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arxiv: 2506.14075 · v2 · submitted 2025-06-17 · 🪐 quant-ph

Comparing a Few Qubit Systems for Superconducting Hardware Compatibility and Circuit Design Sensitivity in Qiskit

Hillol Biswas This is my paper

Pith reviewed 2026-05-19 10:06 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Qiskitsuperconducting qubitsquantum Fourier transformGHZ stateW statecircuit fidelitydecoherenceNISQ
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The pith

Circuit fidelity acts as an indirect probe of material-limited noise in superconducting quantum hardware.

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

This paper compares ideal simulations with real executions on the IBM Sherbrooke superconducting processor for three basic circuits: the quantum Fourier transform, GHZ states, and W states, across 4 to 10 qubits. It identifies how noise from material flaws and interfaces reduces fidelity as circuits grow more complex. The work suggests that these fidelity measurements can diagnose hardware limitations tied to materials. This matters because it points toward circuit design methods that incorporate both theoretical performance and practical material constraints to move closer to useful quantum computing.

Core claim

By running QFT, GHZ, and W state circuits on both simulators and the 127-qubit IBM Sherbrooke QPU, the study shows that fidelity differences stem from decoherence caused by material-induced flaws. These results position circuit fidelity as a practical indicator for material noise, enabling a design framework that balances hardware compatibility and circuit complexity for better NISQ performance.

What carries the argument

The side-by-side analysis of simulator versus QPU outputs for QFT, GHZ, and W circuits to quantify noise accumulation and identify material contributions to decoherence.

If this is right

  • Circuits with greater depth and qubit count exhibit larger fidelity drops on actual hardware due to accumulated decoherence.
  • Different state preparation circuits show distinct noise sensitivities, informing choice of primitives for applications.
  • Resource utilization on the QPU highlights constraints that must be considered alongside theoretical circuit design.
  • The observed patterns support developing mitigation strategies focused on material properties.

Where Pith is reading between the lines

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

  • Extending this method to other circuit families could reveal which algorithms are most resilient to specific hardware imperfections.
  • Integrating fidelity probes with material characterization data might lead to predictive models for circuit performance before fabrication.
  • This could influence the selection of superconducting materials or interface designs in next-generation quantum processors.

Load-bearing premise

Disparities between simulator and QPU results come mainly from material flaws and interfaces instead of control errors or calibration problems.

What would settle it

Executing the circuits on a superconducting device with significantly improved material quality and checking whether the fidelity gap to simulation narrows as expected.

Figures

Figures reproduced from arXiv: 2506.14075 by Hillol Biswas.

Figure 1
Figure 1. Figure 1: Quantum circuits with 4 qubit: QFT [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Quantum circuits with 4 qubit: GHZ [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Quantum circuits with 4 qubit: W state [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Transpiled Quantum circuits with 4 qubit: QFT [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Transpiled Quantum circuits with 4 qubit: GHZ [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Transpiled Quantum circuits with 4 qubit: W state [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: 4-qubit W state multi-vector plot from statevector before measurement [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: 4-qubit W state multi-vector plot from state vector after measurement [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: 4-qubit QFT state city plot from state vector before measurement [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: This 4-qubit QFT state city plot from statevector after measurement [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: GHZ state – 4 qubit Qsphere from statevector before measurement [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: GHZ state – 4 qubit Qsphere from statevector after measurement [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: 4 Qubit QFT Aer Simulator and IBM Sherbrooke histogram [PITH_FULL_IMAGE:figures/full_fig_p014_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: 4 Qubit GHZ Aer Simulator and IBM Sherbrooke histogram [PITH_FULL_IMAGE:figures/full_fig_p014_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: 4 Qubit W state Aer Simulator and IBM Sherbrooke histogram [PITH_FULL_IMAGE:figures/full_fig_p015_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: QFT, GHZ & W state – 4 to 10 qubits - Different metrices plot on qubit number and values in log scale [PITH_FULL_IMAGE:figures/full_fig_p017_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Different Metrics comparison plot. Based on [PITH_FULL_IMAGE:figures/full_fig_p018_17.png] view at source ↗
read the original abstract

The development of complex circuits for practical applications in the current quantum computing ecosystem is based on basic primitives such as Bell states, which provide superposition, entanglement, and coherence. The range of domain-specific quantum applications has been greatly expanded by the availability of simulators and platforms such as IBM Quantum, which are supported by Qiskit. However, disparities between ideal simulator outputs and actual quantum processing unit (QPU) executions in the Noisy Intermediate-Scale Quantum (NISQ) era require the application of quantum error mitigation techniques. Limitations arise from hardware constraints in superconducting qubit systems and from the limited resources of classical simulators as quantum circuits grow. Quantum decoherence, which lowers gate fidelity and builds up at the circuit level with increasing depth, is specifically caused by material-induced flaws and interfaces. This creates a clear connection between circuit reliability, device performance, and material attributes. To address this, the current work uses both simulation and actual hardware on the IBM Sherbrooke 127-qubit processor to study three basic circuit classes over 4 to 10 qubits: the quantum Fourier transform, the Greenberger-Horne-Zeilinger state, and the W state. The study examines trade-offs between circuit complexity, noise robustness, and resource utilization by contrasting simulator and QPU results. The results imply that circuit fidelity can serve as an indirect probe of material-limited noise, opening the door to a framework for designing quantum circuits that accounts for both hardware and materials to achieve scalable quantum advantage.

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

2 major / 2 minor

Summary. The manuscript compares ideal Qiskit simulations against executions on the IBM Sherbrooke 127-qubit superconducting processor for Quantum Fourier Transform, GHZ, and W-state circuits over 4–10 qubits. It claims that observed fidelity discrepancies arise specifically from material-induced decoherence and interfaces, positioning circuit fidelity as an indirect probe of material-limited noise and proposing a design framework that integrates hardware constraints with material attributes to support scalable quantum advantage.

Significance. If the noise attribution can be rigorously isolated and the quantitative results confirm the scaling behavior, the approach could supply a practical diagnostic linking circuit-level performance to materials properties in superconducting qubits. This would be a modest but useful contribution to NISQ circuit optimization by offering an empirical handle on material noise without requiring separate low-level characterization for every device.

major comments (2)
  1. [Abstract] Abstract: the statement that decoherence 'is specifically caused by material-induced flaws and interfaces' is presented as a premise rather than a conclusion supported by data. No T1/T2 times, randomized-benchmarking error budgets, or gate-calibration metrics are referenced to separate material noise from control-pulse errors, crosstalk, or readout infidelity, leaving the central claim that fidelity serves as a material-noise probe unsubstantiated.
  2. [Results] Results section (comparison of simulator vs. QPU outputs): the abstract describes the experimental setup and the three circuit classes but supplies no numerical fidelity values, error bars, statistical tests, or data-exclusion criteria for the 4–10 qubit runs. Without these, the claimed disparities and their attribution to material noise cannot be evaluated.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'the range of domain-specific quantum applications has been greatly expanded' would benefit from one or two concrete citations to prior Qiskit or IBM Quantum work on these primitives.
  2. [Methods] Methods: clarify how 'resource utilization' is quantified (gate count, depth, or qubit overhead) and whether any error-mitigation techniques were applied to the QPU runs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback. The comments highlight opportunities to strengthen the presentation of our central claims and to improve the quantitative detail in the results. We address each major comment below and indicate the revisions made to the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the statement that decoherence 'is specifically caused by material-induced flaws and interfaces' is presented as a premise rather than a conclusion supported by data. No T1/T2 times, randomized-benchmarking error budgets, or gate-calibration metrics are referenced to separate material noise from control-pulse errors, crosstalk, or readout infidelity, leaving the central claim that fidelity serves as a material-noise probe unsubstantiated.

    Authors: We acknowledge that the original abstract wording presented material-induced decoherence as an established fact rather than a literature-supported premise. In the revised version we have rephrased the statement to read that material defects and interfaces are widely recognized in the superconducting-qubit literature as dominant decoherence channels, and that our circuit-fidelity measurements are intended as an indirect diagnostic of their contribution. We have added three key references on material-loss mechanisms and explicitly note that our study does not isolate material noise from control or readout errors; instead it demonstrates that fidelity trends across circuit families can serve as a practical proxy when full low-level characterization is unavailable. We did not perform independent T1/T2 or randomized-benchmarking runs, as the experimental focus was on end-to-end circuit execution on the same device used for all three circuit classes. revision: partial

  2. Referee: [Results] Results section (comparison of simulator vs. QPU outputs): the abstract describes the experimental setup and the three circuit classes but supplies no numerical fidelity values, error bars, statistical tests, or data-exclusion criteria for the 4–10 qubit runs. Without these, the claimed disparities and their attribution to material noise cannot be evaluated.

    Authors: We agree that explicit numerical results strengthen the manuscript. The revised results section now reports average state fidelities (with standard deviations) for each circuit family at 4, 6, 8, and 10 qubits, obtained from 1024 shots per circuit and averaged over five independent hardware executions. Error bars reflect the observed run-to-run variation. We have added a short paragraph describing the statistical procedure and the data-exclusion rule (runs were discarded only if the device calibration log indicated a >5 % deviation from nominal readout fidelity on the day of execution). These additions allow direct comparison of simulator–QPU discrepancies and support the claim that fidelity degradation scales with circuit depth in a manner consistent with material-limited noise. revision: yes

Circularity Check

0 steps flagged

No significant circularity in empirical comparison

full rationale

The manuscript performs an empirical comparison of ideal simulator outputs against actual executions on the IBM Sherbrooke 127-qubit QPU for QFT, GHZ, and W-state circuits across 4–10 qubits. No derivation chain, equations, fitted parameters presented as predictions, or self-referential definitions appear in the provided text. The central implication—that circuit fidelity can indirectly probe material-limited noise—is an interpretive claim drawn from observed simulator-QPU disparities rather than a mathematical reduction to inputs by construction. The work is self-contained as a standard observational hardware evaluation study without load-bearing self-citations, ansatzes, or uniqueness theorems.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that simulator-QPU differences are dominated by material-induced decoherence; no free parameters or new entities are introduced.

axioms (1)
  • domain assumption Disparities between ideal simulator outputs and actual QPU executions arise specifically from material-induced flaws and interfaces causing decoherence.
    Invoked in the abstract when linking decoherence to material attributes and circuit reliability.

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Forward citations

Cited by 1 Pith paper

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  1. Power Network SCADA Quantum Communications: A Comparison of BB84, B92, E91, and SGS04 Quantum Key Distribution Protocols

    quant-ph 2026-03 unverdicted novelty 2.0

    Simulation-based comparison of BB84, B92, E91, and SARG04 QKD protocols on power-system SCADA datasets indicates a path toward quantum-secured SCADA/PMU networks.

Reference graph

Works this paper leans on

58 extracted references · 58 canonical work pages · cited by 1 Pith paper · 1 internal anchor

  1. [1]

    on the Einstein Podolsky Rosen Paradox,

    J. S. BELL, “on the Einstein Podolsky Rosen Paradox,” John S Bell Found. Quantum Mech., vol. 1, no. 3, pp. 7–12, 2001, doi: 10.1142/9789812386540_0002

    work page doi:10.1142/9789812386540_0002 2001

  2. [2]

    Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels,

    C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels,” vol. 70, no. 13, 1993

    work page 1993

  3. [3]

    The IBM Quantum heavy hex lattice

    P. Nation, H. Paik, A. Cross, and Z. Nazario, “The IBM Quantum heavy hex lattice.” [Online]. Available: https://www.ibm.com/quantum/blog/heavy- hex-lattice

    work page

  4. [4]

    Simple All-Microwave Entangling Gate for Fixed-Frequency Superconducting Qubits,

    J. M. Chow et al., “Simple All-Microwave Entangling Gate for Fixed-Frequency Superconducting Qubits,” Phys. Rev. Lett., vol. 107, no. 8, p. 80502, Aug. 2011, doi: 10.1103/PhysRevLett.107.080502

    work page doi:10.1103/physrevlett.107.080502 2011

  5. [5]

    Quantum-centric supercomputing: a new computational framework for chemistry,

    J. Gambetta, “Quantum-centric supercomputing: a new computational framework for chemistry,” in American Chemical Society (ACS) Spring Meeting, 2025

    work page 2025

  6. [6]

    Quantum computing with Qiskit

    A. Javadi-Abhari et al., “Quantum computing with Qiskit,” pp. 1–19, 2024, [Online]. Available: http://arxiv.org/abs/2405.08810

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  7. [7]

    IBM and PINQ2 unveil utility-scale quantum computer in Québec

    “IBM and PINQ2 unveil utility-scale quantum computer in Québec.” [Online]. Available: https://research.ibm.com/blog/ibm-pinq2-quantum- computer-install

    work page

  8. [8]

    IBM Quantum

    “IBM Quantum.” [Online]. Available: https://quantum.ibm.com/

    work page

  9. [9]

    Simulating Physics with Computers,

    R. P. Feynman, “Simulating Physics with Computers,” vol. 21, pp. 467–488, 1982. 2

    work page 1982

  10. [10]

    Quantum Theory, the Church- Turing Principle and the Universal Quantum Computer,

    D. Deutsch, “Quantum Theory, the Church- Turing Principle and the Universal Quantum Computer,” Proc. R. Soc. Lond. A. Math. Phys. Sci., vol. 400, no. No. 1818(Jul. 8, 1985), pp. 97–117, 1985

    work page 1985

  11. [11]

    Quantum complexity theory,

    E. Bernstein and U. Vaziranit, “Quantum complexity theory,” Proc. Annu. ACM Symp. Theory Comput., vol. Part F1295, pp. 11–20, 1993, doi: 10.1145/167088.167097

    work page doi:10.1145/167088.167097 1993

  12. [12]

    Rapid solution of problems by quantum computation,

    D. Deutsch and R. Jozsa, “Rapid solution of problems by quantum computation,” Proc. R. Soc. London. Ser. A Math. Phys. Sci., vol. 439, no. 1907, pp. 553–558, 1992

    work page 1907

  13. [13]

    Algorithms for Quantum Computation : Discrete Log and Factoring,

    P. W. Shor, T. B. Labs, M. Ave, and M. Hill, “Algorithms for Quantum Computation : Discrete Log and Factoring,” Proc. 35th Annu. Symp. Found. Comput. Sci., p. 124, 1994

    work page 1994

  14. [14]

    Proceedings of the Twenty-Eighth Annual

    L. K. Grover, “A fast quantum mechanical algorithm for database search,” Proc. Annu. ACM Symp. Theory Comput., vol. Part F1294, pp. 212–219, 1996, doi: 10.1145/237814.237866

    work page doi:10.1145/237814.237866 1996

  15. [15]

    On the power of quantum computation,

    D. R. Simon, “On the power of quantum computation,” SIAM J. Comput., vol. 26, no. 5, pp. 1474–1483, 1997, doi: 10.1137/S0097539796298637

    work page doi:10.1137/s0097539796298637 1997

  16. [16]

    Operating Quantum States in Single Magnetic Molecules : Implementation of Grover ’ s Quantum Algorithm,

    C. Godfrin et al., “Operating Quantum States in Single Magnetic Molecules : Implementation of Grover ’ s Quantum Algorithm,” vol. 187702, no. November, pp. 1–5, 2017, doi: 10.1103/PhysRevLett.119.187702

    work page doi:10.1103/physrevlett.119.187702 2017

  17. [17]

    Coherent control of macroscopic quantum states in a single-Cooper-pair box,

    Y . Nakamura, Y . A. Pashkin, and J. S. Tsai, “Coherent control of macroscopic quantum states in a single-Cooper-pair box,” Nature, vol. 398, no. 6730, pp. 786–788, 1999, doi: 10.1038/19718

    work page doi:10.1038/19718 1999

  18. [18]

    Josephson Persistent-Current Qubit,

    J. P. Qubit and C. H. Van Der, “Josephson Persistent-Current Qubit,” 1999

    work page 1999

  19. [19]

    Superconducting circuits for quantum information: An outlook,

    M. H. Devoret and R. J. Schoelkopf, “Superconducting circuits for quantum information: An outlook,” Science (80-. )., vol. 339, no. 6124, pp. 1169–1174, 2013, doi: 10.1126/science.1231930

    work page doi:10.1126/science.1231930 2013

  20. [20]

    Implementing a strand of a scalable fault-tolerant quantum computing fabric,

    J. M. Chow et al., “Implementing a strand of a scalable fault-tolerant quantum computing fabric,” Nat. Commun., vol. 5, pp. 1–9, 2014, doi: 10.1038/ncomms5015

    work page doi:10.1038/ncomms5015 2014

  21. [21]

    AbuGhanem, IBM Quantum Computers: Evolution, Performance, and Future Directions, The Journal of Supercom- puting81, 687 (2025), arXiv:2410.00916 [quant-ph]

    M. AbuGhanem, “IBM Quantum Computers: Evolution, Performance, and Future Directions,” pp. 1–29, 2024, [Online]. Available: http://arxiv.org/abs/2410.00916

    work page arXiv 2024

  22. [22]

    Quantum measurements and the Abelian Stabilizer Problem,

    A. Y . Kitaev, “Quantum measurements and the Abelian Stabilizer Problem,” pp. 1–22, 1995, [Online]. Available: http://arxiv.org/abs/quant- ph/9511026

    work page arXiv 1995

  23. [23]

    An improved quantum Fourier transform algorithm and applications,

    L. Hales and S. Hallgren, “An improved quantum Fourier transform algorithm and applications,” in Proceedings 41st Annual Symposium on Foundations of Computer Science, 2000, pp. 515–

    work page 2000

  24. [24]

    doi: 10.1109/SFCS.2000.892139

    work page doi:10.1109/sfcs.2000.892139 2000

  25. [25]

    Quantum Computer Simulator Based on the Circuit Model of Quantum Computation,

    I. G. Karafyllidis, “Quantum Computer Simulator Based on the Circuit Model of Quantum Computation,” vol. 52, no. 8, pp. 1590–1596, 2005

    work page 2005

  26. [26]

    A quantum Fourier transform (QFT) based note detection algorithm,

    S. Kashani, M. Alqasemi, and J. Hammond, “A quantum Fourier transform (QFT) based note detection algorithm,” pp. 1–36, 2022, [Online]. Available: http://arxiv.org/abs/2204.11775

    work page arXiv 2022

  27. [27]

    Efficient and scalable quantum walk algorithms via the quantum Fourier transform,

    A. Shakeel, “Efficient and scalable quantum walk algorithms via the quantum Fourier transform,” Quantum Inf. Process., vol. 19, no. 9, pp. 1–20, 2020, doi: 10.1007/s11128-020-02834-y

    work page doi:10.1007/s11128-020-02834-y 2020

  28. [28]

    Quantum Fourier Transformation Circuits Compilation,

    Y . Jin et al., “Quantum Fourier Transformation Circuits Compilation,” arXiv Prepr. arXiv2312.16114, 2023

    work page arXiv 2023

  29. [29]

    Quantum Fourier Transform using Dynamic Circuits,

    E. Bäumer, V . Tripathi, A. Seif, D. Lidar, and D. S. Wang, “Quantum Fourier Transform using Dynamic Circuits,” pp. 1–9, 2024, doi: 10.1103/PhysRevLett.133.150602

    work page doi:10.1103/physrevlett.133.150602 2024

  30. [30]

    An improved QFT-based quantum comparator and extended modular arithmetic using one ancilla qubit,

    Y . Yuan et al., “An improved QFT-based quantum comparator and extended modular arithmetic using one ancilla qubit,” New J. Phys., vol. 25, no. 10, pp. 1–10, 2023, doi: 10.1088/1367-2630/acfd52

    work page doi:10.1088/1367-2630/acfd52 2023

  31. [31]

    Springer Nature, Feb

    D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going Beyond Bell’s Theorem,” Bell’ s Theorem, Quantum Theory and Conceptions of the Universe, no. 3, pp. 69–72, 1989, doi: 10.1007/978- 94-017-0849-4_10

    work page doi:10.1007/978- 1989

  32. [32]

    Bell’s theorem without 3 inequalities,

    D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without 3 inequalities,” Am. J. Phys., vol. 58, no. 12, pp. 1131– 1143, Dec. 1990, doi: 10.1119/1.16243

    work page doi:10.1119/1.16243 1990

  33. [33]

    The computational power of the W and GHZ states,

    E. D’Hondt and P. Panangaden, “The computational power of the W and GHZ states,” Quantum Inf. Comput., vol. 6, no. 2, pp. 173–183, 2006, doi: 10.26421/qic6.2-3

    work page doi:10.26421/qic6.2-3 2006

  34. [34]

    Generating and stabilizing the greenberger-horne- zeilinger state in circuit QED: Joint measurement, zeno effect, and feedback,

    W. Feng, P. Wang, X. Ding, L. Xu, and X. Q. Li, “Generating and stabilizing the greenberger-horne- zeilinger state in circuit QED: Joint measurement, zeno effect, and feedback,” Phys. Rev. A - At. Mol. Opt. Phys., vol. 83, no. 4, 2011, doi: 10.1103/PhysRevA.83.042313

    work page doi:10.1103/physreva.83.042313 2011

  35. [35]

    Proposal for generating and detecting multi-qubit GHZ states in circuit QED,

    L. S. Bishop et al., “Proposal for generating and detecting multi-qubit GHZ states in circuit QED,” New J. Phys., vol. 11, pp. 1–9, 2009, doi: 10.1088/1367-2630/11/7/073040

    work page doi:10.1088/1367-2630/11/7/073040 2009

  36. [36]

    Simple loss-tolerant protocol for GHZ-state distribution in a quantum network,

    H. Shimizu, W. Roga, D. Elkouss, and M. Takeoka, “Simple loss-tolerant protocol for GHZ-state distribution in a quantum network,” pp. 3–14, 2024, doi: 10.1103/PhysRevA.111.022624

    work page doi:10.1103/physreva.111.022624 2024

  37. [37]

    Creating and controlling global Greenberger- Horne-Zeilinger entanglement on quantum processors,

    Z. Bao et al., “Creating and controlling global Greenberger- Horne-Zeilinger entanglement on quantum processors,” Nat. Commun., pp. 1–7, 2024, doi: 10.1038/s41467-024-53140-5

    work page doi:10.1038/s41467-024-53140-5 2024

  38. [38]

    Generation and Preservation of Large Entangled States on Physical Quantum Devices,

    J. F. Kam, H. Kang, C. D. Hill, G. J. Mooney, and L. C. L. Hollenberg, “Generation and Preservation of Large Entangled States on Physical Quantum Devices,” pp. 1–26, 2023, [Online]. Available: http://arxiv.org/abs/2312.15170

    work page arXiv 2023

  39. [39]

    Three qubits can be entangled in two inequivalent ways,

    W. Dü, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A, vol. 62, pp. 1–12, 2000, [Online]. Available: https://journals.aps.org/pra/pdf/10.1103/PhysRevA.62. 062314

    work page doi:10.1103/physreva.62 2000

  40. [40]

    Bartlett

    H. Buhrman, M. Folkertsma, B. Loff, and N. M. P. Neumann, “State preparation by shallow circuits using feed forward,” pp. 1–38, 2023, doi: 10.22331/q- 2024-12-09-1552

    work page doi:10.22331/q- 2023

  41. [41]

    Yeh, Scaling W State Circuits in the qudit Clifford Hierarchy, vol

    L. Yeh, Scaling W State Circuits in the qudit Clifford Hierarchy, vol. 1, no. 1. Association for Computing Machinery, 2023. doi: 10.1145/3594671.3594687

    work page doi:10.1145/3594671.3594687 2023

  42. [42]

    A novel integrated quantum circuit for high- order W-state generation and its highly precise characterization,

    R. Heilmann, M. Gräfe, S. Nolte, and A. Szameit, “A novel integrated quantum circuit for high- order W-state generation and its highly precise characterization,” Sci. Bull., vol. 60, no. 1, pp. 96– 100, 2015, doi: 10.1007/s11434-014-0688-5

    work page doi:10.1007/s11434-014-0688-5 2015

  43. [43]

    Deterministic local doubling of W states,

    C. Yesilyurt et al., “Deterministic local doubling of W states,” J. Opt. Soc. Am. B, vol. 33, no. 11, pp. 2313–2319, 2016, doi: 10.1364/JOSAB.33.002313

    work page doi:10.1364/josab.33.002313 2016

  44. [44]

    Implementation of the Quantum Fourier Transform,

    Y . S. Weinstein, M. A. Pravia, E. M. Fortunato, S. Lloyd, and D. G. Cory, “Implementation of the Quantum Fourier Transform,” Phys. Rev. Lett., vol. 86, no. 9, pp. 1889–1891, Feb. 2001, doi: 10.1103/PhysRevLett.86.1889

    work page doi:10.1103/physrevlett.86.1889 2001

  45. [45]

    A 10-Cluster Entanglement Network on IBM’s 127-Qubit Quantum Computer Osaka

    “A 10-Cluster Entanglement Network on IBM’s 127-Qubit Quantum Computer Osaka.”

    work page

  46. [46]

    Implementing Shor’s algorithm on Josephson charge qubits,

    J. J. Vartiainen, A. O. Niskanen, M. Nakahara, and M. M. Salomaa, “Implementing Shor’s algorithm on Josephson charge qubits,” Phys. Rev. A, vol. 70, no. 1, p. 12319, Jul. 2004, doi: 10.1103/PhysRevA.70.012319

    work page doi:10.1103/physreva.70.012319 2004

  47. [47]

    QFT-Layput

    I. Qiskit, “QFT-Layput.” [Online]. Available: https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit. library.QFT

    work page

  48. [48]

    Quantum Approximate Optimization Algorithm : Performance , Mechanism , and Implementation on Near-Term Devices,

    L. Zhou, S. Wang, S. Choi, H. Pichler, and M. D. Lukin, “Quantum Approximate Optimization Algorithm : Performance , Mechanism , and Implementation on Near-Term Devices,” Phys. Rev. X, vol. 10, no. 2, p. 21067, 2020, doi: 10.1103/PhysRevX.10.021067

    work page doi:10.1103/physrevx.10.021067 2020

  49. [49]

    Finding low-energy conformations of lattice protein models by quantum annealing Alejandro,

    A. Perdomo-ortiz, N. Dickson, M. Drew- brook, and G. Rose, “Finding low-energy conformations of lattice protein models by quantum annealing Alejandro,” no. November, 2018

    work page 2018

  50. [50]

    Quantum optimization using a 127-qubit gate-model IBM quantum computer can outperform quantum annealers for nontrivial binary optimization problems

    N. Sachdeva et al., “Quantum optimization using a 127-qubit gate-model IBM quantum computer can outperform quantum annealers for nontrivial binary optimization problems”

    work page

  51. [51]

    Early Fault-Tolerant Quantum Computing,

    A. Katabarwa et al., “Early Fault-Tolerant Quantum Computing,” Phys. Rev. Appl., vol. 10, no. 1, p. 1, 2024, doi: 10.1103/PRXQuantum.5.020101

    work page doi:10.1103/prxquantum.5.020101 2024

  52. [52]

    Pulse-efficient circuit transpilation for 4 quantum applications on cross-resonance-based hardware,

    N. Earnest, C. Tornow, D. J. Egger, and C. Gates, “Pulse-efficient circuit transpilation for 4 quantum applications on cross-resonance-based hardware,” vol. 043088, pp. 1–11, 2021, doi: 10.1103/PhysRevResearch.3.043088

    work page doi:10.1103/physrevresearch.3.043088 2021

  53. [53]

    Reliability Testing, Noise And Error Correction Of Real Quantum Computing Devices,

    I. P. Galanis, I. K. Savvas, A. V . Chernov, and M. A. Butakova, “Reliability Testing, Noise And Error Correction Of Real Quantum Computing Devices,” Telfor J., vol. 13, no. 1, pp. 41–46, 2021, doi: 10.5937/telfor2101041g

    work page doi:10.5937/telfor2101041g 2021

  54. [54]

    Advancements in Quantum Computing— Viewpoint: Building Adoption and Competency in Industry,

    S. M.-L. Pfaendler, K. Konson, and F. Greinert, “Advancements in Quantum Computing— Viewpoint: Building Adoption and Competency in Industry,” Datenbank-Spektrum, vol. 24, no. 1, pp. 5– 20, 2024, doi: 10.1007/s13222-024-00467-4

    work page doi:10.1007/s13222-024-00467-4 2024

  55. [55]

    Benchmarking near-term devices with quantum error correction,

    J. R. Wootton, “Benchmarking near-term devices with quantum error correction,” Quantum Sci. Technol., vol. 5, no. 4, 2020, doi: 10.1088/2058- 9565/aba038

    work page doi:10.1088/2058- 2020

  56. [56]

    Demonstration of a quantum error detection code using a square lattice of four superconducting qubits,

    A. D. Córcoles et al., “Demonstration of a quantum error detection code using a square lattice of four superconducting qubits,” Nat. Commun., vol. 6, 2015, doi: 10.1038/ncomms7979

    work page doi:10.1038/ncomms7979 2015

  57. [57]

    Sensor Signal Malicious Data Binary Classification: A Comparison of QNN, and VQC,

    H. Biswas, “Sensor Signal Malicious Data Binary Classification: A Comparison of QNN, and VQC,” in 2024 IEEE Pune Section International Conference (PuneCon), 2024, pp. 1–6. doi: 10.1109/PuneCon63413.2024.10894827

    work page doi:10.1109/punecon63413.2024.10894827 2024

  58. [58]

    Data Encoding for VQC in Qiskit , A Comparison With Novel Hybrid Encoding

    H. Biswas, “Data Encoding for VQC in Qiskit , A Comparison With Novel Hybrid Encoding”

    work page