Pith. sign in

REVIEW 4 major objections 4 minor 60 references

This paper claims that a cheaply computable noise index can rank quantum circuits by fidelity under hardware noise, and that the required metastable noise structure is present on today's devices.

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 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-03 22:32 UTC pith:XG3QDAXH

load-bearing objection λ_M is a plausible heuristic but not a proven error bound; the real value is the Pauli-support counting and the hardware asymmetry data. the 4 major comments →

arxiv 2511.09821 v2 pith:XG3QDAXH submitted 2025-11-12 quant-ph

Uncovering and Circumventing Noise in Quantum Algorithms via Metastability

Antonio Sannia , Pratik Sathe , Luis Pedro Garc\'ia-Pintos This is my paper
classification quant-ph MSC 81P68 PACS 03.65.Yz03.67.Lx
keywords metastabilitynoise resiliencevariational quantum algorithmsnoise-induced barren plateausadiabatic state preparationquantum annealingPauli twirlingLiouvillian spectrum
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.

Metastability is the observation that noise does not attack all components of a quantum state uniformly: some decay channels relax almost immediately while others persist for a long time. The authors' key claim is that an algorithm's robustness is governed by how its state decomposition overlaps the fast-decaying channels, captured by a single noise vulnerability index λ_M defined as the minimum real part of the summed Liouvillian eigenvalues over the circuit's Pauli modes. They argue that circuits with larger (less negative) λ_M, and fewer modes at the minimum, produce final states closer to the ideal state, and they give an efficient recipe to upper-bound λ_M for stabilizer-initialized, layered circuits without simulating the algorithm. They verify the prediction numerically in variational circuits and analog adiabatic state preparation, and experimentally on superconducting gate processors and quantum annealers, where the symmetry-dependent error asymmetry matches the theory. If the claim holds, noise-aware ansatz selection becomes a practical design rule for near-term hardware, no error correction overhead required.

Core claim

The paper's central claim is that a quantum algorithm's noise sensitivity is governed by the Pauli strings present in its state and how those strings decay under the hardware noise. The index λ_M of Eq. (6) is the minimum real part of the summed Liouvillian eigenvalues over those strings; the authors show that larger (less negative) λ_M means better worst-case fidelity, while the count of strings hitting the minimum separates otherwise-tied circuits. They demonstrate this by counting σ_y-containing strings in hardware-efficient ansatzes (predicting and then observing higher resilience for a=y rotations), by an analytical single-qubit rotation where Y-axis beats X-axis under σ_x-dominated noi

What carries the argument

The noise vulnerability index λ_M (Eq. 6): the minimum over all Pauli-mode paths of the real part of the sum of Liouvillian eigenvalues encountered along the circuit, together with the multiplicity of that minimum. It quantifies worst-case exposure to fast-decaying noise modes. The supporting machinery is the Pauli-string decomposition of the state under Clifford layers (stabilizer support tracking), which lets Algorithm 1 accumulate logarithms of Pauli weights to upper-bound λ_M without simulating non-Clifford layers.

Load-bearing premise

The efficiency claims rest on the state's Pauli support remaining small enough to track (stabilizer input plus non-Clifford gates that do not enlarge the support), and the error bound on the Pauli-twirled, unital Markovian description of the hardware noise being accurate.

What would settle it

Measure fidelity decay under anisotropic Pauli noise (γx≫γy) preparing |1⟩ via an X-rotation versus a Y-rotation over time π; if the Y-rotation does not deliver the higher fidelity, the λ_M ordering is not predictive. Alternatively, run a circuit whose non-Clifford layers provably enlarge the Pauli support; if the upper bound still tracks errors, the support-trackability premise is not the operative mechanism.

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

If this is right

  • Variational circuits can be screened for noise resilience before execution by computing λ̃_M, and the screening predicts the depth at which noise-induced barren plateaus erase the cost landscape.
  • A single-qubit analytical example shows that under σ_x-dominated noise, a Y-rotation achieves final fidelity roughly e^{-2εT} while an X-rotation gives e^{-γx T}, a directly testable ordering.
  • Adiabatic state preparation can be made resilient by choosing initial Hamiltonians whose instantaneous state support avoids the dominant noise strings, with the W-state example quantifying the gain.
  • Because Algorithm 1 never depends on the non-Clifford layers, the framework is compatible with quantum advantage in principle: resilience can be certified without a full classical simulation.
  • Gate-model and annealing hardware benchmarks indicate the symmetry-dependent error asymmetry is present in actual machines, making the design rule immediately actionable.

Where Pith is reading between the lines

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

  • The authors do not discuss using λ̃_M as an optimization target; a natural extension is to include it as a penalty in the classical parameter update of a variational circuit, steering parameters toward metastable regions of the noise spectrum.
  • The support-set trackability assumption is the practical bottleneck; for circuits whose non-Clifford gates do enlarge the Pauli support, one could probe whether truncating low-weight strings preserves the fidelity ranking, a testable approximation for generic ansatzes.
  • The annealing results involve non-unital noise, which the main formal framework excludes; if the symmetry-based predictions hold there, a non-unital generalization of Eq. (6) would likely extend the method to thermalization-dominated hardware.
  • A direct experiment could compare two circuits with identical λ_M but different multiplicities; the theory predicts the one with fewer vulnerable modes decays slower, separating worst-case indexing from average-case behavior.

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

4 major / 4 minor

Summary. The paper introduces a noise-resilience framework based on metastability in open quantum systems. It defines a metric λ_M, the minimum over decay rates of the noise superoperator eigenmodes appearing in the circuit evolution, and claims that this index bounds errors in noisy implementations such that smaller values indicate greater fidelity. The framework is applied to two settings: digital variational quantum algorithms (hardware-efficient ansatze) and analog adiabatic state preparation, supplemented by experiments on IBM superconducting processors and D-Wave annealers. The authors argue that noise-aware algorithm design can exploit metastable noise to achieve intrinsic resilience without full classical simulation, and they propose an efficient classical procedure (Algorithm 1) to upper-bound λ_M under assumptions on stabilizer inputs and Pauli-support tractability.

Significance. If the central claim were established, the paper would offer a practical, efficiently computable criterion for selecting noise-resilient quantum circuits, potentially valuable for NISQ algorithm design. The paper's strengths include explicit analytical examples, a concrete combinatorial analysis in the Supplemental Material, and real-device benchmarks on IBM and D-Wave hardware. However, the central theoretical claim—that λ_M bounds the error between noisy and ideal states—is not supported by the formalism. The metric is defined as a minimum over decay rates and deliberately ignores expansion amplitudes, so it cannot by itself bound trace distance, fidelity, or cost-function error. The paper's own VQA example illustrates this: both ansatze have λ_M = -∞, and the actual discrimination comes from an ad hoc degeneracy count in the Supplemental Material. Consequently, the proposed metric functions as a heuristic for comparing circuit symmetries under specific noise models, but the claimed general error bound is not established. The efficient upper-bound procedure also rests on restrictive assumptions about Pauli-support growth that are not shown to hold for generic variational circuits

major comments (4)
  1. [Sec. III, Eq. (6)] The abstract and Sec. III claim that λ_M 'bounds errors in noisy implementations, with smaller values indicating greater fidelity.' Eq. (6) defines λ_M as the minimum real part of summed Liouvillian eigenvalues over eigenmode sequences, explicitly 'irrespective of the amplitude of its associated eigenvector.' The actual state error in Eq. (5) is a sum of terms α exp(Σλ) r, and a mode with the smallest (most negative) decay rate may have negligible amplitude, while modes with larger decay rates may dominate. No theorem is given connecting λ_M to trace distance or fidelity. As stated, λ_M is a worst-case decay-rate indicator, not an error bound, and the central claim is therefore an overclaim.
  2. [Sec. IV.B and Supplemental Material] The paper's own VQA benchmark contradicts the use of λ_M as a discriminating resilience metric. With q_y=0, both the a=x and a=y ansatze have λ_M → -∞ (Sec. IV.B), so λ_M itself does not separate the circuits. The discrimination is instead made by counting the number of final right eigenvectors corresponding to the minimum, as described in the Supplemental Material. That count also ignores amplitudes (it only tracks support-set membership), and no theorem connects this degeneracy count to the gradient decay, cost error, or fidelity. Thus the claim that 'parameterized circuits that minimize λ_M are also the ones that mitigate NIBPs the most' is not established by the presented analysis.
  3. [Sec. VI, Algorithm 1] The efficient upper-bound procedure assumes that non-Clifford gates 'do not change the set of Pauli strings that generate the qubits state at each layer,' as in the hardware-efficient ansatz. For generic variational circuits with non-Clifford rotations, the Pauli-support set can grow exponentially, so the claimed polynomial-time computability does not extend to the broad class of algorithms suggested in the paper. Moreover, Algorithm 1 returns an upper bound on a decay rate, not on the resulting state error; even if λ̃_M is efficiently computable, it inherits the same amplitude-blindness problem as λ_M. The text should state this limitation explicitly and avoid implying that the procedure certifies fidelity.
  4. [Secs. V and IX] The experimental sections are presented as validation, but the connection to the theoretical metric is loose. In the IBM experiment, the noise parameters q_x=q_z=0.5, q_y=0 are chosen rather than measured or fitted from the device, and no statistical uncertainty or device calibration data are given. In the D-Wave experiment, the paper admits (Sec. IX) that the relevant noise is non-unital, whereas the theoretical framework assumes unital noise; the observed forward/reverse asymmetry is interpreted through symmetry arguments but is not quantitatively linked to λ_M or to the metastability criterion. These experiments illustrate a plausible phenomenon but do not validate the central bound claim.
minor comments (4)
  1. [Sec. VIII.B] Eq. (16) states |1⟩⟨1| = I - σ_z, which is missing the factor 1/2. This appears to be a typo, but it affects the subsequent analytical comparison of fidelities and should be corrected.
  2. [Throughout] There are several typographical errors, e.g., 'Inizialitizing' in Sec. IV.B and 'dicussions' in the Acknowledgements. These should be fixed before publication.
  3. [Sec. VI, Algorithm 1] The naming 'upper bound to noise resilience' is confusing because λ_M is non-positive and larger values (closer to zero) correspond to better resilience. The 'upper bound' is actually an upper bound on the decay rate (or a lower bound on resilience). Clarify the direction of the bound.
  4. [Sec. III, Eq. (5)] The notation α^1_i1 α^2_i1,i2 ... α^L_iL-1,iL is never fully defined recursively; in particular, the action of U_k on a right eigenmatrix r^{k-1} is described only in words. A precise definition of α^k in terms of the biorthogonal basis would improve rigor.

Circularity Check

0 steps flagged

No significant circularity; the noise parameters are chosen, not fitted, and the ansatz comparison follows from the assumed noise model rather than from the measured data, though the claimed fidelity bound is underived.

full rationale

The derivation chain is self-contained. The noise parameters used in the numerical and experimental comparisons are fixed in advance (q_x = q_z = 0.5, q_y = 0 in Sec. IV; gamma_z = sqrt(1/T), gamma_x = gamma_y = 0 in Sec. VIII), not fitted to the IBM or D-Wave results, so the experimental agreement is not a fitted-input-called-prediction artifact. The index lambda_M in Eq. (6) and the supplementary degeneracy count are derived algebraically from the assumed Pauli noise channel and the Pauli-support structure of the circuits; they are not defined in terms of the measured fidelities or cost-function values. The paper itself discloses that lambda_M saturates to -infinity for both hardware-efficient ansatze and that discrimination is delegated to counting the number of final right eigenvectors attaining that minimum (Sec. IV.B and Supplement). This is a post-hoc metric-selection or overclaim concern, not circularity: the count is an additional derived quantity rather than an input, and no parameter is being renamed as a prediction. The self-citations present ([22], [38], [39]) are contextual or contrastive and are not load-bearing; none is used as a uniqueness theorem or to forbid alternative explanations. The abstract's statement that the index 'bounds errors in noisy implementations' is asserted rather than proved, and the neglect of expansion amplitudes in Eq. (5) is a genuine correctness risk, but an unproven bound is not a circular reduction under the criteria used here.

Axiom & Free-Parameter Ledger

2 free parameters · 5 axioms · 0 invented entities

No genuinely new physical entities are introduced. The framework rests on chosen noise models and restrictive circuit-structure assumptions; the experimental 'metastability' claim is not backed by spectral measurements.

free parameters (2)
  • Pauli noise strengths q_x = q_z = 0.5, q_y = 0 = qx=qz=0.5, qy=0
    Chosen anisotropic noise model in the hardware-efficient ansatz numerics (Sec. IV.B, Eq. 7). Setting q_y=0 makes σ_y modes decay infinitely fast, which is what separates the two ansatze; it is not independently measured.
  • Dissipation rates for adiabatic W-state example = γ_z = sqrt(1/T), γ_x = γ_y = 0, T = 100
    Chosen in Sec. VIII to make only σ_z noise act; the contrast between the (z) and (x) initializations depends on this choice.
axioms (5)
  • standard math Noise in each layer is Markovian and the Liouvillian has a spectral decomposition with no exceptional points
    Used throughout (Sec. II, Eq. 2); standard open-quantum-systems assumption, but exceptional points are excluded by fiat.
  • domain assumption The relevant noise channels e^{L_k} are unital
    Sec. III states unitality is assumed so noise drives to I/2^n; the D-Wave section later admits its noise is non-unital, so the framework does not apply there as stated.
  • domain assumption Pauli twirling gives a compact, accurate approximate noise model e^{L_k} ≈ (1−Σp)ρ + Σp PρP with N_k = O(poly(n))
    Sec. VI Eq. (9); needed for efficient λ̃_M but approximate and may miss non-Pauli coherent errors.
  • ad hoc to paper The circuit has stabilizer input, Clifford layers interleaved with non-Clifford gates that do not enlarge the Pauli-support set, and the support set can be tracked classically
    Algorithm 1 precondition (Sec. VI). This excludes general VQAs and is the key restriction making the upper bound efficient.
  • domain assumption The adiabatic theorem remains approximately valid in the simulated noisy evolution and closed-system simulation gives the ideal energy for D-Wave
    Used in Sec. VIII-IX to define Ebar; for open noisy systems the ideal adiabatic state is not the fixed point of the noisy evolution.

pith-pipeline@v1.3.0-alltime-deepseek · 13872 in / 16410 out tokens · 172658 ms · 2026-08-03T22:32:18.295458+00:00 · methodology

0 comments
read the original abstract

The presence of noise is the primary challenge in realizing fault-tolerant quantum computers. In this work, we introduce and experimentally validate a novel strategy to circumvent noise by exploiting the phenomenon of metastability, where a dynamical system exhibits a separation of time scales in its evolution. We demonstrate that if quantum hardware noise exhibits metastability, both digital and analog algorithms can be designed in a noise-aware fashion to achieve intrinsic resilience. We develop a general theoretical framework and introduce an efficiently computable noise vulnerability metric that avoids the need for full classical simulation of the quantum algorithm. We show that the noise vulnerability index bounds errors in noisy implementations, with smaller values indicating greater fidelity between the achieved and target quantum states. We illustrate the use of our framework with applications to variational quantum algorithms and analog adiabatic state preparation. Crucially, we provide experimental evidence supporting the presence of metastable noise in gate-model quantum processors and quantum annealing devices. Thus, we establish that the noise properties in near-term quantum hardware can directly inform practical implementation strategies, enabling the preparation of final noisy states that more closely approximate the ideal ones.

Figures

Figures reproduced from arXiv: 2511.09821 by Antonio Sannia, Luis Pedro Garc\'ia-Pintos, Pratik Sathe.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration contrasting a noise-sensitive [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Ansatz used in the numerical simulations. (b) [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Difference between the observable expectation values [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Fidelity evolution over time for the Adiabatic State [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Annealing schedules implemented in the D-Wave devices. The forward protocol is shown in red, while the [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

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

60 extracted references · 2 canonical work pages

  1. [1]

    Preskill, Quantum Computing in the NISQ era and beyond, Quantum2, 79 (2018)

    J. Preskill, Quantum Computing in the NISQ era and beyond, Quantum2, 79 (2018)

    2018

  2. [2]

    Stilck Fran¸ ca and R

    D. Stilck Fran¸ ca and R. Garc ´ ıa-Patr´ on, Limitations of optimization algorithms on noisy quantum devices, Nat. Phys.17, 1221–1227 (2021)

    2021

  3. [3]

    Z. Cai, R. Babbush, S. C. Benjamin, S. Endo, W. J. Hug- gins, Y. Li, J. R. McClean, and T. E. O’Brien, Quantum error mitigation, Rev. Mod. Phys.95, 045005 (2023)

    2023

  4. [4]

    B. A. W. Brinkman, H. Yan, A. Maffei, I. M. Park, A. Fontanini, J. Wang, and G. La Camera, Metastable dynamics of neural circuits and networks, Applied Physics Reviews9, 10.1063/5.0062603 (2022)

    work page doi:10.1063/5.0062603 2022

  5. [5]

    Langer, Statistical theory of the decay of metastable states, Annals of Physics54, 258–275 (1969)

    J. Langer, Statistical theory of the decay of metastable states, Annals of Physics54, 258–275 (1969)

    1969

  6. [6]

    H¨ anggi, P

    P. H¨ anggi, P. Talkner, and M. Borkovec, Reaction-rate theory: fifty years after Kramers, Rev. Mod. Phys.62, 251–341 (1990)

    1990

  7. [7]

    Tognoli and J

    E. Tognoli and J. A. S. Kelso, The metastable brain, Neuron81, 35–48 (2014)

    2014

  8. [8]

    Macieszczak, M

    K. Macieszczak, M. Gut ¸˘ a, I. Lesanovsky, and J. P. Garra- han, Towards a theory of metastability in open quantum dynamics, Phys. Rev. Lett.116, 240404 (2016)

    2016

  9. [9]

    Y. Wu, S. Kolkowitz, S. Puri, and J. D. Thompson, Era- sure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays, Nat. Commun.13, 10.1038/s41467-022-32094-6 (2022)

    doi:10.1038/s41467-022-32094-6 2022

  10. [10]

    N. Chen, L. Li, W. Huie, M. Zhao, I. Vetter, C. H. Greene, and J. P. Covey, Analyzing the Rydberg-based optical-metastable-ground architecture for 171Yb, Phys. Rev. A105, 10.1103/PhysRevA.105.052438 (2022)

    work page doi:10.1103/physreva.105.052438 2022

  11. [11]

    Darbha, M

    S. Darbha, M. Kornjaˇ ca, F. Liu, J. Balewski, M. R. Hirsbrunner, P. L. S. Lopes, S.-T. Wang, R. Van Beeu- 9 men, K. Klymko, and D. Camps, Long-lived oscillations of metastable states in neutral atom systems, Physi. Rev. B110, 10.1103/physrevb.110.155114 (2024)

    doi:10.1103/physrevb.110.155114 2024

  12. [12]

    D. T. C. Allcock, W. C. Campbell, J. Chiaverini, I. L. Chuang, E. R. Hudson, I. D. Moore, A. Ransford, C. Ro- man, J. M. Sage, and D. J. Wineland, omg blueprint for trapped ion quantum computing with metastable states, App. Phys. Lett.119, 10.1063/5.0069544 (2021)

    doi:10.1063/5.0069544 2021

  13. [13]

    X. Shi, J. Sinanan-Singh, K. DeBry, S. L. Todaro, I. L. Chuang, and J. Chiaverini, Long-lived metastable-qubit memory, Phys. Rev. A111, L020601 (2025)

    2025

  14. [14]

    Labay-Mora, R

    A. Labay-Mora, R. Zambrini, and G. L. Giorgi, Quan- tum associative memory with a single driven-dissipative nonlinear oscillator, Phys. Rev. Lett.130, 190602 (2023)

    2023

  15. [15]

    Labay-Mora, E

    A. Labay-Mora, E. Fiorelli, R. Zambrini, and G. L. Giorgi, Theoretical framework for quantum associative memories, Quantum Sci. Technol.10, 035050 (2025)

    2025

  16. [16]

    Botzung and E

    T. Botzung and E. Fiorelli, Error recovery protocols within metastable decoherence-free subspaces (2025), arXiv:2506.19631 [quant-ph]

    Pith/arXiv arXiv 2025

  17. [17]

    D. A. Lidar and T. A. Brun,Quantum error correction (Cambridge university press, 2013)

    2013

  18. [18]

    B. M. Terhal, Quantum error correction for quantum memories, Rev. Mod. Phys.87, 307 (2015)

    2015

  19. [19]

    D. A. Lidar, I. L. Chuang, and K. B. Whaley, Decoherence-free subspaces for quantum computation, Phys. Rev. Lett.81, 2594 (1998)

    1998

  20. [20]

    D. A. Lidar, Review of decoherence-free subspaces, noise- less subsystems, and dynamical decoupling, Quantum Information and Computation for Chemistry , 295–354 (2014)

    2014

  21. [21]

    Funcke and J

    N. Funcke and J. Berberich, Robustness of optimal quan- tum annealing protocols, New Journal of Physics26, 093040 (2024)

    2024

  22. [22]

    L. P. Garc ´ ıa-Pintos, T. O’Leary, T. Biswas, J. Bringe- watt, L. Cincio, L. T. Brady, and Y.-K. Liu, Re- silience–runtime tradeoff relations for quantum algo- rithms, Rep. Prog. Phys.88, 037601 (2025)

    2025

  23. [23]

    Berberich, D

    J. Berberich, D. Fink, and C. Holm, Robustness of quan- tum algorithms against coherent control errors, Phys. Rev. A109, 012417 (2024)

    2024

  24. [24]

    Berberich, T

    J. Berberich, T. Fellner, R. L. Kosut, and C. Holm, Robustness of quantum algorithms: Worst-case fi- delity bounds and implications for design (2025), arXiv:2509.08481 [quant-ph]

    arXiv 2025

  25. [25]

    Zeng and X.-H

    J. Zeng and X.-H. Deng, Fundamental costs of noise- robust quantum control: Speed limits and complexity (2025), arXiv:2510.07183 [quant-ph]

    arXiv 2025

  26. [26]

    Peruzzo, J

    A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’Brien, A variational eigenvalue solver on a photonic quantum pro- cessor, Nat. Commun.5, 10.1038/ncomms5213 (2014)

    doi:10.1038/ncomms5213 2014

  27. [27]

    Cerezo, A

    M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, and P. J. Coles, Variational quantum algo- rithms, Nature Reviews Physics3, 625–644 (2021)

    2021

  28. [28]

    Farhi, J

    E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, Quantum computation by adiabatic evolution (2000)

    2000

  29. [29]

    Albash and D

    T. Albash and D. A. Lidar, Adiabatic quantum computation, Rev. Mod. Phys.90, 10.1103/RevMod- Phys.90.015002 (2018)

    doi:10.1103/revmod- 2018

  30. [30]

    M. W. Johnson, M. H. S. Amin, S. Gildert, T. Lant- ing, F. Hamze, N. Dickson, R. Harris, A. J. Berkley, J. Johansson, P. Bunyk, E. M. Chapple, C. Enderud, J. P. Hilton, K. Karimi, E. Ladizinsky, N. Ladizinsky, T. Oh, I. Perminov, C. Rich, M. C. Thom, E. Tolkacheva, C. J. S. Truncik, S. Uchaikin, J. Wang, B. Wilson, and G. Rose, Quantum annealing with manu...

    2011

  31. [31]

    Breuer, F

    H.-P. Breuer, F. Petruccione,et al.,The theory of open quantum systems(Oxford University Press on Demand, 2002)

    2002

  32. [32]

    Gorini, A

    V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, Completely positive dynamical semigroups of n-level sys- tems, J. Math. Phys.17, 821 (1976)

    1976

  33. [33]

    Lindblad, On the generators of quantum dynamical semigroups, Commun

    G. Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys.48, 119 (1976)

    1976

  34. [34]

    Minganti, A

    F. Minganti, A. Miranowicz, R. W. Chhajlany, and F. Nori, Quantum exceptional points of non-hermitian Hamiltonians and Liouvillians: The effects of quantum jumps, Phys. Rev. A100, 062131 (2019)

    2019

  35. [35]

    Diehl, A

    S. Diehl, A. Micheli, A. Kantian, B. Kraus, H. P. B¨ uchler, and P. Zoller, Quantum states and phases in driven open quantum systems with cold atoms, Nat. Phys.4, 878–883 (2008)

    2008

  36. [36]

    Verstraete, M

    F. Verstraete, M. M. Wolf, and J. Ignacio Cirac, Quan- tum computation and quantum-state engineering driven by dissipation, Nat. Phys.5, 633–636 (2009)

    2009

  37. [37]

    P. M. Harrington, E. J. Mueller, and K. W. Murch, Engi- neered dissipation for quantum information science, Na- ture Reviews Physics4, 660–671 (2022)

    2022

  38. [38]

    Sannia, R

    A. Sannia, R. Mart ´ ınez-Pe˜ na, M. C. Soriano, G. L. Giorgi, and R. Zambrini, Dissipation as a resource for Quantum Reservoir Computing, Quantum8, 1291 (2024)

    2024

  39. [39]

    Sannia, F

    A. Sannia, F. Tacchino, I. Tavernelli, G. L. Giorgi, and R. Zambrini, Engineered dissipation to mitigate bar- ren plateaus, npj Quantum Inf.10, 10.1038/s41534-024- 00875-0 (2024)

    doi:10.1038/s41534-024- 2024

  40. [40]

    Miet al., Stable quantum-correlated many-body states through engineered dissipation, Science383, 1332 (2024)

    X. Miet al., Stable quantum-correlated many-body states through engineered dissipation, Science383, 1332 (2024)

    2024

  41. [41]

    F. B. Maciejewski, J. Biamonte, S. Hadfield, and D. Venturelli, Improving quantum approximate opti- mization by noise-directed adaptive remapping (2024), arXiv:2404.01412 [quant-ph]

    arXiv 2024

  42. [42]

    S. Wang, E. Fontana, M. Cerezo, K. Sharma, A. Sone, L. Cincio, and P. J. Coles, Noise-induced barren plateaus in variational quantum algorithms, Nat. Commun.12, 10.1038/s41467-021-27045-6 (2021)

    doi:10.1038/s41467-021-27045-6 2021

  43. [43]

    Larocca, S

    M. Larocca, S. Thanasilp, S. Wang, K. Sharma, J. Bia- monte, P. J. Coles, L. Cincio, J. R. McClean, Z. Holmes, and M. Cerezo, Barren plateaus in variational quantum computing, Nature Reviews Physics7, 174–189 (2025)

    2025

  44. [44]

    Emerson, M

    J. Emerson, M. Silva, O. Moussa, C. Ryan, M. Lafor- est, J. Baugh, D. G. Cory, and R. Laflamme, Sym- metrized characterization of noisy quantum processes, Science317, 1893–1896 (2007)

    2007

  45. [45]

    Magesan, J

    E. Magesan, J. M. Gambetta, and J. Emerson, Scalable and robust randomized benchmarking of quantum pro- cesses, Phys. Rev. Lett.106, 180504 (2011)

    2011

  46. [46]

    Cai and S

    Z. Cai and S. C. Benjamin, Constructing smaller pauli twirling sets for arbitrary error channels, Sci. Rep.9, 10.1038/s41598-019-46722-7 (2019)

    doi:10.1038/s41598-019-46722-7 2019

  47. [47]

    Erhard, J

    A. Erhard, J. J. Wallman, L. Postler, M. Meth, R. Stricker, E. A. Martinez, P. Schindler, T. Monz, J. Emerson, and R. Blatt, Characterizing large-scale quantum computers via cycle benchmarking, Nat. Com- 10 mun.10, 10.1038/s41467-019-13068-7 (2019)

    doi:10.1038/s41467-019-13068-7 2019

  48. [48]

    Magesanet al., Efficient measurement of quantum gate error by interleaved randomized benchmarking, Phys

    E. Magesanet al., Efficient measurement of quantum gate error by interleaved randomized benchmarking, Phys. Rev. Lett.109, 080505 (2012)

    2012

  49. [49]

    Gottesman, The Heisenberg representation of quan- tum computers (1998), arXiv:quant-ph/9807006 [quant- ph]

    D. Gottesman, The Heisenberg representation of quan- tum computers (1998), arXiv:quant-ph/9807006 [quant- ph]

    Pith/arXiv arXiv 1998

  50. [50]

    Aaronson and D

    S. Aaronson and D. Gottesman, Improved simulation of stabilizer circuits, Phys. Rev. A70, 052328 (2004)

    2004

  51. [51]

    D¨ ur, G

    W. D¨ ur, G. Vidal, and J. I. Cirac, Three qubits can be entangled in two inequivalent ways, Phys. Rev. A62, 062314 (2000)

    2000

  52. [52]

    Cabello, Bell’s theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states, Phys

    A. Cabello, Bell’s theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states, Phys. Rev. A65, 032108 (2002)

    2002

  53. [53]

    Agrawal and A

    P. Agrawal and A. Pati, Perfect teleportation and su- perdense coding withwstates, Phys. Rev. A74, 062320 (2006)

    2006

  54. [54]

    Kairys, A

    P. Kairys, A. D. King, I. Ozfidan, K. Boothby, J. Ray- mond, A. Banerjee, and T. S. Humble, Simulating the Shastry-Sutherland Ising Model Using Quantum Anneal- ing, PRX Quantum1, 020320 (2020)

    2020

  55. [55]

    A. D. King, C. Nisoli, E. D. Dahl, G. Poulin-Lamarre, and A. Lopez-Bezanilla, Qubit spin ice, Science373, 576 (2021)

    2021

  56. [56]

    A. D. King, A. Nocera, M. M. Rams, J. Dziarmaga, R. Wiersema, W. Bernoudy, J. Raymond, N. Kaushal, N. Heinsdorf, R. Harris, K. Boothby, F. Altomare, M. Asad, A. J. Berkley, M. Boschnak, K. Chern, H. Christiani, S. Cibere, J. Connor, M. H. Dehn, R. Desh- pande, S. Ejtemaee, P. Farre, K. Hamer, E. Hoskinson, S. Huang, M. W. Johnson, S. Kortas, E. Ladizinsky...

    2025

  57. [57]

    Morrell, M

    Z. Morrell, M. Vuffray, S. Misra, and C. Coffrin, Quantu- mAnnealing: A Julia Package for Simulating Dynamics of Transverse Field Ising Models (2024), arXiv:2404.14501

    Pith/arXiv arXiv 2024

  58. [58]

    Marshall, E

    J. Marshall, E. G. Rieffel, and I. Hen, Thermalization, freeze-out, and noise: Deciphering experimental quan- tum annealers, Phys. Rev. Appl.8, 064025 (2017)

    2017

  59. [59]

    Marshall, D

    J. Marshall, D. Venturelli, I. Hen, and E. G. Rieffel, Power of pausing: Advancing understanding of thermal- ization in experimental quantum annealers, Phys. Rev. Appl.11, 044083 (2019)

    2019

  60. [60]

    UNCOVERING AND CIRCUMVENTING NOISE IN QUANTUM ALGORITHMS VIA MET AST ABILITY

    Z. Morrell, M. Vuffray, A. Y. Lokhov, A. B¨ artschi, T. Al- bash, and C. Coffrin, Signatures of open and noisy quan- tum systems in single-qubit quantum annealing, Phys. Rev. Appl.19, 034053 (2023). SUPPLEMENT AL MA TERIAL FOR “UNCOVERING AND CIRCUMVENTING NOISE IN QUANTUM ALGORITHMS VIA MET AST ABILITY” I. NOISE RESILIENCE FOR THE HARDW ARE-EFFICIENT ANS...

    2023