Pith

open record

sign in
Browse

arxiv: 2606.00501 · v1 · pith:TWJQRVZB · submitted 2026-05-30 · quant-ph · cs.DC· cs.NI

Joint Optimization of Qubit Leasing and Quantum Circuit Distribution

Anoushka Dey , Gaurav S. Kasbekar This is my paper

Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 reserved 2026-06-28 18:57 UTCgrok-4.3pith:TWJQRVZBrecord.jsonopen to challenge →

Figure 1
Figure 1. Figure 1: The figure illustrates the system model. The agent leases resources from multiple QCs (QC [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] reproduced from arXiv: 2606.00501
classification quant-ph cs.DCcs.NI
keywords qubit leasingquantum circuit distributioninteger linear programmingNP-completegreedy algorithmquantum networksdistributed quantum computing
0
0 comments X

The pith

The JQLQCD problem of leasing qubits and distributing a quantum circuit across networked computers admits a full integer linear programming formulation that is NP-complete yet solvable exactly in special cases.

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

An agent must decide how many qubits to lease from each of several connected quantum computers, where to store each circuit qubit across time slots, which computer executes each gate, and whether to move qubits by physical migration or teleportation. The paper encodes these four decisions plus their costs into one integer linear program. It proves the resulting optimization problem is NP-complete but identifies special cases solvable in closed form or polynomial time, and supplies a greedy algorithm with local search that works well on large instances in simulations. A reader would care because the model shows how to allocate scarce quantum hardware across a network without owning it outright.

Core claim

The joint qubit leasing and quantum circuit distribution (JQLQCD) problem is formulated as a comprehensive integer linear program that optimizes leasing amounts, storage assignments over time, gate execution locations, and qubit movement choices between migration and teleportation. The problem is NP-complete. Several special cases admit optimal closed-form or polynomial-time solutions. A greedy algorithm with local search refinement solves large general instances effectively according to numerical computations.

What carries the argument

The integer linear programming formulation of the JQLQCD problem, which treats leasing quantities, time-dependent storage locations, gate execution sites, and movement modes as decision variables subject to linear cost and capacity constraints.

If this is right

  • The NP-completeness result implies that no polynomial-time algorithm exists for the general case unless P equals NP.
  • Closed-form or polynomial solutions exist for the identified special cases of the JQLQCD problem.
  • The greedy algorithm with local search refinement yields good solutions for large instances as shown by the numerical experiments.
  • The ILP formulation directly encodes the four decisions and their costs, enabling exact optimization when instance size permits.

Where Pith is reading between the lines

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

  • If the linear cost model matches real hardware pricing, network operators could use the ILP to set leasing rates that minimize total circuit execution cost.
  • Incorporating explicit network topology or decoherence times would turn the current formulation into a more constrained variant that still fits the same decision structure.
  • The same four-decision pattern could be reused for other distributed quantum tasks such as entanglement generation or measurement-based computation.
  • Running the greedy algorithm on hardware traces from actual quantum networks would test whether the simulated performance holds when migration and teleportation latencies are measured rather than modeled.

Load-bearing premise

All leasing, storage, execution, migration, and teleportation costs can be expressed as linear terms in an integer program without unmodeled quantum noise or decoherence during movement.

What would settle it

Solve a small JQLQCD instance to optimality with an ILP solver and compare the resulting total cost against the output of the proposed greedy algorithm; a large gap on instances with known topology would falsify the claim that the heuristic performs well.

Figures

Figures reproduced from arXiv: 2606.00501 by Anoushka Dey, Gaurav S. Kasbekar.

Figure 2
Figure 2. Figure 2: The figure shows the total cost versus number of gates for the greedy [PITH_FULL_IMAGE:figures/full_fig_p018_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The figure shows the execution time versus number of gates for the [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The figure shows the total cost versus number of QCs for the greedy [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The figure shows the execution time versus number of QCs for the [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The figure shows the total cost versus makespan weight [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 11
Figure 11. Figure 11: The figure compares the execution times of the optimal, greedy, and [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: The figure compares the total costs under the optimal, greedy, and [PITH_FULL_IMAGE:figures/full_fig_p020_12.png] view at source ↗
Figure 10
Figure 10. Figure 10: The figure compares the total costs under the optimal, greedy, and [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 16
Figure 16. Figure 16: The figure shows the sensitivity to QC scoring weights for different [PITH_FULL_IMAGE:figures/full_fig_p021_16.png] view at source ↗
Figure 15
Figure 15. Figure 15: The figure shows the total costs under the greedy and SA algorithms. [PITH_FULL_IMAGE:figures/full_fig_p021_15.png] view at source ↗
read the original abstract

We consider an agent, who would like to execute a given quantum circuit using resources leased from a set of quantum computers (QCs) connected by a quantum network. For this purpose, the agent needs to make the following four key decisions: (i) how many qubits to lease from each QC, (ii) at which QCs to store different circuit qubits in different time slots, (iii) at which QC to execute each gate in the circuit, and (iv) how to move qubits between QCs, choosing between migration and teleportation. We refer to this problem facing the agent as the joint qubit leasing and quantum circuit distribution (JQLQCD) problem, and provide a comprehensive integer linear programming (ILP) formulation for it. We show that the JQLQCD problem is NP-complete. Next, we identify several special cases in which the problem can be optimally solved in closed form or via polynomial-time algorithms. Also, we propose a greedy algorithm with local search refinement to solve large instances of the general JQLQCD problem. Finally, we evaluate the performance of the proposed greedy algorithm using extensive numerical computations.

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.

Referee Report

1 major / 1 minor

Summary. The manuscript defines the joint qubit leasing and quantum circuit distribution (JQLQCD) problem, which involves four key decisions for executing a quantum circuit on leased quantum computers connected by a network: qubit leasing quantities, qubit storage locations over time, gate execution locations, and qubit movement via migration or teleportation. It provides a comprehensive integer linear programming (ILP) formulation, proves that the problem is NP-complete, identifies special cases solvable optimally in closed form or polynomial time, proposes a greedy algorithm with local search refinement for large instances, and evaluates the algorithm's performance through numerical computations.

Significance. If the results hold, this work offers a foundational optimization approach for practical distributed quantum computing, enabling efficient resource leasing and circuit distribution. The ILP formulation and NP-completeness result establish the problem's computational complexity, while the special cases and heuristic provide actionable solutions. The numerical evaluation demonstrates the heuristic's effectiveness on large instances, which is a strength for practical applicability.

major comments (1)
  1. [Abstract (ILP formulation)] The ILP formulation (as described in the abstract) assumes that all relevant costs (leasing, storage, gate execution, migration, teleportation) can be quantified as linear terms without incorporating unmodeled effects such as quantum noise, decoherence during movement, or explicit network topology constraints. This assumption is load-bearing for the NP-completeness result, special-case algorithms, and numerical performance claims, as violations could make the ILP optimum infeasible or suboptimal on real hardware.
minor comments (1)
  1. The abstract mentions 'extensive numerical computations' but does not specify the instance sizes, metrics, or comparison baselines used in the evaluation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback and the recommendation for major revision. Below we provide a point-by-point response to the single major comment.

read point-by-point responses

  1. Referee: [Abstract (ILP formulation)] The ILP formulation (as described in the abstract) assumes that all relevant costs (leasing, storage, gate execution, migration, teleportation) can be quantified as linear terms without incorporating unmodeled effects such as quantum noise, decoherence during movement, or explicit network topology constraints. This assumption is load-bearing for the NP-completeness result, special-case algorithms, and numerical performance claims, as violations could make the ILP optimum infeasible or suboptimal on real hardware.

    Authors: The JQLQCD model is deliberately formulated as an abstracted optimization problem in which leasing, storage, execution, migration, and teleportation costs are treated as given linear coefficients supplied to the ILP. The NP-completeness proof, the polynomial-time special cases, and the greedy algorithm with local search are all established with respect to this mathematical model; they do not claim to capture every physical phenomenon. Network connectivity is represented through the movement-cost parameters between pairs of quantum computers, which can encode topology. We agree that effects such as noise and decoherence are outside the current scope and that an optimal solution of the ILP could become infeasible once those effects are added. To strengthen the manuscript we will add an explicit paragraph in the introduction (and a short limitations subsection) that states the modeling assumptions, notes that more detailed cost functions incorporating noise can be substituted if available, and clarifies that the framework is intended as a resource-allocation layer rather than a full hardware simulator. This constitutes a partial revision. revision: partial

Circularity Check

0 steps flagged

No circularity: ILP model, NP-completeness proof, and algorithms are independently constructed

full rationale

The paper defines the JQLQCD problem via four explicit decisions, then directly constructs an ILP with linear objective and constraints to encode them. NP-completeness is shown via reduction (standard technique), special cases admit closed-form or poly-time solutions by direct analysis, and the greedy+local-search algorithm is proposed and evaluated numerically on instances. None of these steps reduce to self-definition, fitted parameters renamed as predictions, or load-bearing self-citations. The linear-cost assumption is an explicit modeling choice, not a circular derivation. The contribution is a modeling and algorithmic proposal that remains self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Review based solely on abstract; full details of modeling assumptions unavailable. Relies on standard ILP modeling assumptions for quantum network operations.

axioms (2)
  • domain assumption Costs for qubit leasing, storage, gate execution, migration and teleportation can be expressed as linear objective and constraint terms in an ILP.
    Abstract states a comprehensive ILP formulation is provided for the four key decisions.
  • standard math The JQLQCD decision problem is in NP and NP-hard.
    Abstract claims the problem is shown to be NP-complete.

pith-pipeline@v0.9.1-grok · 5735 in / 1385 out tokens · 21321 ms · 2026-06-28T18:57:37.896068+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

71 extracted references · 4 canonical work pages · 1 internal anchor

  1. [1]

    Distributed quantum computing: a survey,

    M. Caleffi, M. Amoretti, D. Ferrari, J. Illiano, A. Manzalini, and A. S. Cacciapuoti, “Distributed quantum computing: a survey,”Computer Networks, vol. 254, p. 110672, 2024

    2024

  2. [2]

    Review of distributed quantum computing: From single QPU to high performance quantum computing,

    D. Barral, F. J. Cardama, G. D ´ıaz-Camacho, D. Fa ´ılde, I. F. Llovo, M. Mussa-Juane, J. V ´azquez-P´erez, J. Villasuso, C. Pi ˜neiro, N. Costas et al., “Review of distributed quantum computing: From single QPU to high performance quantum computing,”Computer Science Review, vol. 57, p. 100747, 2025

    2025

  3. [3]

    Towards fault-tolerant distributed quantum computation (FT-DQC): Taxonomy, recent progress, and chal- lenges,

    H. T. Larasati and B.-S. Choi, “Towards fault-tolerant distributed quantum computation (FT-DQC): Taxonomy, recent progress, and chal- lenges,”ICT Express, vol. 11, no. 3, pp. 417–435, 2025

    2025

  4. [4]

    Quantum internet: From communication to distributed computing!

    M. Caleffi, A. S. Cacciapuoti, and G. Bianchi, “Quantum internet: From communication to distributed computing!”ACM SIGCOMM Computer Communication Review, vol. 52, no. 2, pp. 3–7, 2022

    2022

  5. [5]

    Qubit allocation,

    M. Y . Siraichi, V . F. d. Santos, C. Collange, and F. M. Q. a. Pereira, “Qubit allocation,” inProceedings of the International Symposium on Code Generation and Optimization (CGO), 2018, pp. 113–125

    2018

  6. [6]

    An efficient methodology for map- ping quantum circuits to the IBM QX architectures,

    A. Zulehner, A. Paler, and R. Wille, “An efficient methodology for map- ping quantum circuits to the IBM QX architectures,”IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 38, no. 7, pp. 1226–1236, 2018

    2018

  7. [7]

    Full-stack, real-system quantum computer studies: architectural comparisons and design insights,

    P. Murali, N. M. Linke, M. Martonosi, A. J. Abhari, N. H. Nguyen, and C. H. Alderete, “Full-stack, real-system quantum computer studies: architectural comparisons and design insights,” inProceedings of the 46th International Symposium on Computer Architecture (ISCA), 2019, pp. 527–540

    2019

  8. [8]

    Not all qubits are created equal: A case for variability-aware policies for NISQ-era quantum computers,

    S. S. Tannu and M. K. Qureshi, “Not all qubits are created equal: A case for variability-aware policies for NISQ-era quantum computers,” inProceedings of the 24th International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS), 2019, pp. 987–999

    2019

  9. [9]

    Software mitigation of crosstalk on noisy intermediate-scale quantum computers,

    P. Murali, J. M. Baker, A. Javadi-Abhari, F. T. Chong, and M. Martonosi, “Software mitigation of crosstalk on noisy intermediate-scale quantum computers,” inProceedings of the 25th International Conference on Ar- chitectural Support for Programming Languages and Operating Systems (ASPLOS), 2020, pp. 1001–1016

    2020

  10. [10]

    MQT QMAP: Efficient quantum circuit mapping,

    R. Wille and L. Burgholzer, “MQT QMAP: Efficient quantum circuit mapping,” inProceedings of the 2023 International Symposium on Physical Design, 2023

    2023

  11. [11]

    On optimal subarchitectures for quantum circuit mapping,

    T. Peham, L. Burgholzer, and R. Wille, “On optimal subarchitectures for quantum circuit mapping,”ACM Transactions on Quantum Computing, vol. 4, no. 4, pp. 23:1–23:20, July 2023

    2023

  12. [12]

    Mapping quantum circuits to IBM QX architectures using the minimal number of SW AP and H operations,

    R. Wille, L. Burgholzer, and A. Zulehner, “Mapping quantum circuits to IBM QX architectures using the minimal number of SW AP and H operations,” inProceedings of the 53rd Annual Design Automation Conference (DAC), 2016, pp. 1–6

    2016

  13. [13]

    SMT-based layout synthesis approaches for quantum circuits,

    Z.-H. Guo and T.-C. Wang, “SMT-based layout synthesis approaches for quantum circuits,” inProceedings of the International Symposium on Physical Design, 2024, pp. 235–243

    2024

  14. [14]

    Quantum circuit synthesis and compilation optimization: Overview and prospects,

    G. Yan, W. Wu, Y . Chen, K. Pan, X. Lu, Z. Zhou, Y . Wang, R. Wang, and J. Yan, “Quantum circuit synthesis and compilation optimization: Overview and prospects,”arXiv preprint arXiv:2407.00736, 2024. [Online]. Available: https://doi.org/10.48550/arXiv.2407.00736

    work page doi:10.48550/arxiv.2407.00736 2024

  15. [15]

    Pow- ermove: Optimizing compilation for neutral atom quantum computers with zoned architecture,

    J. Ruan, X. Fang, H. Zhang, A. Li, T. Humble, and Y . Ding, “Pow- ermove: Optimizing compilation for neutral atom quantum computers with zoned architecture,” inProceedings of the 30th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 3, 2025, pp. 163–178

    2025

  16. [16]

    Towards a unified multi-target MLIR-based compiler: A heterogeneous compilation framework for high-performance and quantum computing integration,

    M. Letras, J. Echavarria, M. N. Farooqi, M. De Pascale, M. H. Vera, N. Tornow, L. Schulz, and M. Schulz, “Towards a unified multi-target MLIR-based compiler: A heterogeneous compilation framework for high-performance and quantum computing integration,” in2025 IEEE International Conference on Quantum Computing and Engineering (QCE), vol. 2. IEEE, 2025, pp. 28–33

    2025

  17. [17]

    Quantum compiler design for qubit mapping and routing: A cross- architectural survey of superconducting, trapped-ion, and neutral atom systems,

    C. Zhu, X. Wu, Z. Yang, J. Wang, A. Wu, S. Zheng, and X. Wang, “Quantum compiler design for qubit mapping and routing: A cross- architectural survey of superconducting, trapped-ion, and neutral atom systems,”arXiv preprint arXiv:2505.16891, 2025

    work page arXiv 2025

  18. [18]

    Unifying Qubit Routing Across Diverse Quantum ISAs via Canonical Representation

    Z. Yang, K. Zhang, X. Tian, X. Ren, Y . Liu, Y . Li, D. Ding, J. Chen, and Y . Xie, “Unifying qubit routing across diverse quantum ISAs via canonical representation,”arXiv preprint arXiv:2511.04608, 2025

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  19. [19]

    Routing-aware placement for zoned neutral atom-based quantum computing,

    Y . Stade, W.-H. Lin, J. Cong, and R. Wille, “Routing-aware placement for zoned neutral atom-based quantum computing,” in2025 IEEE/ACM International Conference On Computer Aided Design (ICCAD). IEEE, 2025, pp. 1–9

    2025

  20. [20]

    MQT Predictor: Au- tomatic device selection with device-specific circuit compilation for quantum computing,

    N. Quetschlich, L. Burgholzer, and R. Wille, “MQT Predictor: Au- tomatic device selection with device-specific circuit compilation for quantum computing,”ACM Transactions on Quantum Computing, vol. 6, no. 1, pp. 1–26, 2025

    2025

  21. [21]

    Generating compilers for qubit mapping and routing,

    A. Molavi, A. Xu, E. Cecchetti, S. Tannu, and A. Albarghouthi, “Generating compilers for qubit mapping and routing,”Proceedings of the ACM on Programming Languages, vol. 10, no. POPL, pp. 2265– 2294, 2026

    2026

  22. [22]

    Achieving Pareto-optimality in quantum circuit compilation via a multi-objective heuristic optimization approach,

    A. ´Swierkowska, J. Echavarria, L. Schulz, and M. Schulz, “Achieving Pareto-optimality in quantum circuit compilation via a multi-objective heuristic optimization approach,” in2024 IEEE International Conference on Quantum Computing and Engineering (QCE), vol. 2. IEEE, 2024, pp. 306–310

    2024

  23. [23]

    Scalable multi-objective genetic algorithm for quantum circuit optimization,

    R. Ghlib, R. Bouhadouza, and F. Hnaien, “Scalable multi-objective genetic algorithm for quantum circuit optimization,”Scientific Reports, 2026

    2026

  24. [24]

    Compiler design for distributed quantum computing,

    D. Ferrari, A. S. Cacciapuoti, M. Amoretti, and M. Caleffi, “Compiler design for distributed quantum computing,”IEEE Transactions on Quantum Engineering, vol. 2, pp. 1–20, 2021

    2021

  25. [25]

    A modular quantum compila- tion framework for distributed quantum computing,

    D. Ferrari, S. Carretta, and M. Amoretti, “A modular quantum compila- tion framework for distributed quantum computing,”IEEE Transactions on Quantum Engineering, vol. 4, pp. 1–13, 2023

    2023

  26. [26]

    ECDQC: Efficient compilation for distributed quantum computing with linear layout,

    K. Liu, Y . Zhou, H. Luo, L. Xiong, Y . Zhu, E. Casey, J. Cheng, S. Y .- C. Chen, and Z. Liang, “ECDQC: Efficient compilation for distributed quantum computing with linear layout,” in2025 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE, 2025, pp. 1–5

    2025

  27. [27]

    Compiler for distributed quantum computing: a reinforce- ment learning approach,

    P. Promponas, A. Mudvari, L. Della Chiesa, P. Polakos, L. Samuel, and L. Tassiulas, “Compiler for distributed quantum computing: a reinforce- ment learning approach,” inICC 2025-IEEE International Conference on Communications. IEEE, 2025, pp. 4615–4621

    2025

  28. [28]

    Qubit allocation for distributed quantum computing,

    Y . Mao, Y . Liu, and Y . Yang, “Qubit allocation for distributed quantum computing,” inIEEE INFOCOM 2023-IEEE Conference on Computer Communications. IEEE, 2023, pp. 1–10. 23

    2023

  29. [29]

    Time- aware qubit assignment and circuit optimization for distributed quantum computing,

    L. S ¨unkel, J. Stein, M. Zorn, T. Gabor, and C. Linnhoff-Popien, “Time- aware qubit assignment and circuit optimization for distributed quantum computing,” in2025 IEEE International Conference on Quantum Com- puting and Engineering (QCE), vol. 1. IEEE, 2025, pp. 937–947

    2025

  30. [30]

    Evolutionary-based circuit optimization for distributed quan- tum computing,

    L. S ¨unkel, J. Stein, G. Stenzel, M. K ¨olle, T. Gabor, and C. Linnhoff- Popien, “Evolutionary-based circuit optimization for distributed quan- tum computing,” in2025 IEEE International Conference on Quantum Artificial Intelligence (QAI). IEEE, 2025, pp. 261–268

    2025

  31. [31]

    Towards a distributed quantum computing ecosystem,

    D. Cuomo, M. Caleffi, and A. S. Cacciapuoti, “Towards a distributed quantum computing ecosystem,”IET Quantum Communication, vol. 1, no. 1, pp. 3–8, 2020

    2020

  32. [32]

    Efficient distribution of quantum circuits,

    R. G Sundaram, H. Gupta, and C. Ramakrishnan, “Efficient distribution of quantum circuits,” inProceedings of the 35th International Sympo- sium on Distributed Computing (DISC). Schloss Dagstuhl–Leibniz- Zentrum f ¨ur Informatik, 2021, pp. 41–1

    2021

  33. [33]

    Distribution of quantum circuits over general quantum networks,

    R. G. Sundaram, H. Gupta, and C. Ramakrishnan, “Distribution of quantum circuits over general quantum networks,” inProceedings of the IEEE International Conference on Quantum Computing and Engi- neering (QCE), 2022, pp. 415–425

    2022

  34. [34]

    Automated distribution of quantum circuits via hypergraph partitioning,

    P. Andr ´es-Mart´ınez and C. Heunen, “Automated distribution of quantum circuits via hypergraph partitioning,”Physical Review A, vol. 100, no. 3, p. 032308, 2019

    2019

  35. [35]

    Optimized quan- tum circuit partitioning,

    O. Daei, K. Navi, and M. Zomorodi-Moghadam, “Optimized quan- tum circuit partitioning,”International Journal of Theoretical Physics, vol. 59, pp. 3804–3820, 2020

    2020

  36. [36]

    Circuit partitioning for multi-core quantum architectures with deep reinforcement learning,

    A. Pastor, P. Escofet, S. B. Rached, E. Alarc ´on, P. Barlet-Ros, and S. Abadal, “Circuit partitioning for multi-core quantum architectures with deep reinforcement learning,” inProceedings of the IEEE Interna- tional Symposium on Circuits and Systems (ISCAS), 2024, pp. 1–5

    2024

  37. [37]

    Generalised circuit partitioning for distributed quantum computing,

    F. Burt, K.-C. Chen, and K. K. Leung, “Generalised circuit partitioning for distributed quantum computing,” in2024 IEEE International Con- ference on Quantum Computing and Engineering (QCE), vol. 2. IEEE, 2024, pp. 173–178

    2024

  38. [38]

    A multilevel framework for partitioning quantum circuits,

    ——, “A multilevel framework for partitioning quantum circuits,”Quan- tum, vol. 10, p. 1984, 2026

    1984

  39. [39]

    Efficient time-aware partitioning of quantum circuits for distributed quantum computing,

    R. P. Wu, C. Ranaweera, S. Rajasegarar, R. R. Joseph, J. Choi, and S. W. Loke, “Efficient time-aware partitioning of quantum circuits for distributed quantum computing,” in2026 International Conference on Quantum Communications, Networking, and Computing (QCNC). IEEE, 2026, pp. 720–724

    2026

  40. [40]

    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, 2025

    2025

  41. [41]

    Entanglement-efficient distri- bution of quantum circuits over large-scale quantum networks,

    F. Burt, K.-C. Chen, and K. K. Leung, “Entanglement-efficient distri- bution of quantum circuits over large-scale quantum networks,” in2025 IEEE International Conference on Quantum Computing and Engineer- ing (QCE), vol. 1. IEEE, 2025, pp. 1111–1122

    2025

  42. [42]

    Distributing quantum circuits using pre-distributed entanglement pairs over quantum networks,

    Y . Yang, R. G. Sundaram, and H. Gupta, “Distributing quantum circuits using pre-distributed entanglement pairs over quantum networks,” in 2026 International Conference on Quantum Communications, Network- ing, and Computing (QCNC). IEEE, 2026, pp. 252–258

    2026

  43. [43]

    Efficient execution of multiple quantum circuits over a quantum network,

    ——, “Efficient execution of multiple quantum circuits over a quantum network,” in2025 IEEE International Conference on Quantum Comput- ing and Engineering (QCE), vol. 1. IEEE, 2025, pp. 1123–1133

    2025

  44. [44]

    Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,

    C. H. Bennett, G. Brassard, C. Cr ´epeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,”Physical Review Letters, vol. 70, no. 13, pp. 1895–1899, 1993

    1993

  45. [45]

    Quantum repeaters: The role of imperfect local operations in quantum communication,

    H.-J. Briegel, W. D ¨ur, J. I. Cirac, and P. Zoller, “Quantum repeaters: The role of imperfect local operations in quantum communication,”Physical Review Letters, vol. 81, no. 26, pp. 5932–5935, 1998

    1998

  46. [46]

    FENDI: Toward high-fidelity entanglement distribution in the quantum internet,

    H. Gu, Z. Li, R. Yu, X. Wang, F. Zhou, J. Liu, and G. Xue, “FENDI: Toward high-fidelity entanglement distribution in the quantum internet,” IEEE/ACM Transactions on Networking, vol. 32, no. 6, pp. 5033–5048, 2024

    2024

  47. [47]

    Optimal routing and end-to-end entanglement distribution in quantum networks,

    J. Halder, A. Rajabov, R. Bassoli, F. H. Fitzek, and G. P. Fettweis, “Optimal routing and end-to-end entanglement distribution in quantum networks,”Scientific Reports, vol. 14, no. 1, p. 19262, 2024

    2024

  48. [48]

    Optimal entanglement distribution policies in homogeneous repeater chains with cutoffs,

    ´A. G. I ˜nesta, G. Vardoyan, L. Scavuzzo, and S. Wehner, “Optimal entanglement distribution policies in homogeneous repeater chains with cutoffs,”npj Quantum Information, vol. 9, no. 46, 2023

    2023

  49. [49]

    Cost-aware high-fidelity entanglement distribution and purification in the quantum internet,

    H. Gu, Z. Li, X. Wang, D. Yang, G. Xue, and R. Yu, “Cost-aware high-fidelity entanglement distribution and purification in the quantum internet,”IEEE Transactions on Networking, vol. 34, pp. 681–696, 2025

    2025

  50. [50]

    Distribution and purification of entanglement states in quantum networks,

    X. Fan, Y . Yang, H. Gupta, and C. Ramakrishnan, “Distribution and purification of entanglement states in quantum networks,” in2025 International Conference on Quantum Communications, Networking, and Computing (QCNC). IEEE, 2025, pp. 74–82

    2025

  51. [51]

    Optimized dis- tribution of entanglement graph states in quantum networks,

    X. Fan, C. Zhan, H. Gupta, and C. Ramakrishnan, “Optimized dis- tribution of entanglement graph states in quantum networks,”IEEE Transactions on Quantum Engineering, vol. 6, 2025

    2025

  52. [52]

    Resource allocation in quan- tum networks for distributed quantum computing,

    C. Cicconetti, M. Conti, and A. Passarella, “Resource allocation in quan- tum networks for distributed quantum computing,” inProceedings of the IEEE International Conference on Smart Computing (SMARTCOMP), 2022, pp. 124–132

    2022

  53. [53]

    Quantum cloud computing: Trends and challenges,

    M. Golec, E. S. Hatay, M. Golec, M. Uyar, M. Golec, and S. S. Gill, “Quantum cloud computing: Trends and challenges,”Journal of Economy and Technology, vol. 2, pp. 190–199, 2024

    2024

  54. [54]

    Quantum Cloud Computing: A Review, Open Problems, and Future Directions

    H. T. Nguyen, P. Krishnan, D. Krishnaswamy, M. Usman, and R. Buyya, “Quantum cloud computing: a review, open problems, and future direc- tions,”arXiv preprint arXiv:2404.11420, 2024

    work page Pith review arXiv 2024

  55. [55]

    NP-Complete scheduling problems,

    J. D. Ullman, “NP-Complete scheduling problems,”Journal of Computer and System Sciences, vol. 10, no. 3, pp. 384–393, 1975

    1975

  56. [56]

    M. R. Garey and D. S. Johnson,Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, 1979

    1979

  57. [57]

    Complexity of scheduling under precedence constraints,

    J. K. Lenstra and A. H. G. R. Kan, “Complexity of scheduling under precedence constraints,”Operations Research, vol. 26, no. 1, pp. 22–35, 1978

    1978

  58. [58]

    Kleinberg and E

    J. Kleinberg and E. Tardos,Algorithm design. Pearson Education India, 2006

    2006

  59. [59]

    On the complexity of quantum circuit compilation,

    A. Botea, A. Kishimoto, and R. Marinescu, “On the complexity of quantum circuit compilation,”Proceedings of the Eleventh International Symposium on Combinatorial Search (SOCS), pp. 138–142, 2018

    2018

  60. [60]

    NP-complete scheduling problems,

    J. D. Ullman, “NP-complete scheduling problems,”Journal of Computer and System Sciences, vol. 10, no. 3, pp. 384–393, 1975

    1975

  61. [61]

    Optimization and approximation in deterministic sequencing and scheduling: A survey,

    R. L. Graham, E. L. Lawler, J. K. Lenstra, and A. H. G. Rin- nooy Kan, “Optimization and approximation in deterministic sequencing and scheduling: A survey,”Annals of Discrete Mathematics, vol. 5, pp. 287–326, 1979

    1979

  62. [62]

    Graph minors. II. algorithmic aspects of tree-width,

    N. Robertson and P. D. Seymour, “Graph minors. II. algorithmic aspects of tree-width,”Journal of Algorithms, vol. 7, no. 3, pp. 309–322, 1986

    1986

  63. [63]

    A partialk-arboretum of graphs with bounded treewidth,

    H. L. Bodlaender, “A partialk-arboretum of graphs with bounded treewidth,”Theoretical Computer Science, vol. 209, no. 1-2, pp. 1–45, 1998

    1998

  64. [64]

    R. G. Downey and M. R. Fellows,Fundamentals of Parameterized Complexity. Springer, 2013

    2013

  65. [65]

    Cygan, F

    M. Cygan, F. V . Fomin, Łukasz Kowalik, D. Lokshtanov, D. Marx, M. Pilipczuk, M. Pilipczuk, and S. Saurabh,Parameterized Algorithms. Springer, 2015

    2015

  66. [66]

    T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein,Introduction to Algorithms, 3rd ed. MIT Press, 2009

    2009

  67. [67]

    D. E. Knuth,The Art of Computer Programming, Volume 1: Fundamen- tal Algorithms, 3rd ed. Addison-Wesley, 1997

    1997

  68. [68]

    Bounds on multiprocessing timing anomalies,

    R. L. Graham, “Bounds on multiprocessing timing anomalies,”SIAM Journal on Applied Mathematics, vol. 17, no. 2, pp. 416–429, 1969

    1969

  69. [69]

    Optimal scheduling for two- processor systems,

    E. G. Coffman, Jr., and R. L. Graham, “Optimal scheduling for two- processor systems,”Acta Informatica, vol. 1, no. 3, pp. 200–213, 1972

    1972

  70. [70]

    M. A. Nielsen and I. L. Chuang,Quantum computation and quantum information. Cambridge University Press, 2010

    2010

  71. [71]

    Worst-case performance bounds for simple one-dimensional packing algorithms,

    D. S. Johnson, A. Demers, J. D. Ullman, M. R. Garey, and R. L. Graham, “Worst-case performance bounds for simple one-dimensional packing algorithms,”SIAM Journal on Computing, vol. 3, no. 4, pp. 299–325, 1974

    1974