URL https://pubs.acs.org/doi/10.1021/acs. jctc.4c00352. https://doi.org/10.1021/acs. jctc.4c00352

  41. [41]

    & Izmaylov, A

    Choi, S., Loaiza, I. & Izmaylov, A. F. Fluid fermionic fragments for optimizing quan- tum measurements of electronic hamiltoni- ans in the variational quantum eigensolver 7, 889. URL https://quantum-journal.org/ papers/q-2023-01-03-889/. https://doi.org/ 10.22331/q-2023-01-03-889

  42. [42]

    F.et al.Measurements as a roadblock to near-term practical quantum advantage in chemistry: Resource analysis 4(3), 033154

    Gonthier, J. F.et al.Measurements as a roadblock to near-term practical quantum advantage in chemistry: Resource analysis 4(3), 033154. URL https://link.aps.org/ doi/10.1103/PhysRevResearch.4.033154. https://doi.org/10.1103/PhysRevResearch. 4.033154

  43. [43]

    & Somma, R

    Knill, E., Ortiz, G. & Somma, R. D. Opti- mal quantum measurements of expectation values of observables.Phys. Rev. A75, 012328 (2007). URL https://link.aps.org/ doi/10.1103/PhysRevA.75.012328. https:// doi.org/10.1103/PhysRevA.75.012328

  44. [44]

    V.et al.Quantum-enhanced markov chain monte carlo for combinatorial optimization (2026)

    Marshall, K. V.et al.Quantum-enhanced markov chain monte carlo for combinatorial optimization (2026). URL https://arxiv.org/ abs/2602.06171. 2602.06171

  45. [45]

    W.et al.A scalable and real- time neural decoder for topological quantum codes (2026)

    Senior, A. W.et al.A scalable and real- time neural decoder for topological quantum codes (2026). URL https://arxiv.org/abs/ 2512.07737. 2512.07737

  46. [46]

    Suppressing quantum errors by scaling a sur- face code logical qubit.Nature614(7949), 676–681 (2023)

  47. [47]

    Terhal, B. M. Quantum error correction for quantum memories.Rev. Mod. Phys. 87, 307–346 (2015). URL https://link.aps. org/doi/10.1103/RevModPhys.87.307. https: //doi.org/10.1103/RevModPhys.87.307

  48. [48]

    & Chen, J

    Tan, X., Zhang, F., Chao, R., Shi, Y. & Chen, J. Scalable surface-code decoders with parallelization in time.PRX Quantum4, 040344 (2023). URL https://link.aps.org/ doi/10.1103/PRXQuantum.4.040344. https: //doi.org/10.1103/PRXQuantum.4.040344

  49. [49]

    E., Barnes, K

    Skoric, L., Browne, D. E., Barnes, K. M., Gillespie, N. I. & Campbell, E. T. Parallel window decoding enables scalable fault toler- ant quantum computation.Nature Commu- nications14(1), 7040 (2023). URL https:// doi.org/10.1038/s41467-023-42482-1. https: //doi.org/10.1038/s41467-023-42482-1

  50. [50]

    Fowler, A. G. & Gidney, C. Low overhead quantum computation using lattice surgery (2019). URL https://arxiv.org/abs/1808. 06709. 1808.06709

  51. [51]

    Fowler, A. G. Time-optimal quantum com- putation.arXiv preprint arXiv:1210.4626 (2012)

  52. [52]

    How to factor 2048 bit RSA integers with less than a million noisy qubits.arXiv e-printsarXiv:2505.15917 (2025)

    Gidney, C. How to factor 2048 bit RSA integers with less than a million noisy qubits.arXiv e-printsarXiv:2505.15917 (2025). URL https://arxiv.org/abs/2505. 15917. https://doi.org/10.48550/arXiv.2505. 15917, arXiv:2505.15917 [quant-ph]

  53. [53]

    URL https://arxiv.org/abs/2605.30765

    Chen, Y.et al.Real-time quantum error correction system stack: Architecture, algo- rithms, and engineering practice (2026). URL https://arxiv.org/abs/2605.30765. 2605. 30765

  54. [54]

    A Game of Surface Codes: Large- Scale Quantum Computing with Lattice Surgery.Quantum3, 128 (2019)

    Litinski, D. A Game of Surface Codes: Large- Scale Quantum Computing with Lattice Surgery.Quantum3, 128 (2019). URL https: //doi.org/10.22331/q-2019-03-05-128. https: //doi.org/10.22331/q-2019-03-05-128

  55. [55]

    & Fowler, A

    Gidney, C. & Fowler, A. G. Flexible layout of surface code computations using autoccz states.arXiv preprint arXiv:1905.08916 (2019)

  56. [56]

    M., Kubica, A

    McArdle, S., Dalzell, A. M., Kubica, A. & Brand˜ ao, F. G. The fast for the curious: How to accelerate fault-tolerant quantum appli- cations.arXiv preprint arXiv:2510.26078 16 (2025)

  57. [57]

    H.et al.Fault-tolerant resource estimate for quantum chemical simulations: Case study on li-ion battery electrolyte molecules.Phys

    Kim, I. H.et al.Fault-tolerant resource estimate for quantum chemical simulations: Case study on li-ion battery electrolyte molecules.Phys. Rev. Res.4, 023019 (2022). URL https://link.aps.org/doi/10. 1103/PhysRevResearch.4.023019. https:// doi.org/10.1103/PhysRevResearch.4.023019

  58. [58]

    https://doi.org/10.1016/j

    Caleffi, M.et al.Distributed quantum com- puting: A survey.Computer Networks254, 110672 (2024). https://doi.org/10.1016/j. comnet.2024.110672

  59. [59]

    https: //doi.org/10.1098/rspa.2012.0686

    Beals, R.et al.Efficient distributed quantum computing.Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences469(2153), 20120686 (2013). https: //doi.org/10.1098/rspa.2012.0686

  60. [60]

    Main, D., Drmota, P., Nadlinger, D. P. et al.Distributed quantum computing across an optical network link.Nature638, 383–388 (2025). https://doi.org/10.1038/ s41586-024-08404-x

  61. [61]

    A., Ding, Y

    Liu, C., Wang, M., Stein, S. A., Ding, Y. & Li, A. Quantum memory: A miss- ing piece in quantum computing units (2023). URL https://arxiv.org/abs/2309. 14432. 2309.14432

  62. [62]

    Brandao, F. G. & Svore, K. M. Quan- tum speed-ups for solving semidefinite pro- grams 415–426. URL http://ieeexplore.ieee. org/document/8104077/. https://doi.org/ 10.1109/FOCS.2017.45

  63. [63]

    & Lukin, M

    Cong, I., Choi, S. & Lukin, M. D. Quan- tum convolutional neural networks.Nature Physics15(12), 1273–1278 (2019)

  64. [64]

    G.et al.Distributed quan- tum computing via adaptive circuit knitting (2026)

    Johnson, K. G.et al.Distributed quan- tum computing via adaptive circuit knitting (2026). URL https://arxiv.org/abs/2603. 12411. 2603.12411

  65. [65]

    & Wendin, G

    Dobˇ s´ ıˇ cek, M., Johansson, G., Shumeiko, V. & Wendin, G. Arbitrary accuracy iterative quantum phase estimation algorithm using a single ancillary qubit: A two-qubit bench- mark.Physical Review A76(3), 030306 (2007). https://doi.org/10.1103/PhysRevA. 76.030306

  66. [66]

    P.et al.Optimization by decoded quantum interferometry646(8086), 831–836

    Jordan, S. P.et al.Optimization by decoded quantum interferometry646(8086), 831–836. URL https://www.nature.com/ articles/s41586-025-09527-5. https://doi. org/10.1038/s41586-025-09527-5

  67. [67]

    & Irani, S

    Jiang, J. & Irani, S. Quantum metropolis sampling via weak measurement. URL http: //arxiv.org/abs/2406.16023. 2406.16023

  68. [68]

    & Neumann, N

    Buhrman, H., Folkertsma, M., Loff, B. & Neumann, N. M. P. State preparation by shallow circuits using feed forward.Quan- tum8, 1552 (2024). URL https://doi.org/10. 22331/q-2024-12-09-1552. https://doi.org/ 10.22331/q-2024-12-09-1552

  69. [69]

    URL https://www

    Lacroix, N.et al.Scaling and logic in the colour code on a supercon- ducting quantum processor.Nature 645(8081). URL https://www. nature.com/articles/s41586-025-09061-4. https://doi.org/10.1038/s41586-025-09061-4

  70. [70]

    URL https://link.aps.org/doi/10

    Ali, H.et al.Reducing the error rate of a superconducting logical qubit using analog readout information22(4), 044031. URL https://link.aps.org/doi/10. 1103/PhysRevApplied.22.044031. https:// doi.org/10.1103/PhysRevApplied.22.044031

  71. [71]

    URL https: //arxiv.org/abs/2511.05465

    Ransford, A.et al.Helios: A 98-qubit trapped-ion quantum computer. URL https: //arxiv.org/abs/2511.05465

  72. [72]

    H.et al.High-fidelity readout of trapped-ion qubits100(20), 200502

    Myerson, A. H.et al.High-fidelity readout of trapped-ion qubits100(20), 200502. URL https://link.aps.org/doi/10. 1103/PhysRevLett.100.200502. https://doi. org/10.1103/PhysRevLett.100.200502

  73. [73]

    Quantum computing with atomic qubit arrays: confronting the cost of connectivity

    Saffman, M. Quantum computing with atomic qubit arrays: confronting the cost of connectivity. URL https://arxiv.org/abs/ 2505.11218 17

  74. [74]

    Nature communications5(1), 4213 (2014)

    Peruzzo, A.et al.A variational eigenvalue solver on a photonic quantum processor. Nature communications5(1), 4213 (2014)

  75. [75]

    W., Hassidim, A

    Harrow, A. W., Hassidim, A. & Lloyd, S. Quantum algorithm for linear systems of equations.Physical review letters103(15), 150502 (2009)

  76. [76]

    Variable time amplitude ampli- fication and a faster quantum algorithm for solving systems of linear equations.arXiv preprint arXiv:1010.4458(2010)

    Ambainis, A. Variable time amplitude ampli- fication and a faster quantum algorithm for solving systems of linear equations.arXiv preprint arXiv:1010.4458(2010)

  77. [77]

    Zaman, A., Morrell, H. J. & Wong, H. Y. A step-by-step HHL algorithm walkthrough to enhance understanding of critical quantum computing concepts11, 77117–77131. URL https://ieeexplore.ieee. org/document/10189828/. https://doi.org/ 10.1109/ACCESS.2023.3297658

  78. [78]

    Gily´ en, A., Su, Y., Low, G. H. & Wiebe, N. Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics 193–204 (2019)

  79. [79]

    & Lidar, D

    Albash, T. & Lidar, D. A. Adiabatic quantum computation.Reviews of Modern Physics90(1), 015002 (2018)

  80. [80]

    & Lin, H.-H

    Lu, Y.-C. & Lin, H.-H. Optimizing sparse quantum state preparation with measure- ment and feedforward (2025). URL https: //arxiv.org/abs/2508.21346. 2508.21346

Showing first 80 references.