Pith. sign in

REVIEW 3 major objections 5 minor 53 references

This paper argues that twirling noise, the standard first step in error mitigation, degrades variational quantum algorithms, while preserving biased noise such as amplitude damping helps classical optimisers find better solutions.

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 ↗

Twirling amplitude-damping noise into uniform Pauli/depolarising channels reduces expressivity and gradient magnitudes, while preserving the noise bias yields better VQA optimisation in the studied models.

T0 review reviewed 2026-08-04 challenge →

load-bearing objection Solid new formalism for noise in data re-uploading circuits, but the VQE 'twirling hurts' claim is confounded by fixed-point alignment and needs a non-computational-basis Hamiltonian. the 3 major comments →

arxiv 2510.24050 v2 pith:JIVZVVHG submitted 2025-10-28 quant-ph physics.comp-ph

Exploiting biased noise in variational quantum models

Connor van Rossum , Sally Shrapnel , Riddhi Gupta This is my paper
classification quant-ph physics.comp-ph
keywords variational quantum algorithmsquantum noisetwirlingamplitude dampingerror mitigationtrainabilityexpressivityPauli transfer matrix
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.

The reading

Variational quantum algorithms are trained by a classical optimiser, and this paper claims that the structure of hardware noise—not just its strength—determines how well that optimiser works. Using a Fourier/superoperator model of data re-uploading circuits, it shows that uniform Pauli noise shrinks the model's output range and flattens its gradients, whereas amplitude damping's directional bias leaves extra low-frequency structure for the optimiser to exploit; coherent errors can be absorbed entirely into the parameters. Numerically, a three-qubit variational eigensolver for a transverse-field Ising model reaches lower energies under amplitude damping than under its Pauli- or Clifford-twirled equivalents, and the gap grows with noise strength. The paper's conclusion is that noise symmetrisation, a standard error-mitigation step, can be counterproductive in the variational setting. A sympathetic reader would take this as a concrete challenge to re-examine when twirling helps and when it merely destroys exploitable bias.

Core claim

The central claim is that the structure of noise, not just its strength, determines how well a variational quantum model trains. Using Pauli transfer matrices, the paper derives that Pauli-like noise multiplies each Fourier coefficient by an attenuation factor in [0,1], contracting the model's output range and suppressing gradient magnitudes; amplitude damping adds extra low-frequency terms that partially offset this contraction; coherent errors, being unitary, are exactly absorbed into a reparameterised circuit. For VQE with a transverse-field Ising Hamiltonian, the same amplitude damping channel yields lower relative energy error than its Pauli-twirled or Clifford-twirled equivalents, and

What carries the argument

The Pauli transfer matrix (PTM) superoperator representation of alternating unitary and noise channels. It turns the noisy circuit output into a Fourier-like expansion whose frequencies are fixed by the data-encoding Hamiltonian, so noise acts only on the coefficients. In this representation, Pauli noise factors into diagonal attenuation factors in [0,1], amplitude damping introduces additional low-frequency terms from qubit resets, and coherent errors remain unitary so they can be folded into trainable parameters. Twirling appears as the operation that zeroes off-diagonal PTM entries (Pauli twirl) or further averages the diagonal to a depolarising channel (Clifford twirl); the paper uses th

Load-bearing premise

The load-bearing premise is that the VQE advantage of amplitude damping reflects a general mechanism of preserved expressivity and gradients; if instead the advantage comes from the damping channel's fixed point (|0>^n, energy -3 on the benchmark Hamiltonian) aligning with a low-energy computational basis state—while the twirled channels' fixed point (maximally mixed) has energy 0—then the general claim does not follow.

What would settle it

Run the same VQE comparison on a Hamiltonian whose ground state is not close to the all-|0> computational basis state (e.g., the Heisenberg or XY model, or the same Ising chain with the transverse field much larger than the coupling). If amplitude damping no longer outperforms its Pauli- and Clifford-twirled channels at matched noise strengths, the claimed general advantage is an artifact of fixed-point energy alignment rather than a mechanism of biased-noise-assisted optimisation.

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

If this is right

  • Twirling in standard error-mitigation pipelines should be re-evaluated for variational algorithms; symmetrising amplitude damping converts a manageable, biased channel into a uniformly disruptive one that degrades both expressivity and trainability.
  • Coherent errors do not require twirling or mitigation in these models: because they are unitary, they can be absorbed into the trainable parameters via reparameterisation, leaving expressivity and gradients unchanged.
  • The paper links the amplitude-damping benefit to noise-induced shallow-circuit behaviour, which suppresses barren plateaus; this suggests the benefit should grow with circuit depth.
  • Ansatz design interacts strongly with noise bias: swapping the X- and Z-rotation axes reverses which Pauli noise axis is most damaging, so noise-aware circuit design can be used to align the ansatz with the hardware's dominant bias.
  • VQE performance under non-unital noise degrades far more slowly than under its twirled equivalents, and even reversed (non-physical) amplitude damping outperforms both twirls, indicating the effect is about preserving directional structure rather than the specific direction.

Where Pith is reading between the lines

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

  • The VQE benchmark may partly confound the mechanism: amplitude damping's fixed point (all qubits in |0>) carries energy -3 on the Ising Hamiltonian used, while the twirled channels' fixed point (maximally mixed) has energy 0; an optimiser could be 'exploiting' the damping simply by sliding toward a low-energy computational-basis state. Testing a Hamiltonian whose ground state is not computational-
  • If the advantage survives such tests, the practical upshot is that randomised compiling and Pauli twirling may need to be replaced by bias-preserving noise tailoring, and ansatz axis choice becomes a design parameter: the paper shows swapping X- and Z-rotations reverses which Pauli noise axis is most harmful.
  • A cleaner control than reversed amplitude damping would be a non-unital channel whose fixed point is orthogonal to the computational basis (e.g., a rotation of the damping axis); both twirls of reversed AD coincide with twirls of standard AD, so the existing control still cannot disentangle fixed-point energy from directional gradient effects.
  • These results suggest a new division of labour in error mitigation: instead of symmetrising noise first, one could let the classical optimiser absorb structured noise and reserve mitigation for the residual, more uniform component—an idea the paper gestures at when calling for metrics that separate optimiser-outsourced error mitigation from protocol-removed noise.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper studies how different noise models affect variational quantum algorithms (VQAs). It develops a Pauli-transfer-matrix / Fourier framework for data-re-uploading circuits, analytically showing that diagonal Pauli noise attenuates Fourier coefficients and gradient magnitudes, while amplitude damping introduces additional lower-frequency terms that partially preserve expressivity and trainability. It also claims that coherent unitary errors can be absorbed by reparameterization. Numerically, for a 3-qubit transverse-field Ising VQE, it compares amplitude damping with Pauli- and Clifford-twirled equivalents and finds that the non-unital amplitude-damping channel yields lower-energy solutions. The paper concludes that noise twirling—standard in error mitigation—can degrade variational performance, and that preserving noise bias can be beneficial.

Significance. If the broad claim were established, the paper would challenge conventional noise-symmetrization pipelines for VQAs and motivate bias-preserving circuit designs. The analytic PTM/Fourier treatment of noisy data-reuploading circuits, especially the attenuation factors in Eqs. (22)–(24), is a useful and clean contribution. However, the paper's central VQE evidence is confounded by fixed-point energy alignment between the noise channel and the problem Hamiltonian, so the general conclusion that 'preserving biased noise helps classical optimisers find better solutions' is not currently supported by the numerical experiments. The paper is internally consistent for the models studied, but the scope of the abstract claim exceeds what the evidence establishes.

major comments (3)
  1. [Section II.B, Eq. (13), Fig. 4(c)] The VQE advantage of amplitude damping over its Pauli- and Clifford-twirled versions is confounded by the fixed-point energy of the noise channels. For H = -J∑Z_i Z_{i+1} - h∑X_i with J=1, h=0.5, the amplitude-damping channel has fixed point |000⟩, whose energy is -3, only ~7% above the true ground-state energy E0=-3.232. The Pauli- and Clifford-twirled channels are unital and have the maximally mixed state as their fixed point, with energy 0. Thus the observation that amplitude damping 'maintains strong performance' while twirled channels decay toward zero may simply reflect the energy of the noise channel's fixed point, not a mechanism by which non-unital noise biases the optimiser toward good solutions. The reversed-AD control in Sec. B4 does not remove this confound, because |111⟩ also has energy -3 for this Hamiltonian. To support the general claim, the authors should test a Hamilto
  2. [Abstract; Section II.A; Section II.B, Fig. 4(c)] The statement that coherent errors are 'fully mitigated by re-parameterisation' is too strong as stated. The analytic argument that coherent noise can be absorbed into the trainable parameters relies on the assumption that each W^(l) is an arbitrary unitary (Sec. IV, Eq. (16)), an assumption the authors themselves relax in the Discussion. In the VQE setting, the ansatz is a fixed Trotter circuit with restricted expressibility, and coherent errors injected after each two-qubit gate cannot generally be absorbed into the available single-qubit rotation parameters. The numerical VQE result that coherent noise 'shows no observable degradation' therefore needs either a proof for the restricted ansatz or a clear caveat. As written, the abstract and Section II present the unrestricted result as if it applied to the VQE experiments, which is misleading.
  3. [Section IV, 'Pauli noise modified form'; Section II.B] The comparison between amplitude damping and its twirled counterparts is designed to match the diagonal PTM of the original channel, but the resulting channels have different fixed points. This makes it impossible to attribute the observed performance differences specifically to the removal of noise bias by twirling: the twirled channels are also changing the asymptotic state of the circuit. A fair test of the paper's thesis requires either (i) comparing noise channels that have the same fixed point (or the same fixed-point energy) but different degrees of bias, or (ii) demonstrating that the performance ordering persists when the Hamiltonian is rotated so that the computational-basis fixed point of amplitude damping is not close to the ground state. Without such a control, the central conclusion that 'twirling degrades variational performance' is not cleanly separated from a trivial fix
minor comments (5)
  1. [Section II.A, Section IV, Eq. (25)] The text repeatedly states that noise 'does not alter the frequency spectrum.' For amplitude damping, however, Eq. (25) involves truncated index sequences j' that effectively add lower-frequency contributions associated with shorter effective circuit depth. The statement should be qualified to refer to the ideal data-encoding frequencies, with the caveat that non-unital noise introduces additional lower-frequency terms.
  2. [Appendix B.4, Fig. 7] The reversed-AD control is described as a probe of noise directionality, but for the Hamiltonian in Eq. (13), |111⟩ also has energy -3, just like |000⟩. The text should explicitly note this and justify why the reversed-AD result is not itself explained by fixed-point energy alignment.
  3. [Fig. 3 and Fig. 5] The boxplot figures report only absolute gradient magnitudes. Since the main trainability claim concerns the shape of the gradient distribution, it would strengthen the presentation to report quantiles or variance explicitly, particularly because the boxplots at different noise strengths are visually similar at low gamma.
  4. [Eq. (24)] The definition of n_ω(θ) uses a denominator that is a sum of coefficients; it should be stated that the denominator is assumed nonzero, or a limiting convention should be given for cases where the ideal coefficient sum is zero.
  5. [Section V] The data and code availability statement says materials 'will be made publicly available at time of publishing.' Given the empirical nature of the main VQE claim, providing the code and data with the submission would improve verifiability. The current statement is weaker than the reproducibility standard typical for numerical papers in this area.

Circularity Check

1 steps flagged

VQE 'advantage' of amplitude damping over twirled channels is partially forced by fixed-point energy alignment with the chosen Ising Hamiltonian, not by the proposed optimisation mechanism.

specific steps
  1. other [Section II B / Fig. 4(c), Eq. (13); Appendix A 5a, Eqs. (A31)-(A32)]
    "As the noise strength increases, the quality of the VQE solutions deteriorates, with the estimated energies drifting away from the true ground-state value and approaching zero. ... Amplitude damping generally maintains strong performance ... In contrast, both Pauli-twirled and Clifford-twirled versions of amplitude damping exhibit exponential decay in solution quality."

    The comparison is set up so that the high-noise outcome is fixed by the channel fixed points. For Eq. (13) with J=1, h=0.5, |000> has energy -3 (E0=-3.232), while the unital twirled channels (A32) have fixed point I/8 with energy 0. The non-unital term in the AD PTM (A31) forces rho to |0> as gamma grows, so the AD energy is driven toward -3, whereas the twirled energies are driven to 0. Thus the observed 'advantage' is a predetermined consequence of choosing a Hamiltonian whose computational basis is near-degenerate with the ground state, not evidence that the optimiser exploits a richer gradient profile; the attribution to 'biased noise profiles preserve a richer gradient profile' is not tested by this experiment. The reversed-AD control (whose |111> fixed point also has energy -3) does

full rationale

The Fourier/PTM analysis of data re-uploading circuits is self-contained: Eqs. (22)-(25) derive coefficient attenuation from the PTM and the amplitude-damping reset structure, and the coherent-error reparameterisation follows from unitary closure with a stated restriction on arbitrary W. No load-bearing argument rests on self-citation; refs. [21,27,28] are contextual. The circularity concern is confined to the VQE pillar: because the Hamiltonian and the noise channels are chosen independently, the energy ordering at large noise is essentially the fixed-point energy ordering, so the headline 'non-unital noise yields lower-energy states' is partially equivalent to the construction rather than a test of the proposed training mechanism. Score 6 reflects partial, not total, circularity: the QML gradient/expressivity results and coherent-error mitigation retain independent content.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The central claim rests on the Fourier decomposition of data re-uploading circuits, a blockwise noise model, and the equivalence construction for twirled channels. The VQE comparison additionally depends on the choice of Hamiltonian and noise injection points; these choices can materially change which noise profile appears beneficial.

free parameters (5)
  • ADAM hyperparameters per depth = Table I (lr 0.03-0.30, beta1 0.45-0.75, beta2 0.90-0.99, steps 100-3000)
    Selected via Bayesian optimisation targeting convergence on representative target functions; the optimiser settings can affect which noise channel appears easier to train.
  • Expressivity threshold epsilon and training budget = epsilon=1e-5; 150 steps for L=2
    Hand-chosen thresholds; the reported 'maximum learnable range' depends on them, so cross-noise comparisons are threshold-dependent.
  • VQE Hamiltonian parameters J, h = J=1.0, h=0.5
    Benchmark choice; the ground state is close to the computational-basis states |000>/|111>, which is important for the amplitude-damping comparison.
  • Target function coefficient bounds = not specified ('bounded range')
    The training data distribution is not fully defined, affecting expressivity measurements.
  • Noise injection points = after each two-qubit gate; single-qubit gates noiseless
    Assumed noise placement; if single-qubit gates are noisy the relative performance could change.
axioms (5)
  • standard math Data re-uploading circuits with L layers admit a truncated Fourier series with frequencies fixed by eigenvalues of the encoding Hamiltonian
    Invoked in Sec II.A and IV from Schuld et al. [36]; treated as background.
  • domain assumption Noise is modelled as interleaved channels after each S and W block (Eq. 19)
    Acknowledged simplification in Sec III; real noise can act within blocks and interact with parameterised gates.
  • domain assumption Each trainable block W^(l) is an arbitrary unitary
    Used for coherent-error reparameterisation; Sec III concedes most hardware ansatze are restricted, so coherent errors may escape the expressible subspace.
  • standard math The noiseless circuit with degree matching can achieve zero loss
    From [36]; used to attribute nonzero loss to noise and optimisation.
  • domain assumption Twirled channels are represented by exact equivalent Pauli/depolarising channels without sampling overhead
    Acknowledged in Sec III; physical twirling adds sampling noise and may reduce the observed advantage.

reviewed 2026-08-04 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Exploiting biased noise in variational quantum models." pith.science (2026). https://pith.science/paper/JIVZVVHG

@misc{pith2026251024050,
  author       = {Pith},
  title        = {Pith review of: Exploiting biased noise in variational quantum models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JIVZVVHG}},
  note         = {Machine review of arXiv:2510.24050}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Variational quantum algorithms (VQAs) are promising tools for demonstrating quantum utility on near-term quantum hardware, with applications in optimisation, quantum simulation, and machine learning. While researchers have studied how easy VQAs are to train, the effect of quantum noise on the classical optimisation process is still not well understood. Contrary to expectations, we find that twirling, which is commonly used in standard error-mitigation strategies to symmetrise noise, actually degrades performance in the variational setting, whereas preserving biased or non-unital noise can help classical optimisers find better solutions. Analytically, we study a universal quantum regression model and demonstrate that relatively uniform Pauli channels suppress gradient magnitudes and reduce expressivity, making optimisation more difficult. Conversely, asymmetric noise such as amplitude damping or biased Pauli channels introduces directional bias that can be exploited during optimisation. Numerical experiments on a variational eigensolver for the transverse-field Ising model confirm that non-unital noise yields lower-energy states compared to twirled noise. Finally, we show that coherent errors are fully mitigated by re-parameterisation. These findings challenge conventional noise-mitigation strategies and suggest that preserving noise biases may enhance VQA performance.

Figures

Figures reproduced from arXiv: 2510.24050 by Connor van Rossum, Riddhi Gupta, Sally Shrapnel.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Sampled data points from a degree-three truncated Fourier series, used as the target function for supervised [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Impact of noise on model expressivity. (a) Out [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Effect of noise on gradient magnitudes during training. Box plots show distributions of absolute gradients [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Overview of the VQE setup and the impact of noise [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Effect of noise on gradient magnitudes during training. Box plots show the distribution of absolute gradient values, [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Effect of biased Pauli noise on model expressiv [PITH_FULL_IMAGE:figures/full_fig_p015_6.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

53 extracted references · 36 linked inside Pith

  1. [1]

    A d×ddensity operator in ad-dimensional Hilbert space be- comes ad 2-dimensional vector in Hilbert–Schmidt space, and ˆΛ is ad 2 ×d 2 matrix acting in that space

    Superoperator Dual and Expectation V alues It is often useful to represent a quantum channel Λ as a superoperator ˆΛ acting on vectorised density matrices: |ρ⟩⟩ → |ρ′⟩⟩= ˆΛ|ρ⟩⟩,(A1) where|ρ⟩⟩is the vectorisation of the density matrixρ. A d×ddensity operator in ad-dimensional Hilbert space be- comes ad 2-dimensional vector in Hilbert–Schmidt space, and ˆΛ ...

  2. [2]

    Derivations of Channel Representations We provide here the full derivation of the channel representations used in Section IV, including the Liou- ville superoperator form and the Pauli Transfer Matrix (PTM) transformation. a. Liouville Superoperator Form Consider a unitary operator of the formU(x) =e −ixH , whereHis a Hermitian operator. The corresponding...

  3. [3]

    Derivations for Ideal Quantum Models We provide here the full derivation of the Fourier co- efficients and gradient expressions for the ideal quantum model introduced in Section IV. a. Fourier Coefficients The coefficientsa j,u,v are given by: aj,u,v(θ) = [⟨⟨M|] uL+1 ˆW (L+1) uL+1vL (θ)VvLjL V † jLuL ˆW (L) uLvL−1 (θ)· · ·Vv2j2 V † j2u2 ˆW (2) u2v1 (θ)Vv1...

  4. [4]

    Derivations for Noisy Quantum Models This appendix provides detailed derivations for the ex- pressions used in Section II, including gradient expres- sions under different noise models. a. Pauli Noise The gradient of the output with respect to a parameter θi is: ∂ ˜f ∂θi (x,θ) =d X j eixΛj X u,v ∂˜aj,u,v ∂θi (θ),(A18) where ∂˜aj,u,v ∂θi (θ) =n unv ∂aj,u,v...

  5. [5]

    Resultant Channels from Twirling We examine the effect of Pauli twirling on the PTM of a single qubit channel ˆR, ˆR− →1 4 X i ˆP † i ˆR ˆPi,(A25) where ˆPi are the PTM representations of the Pauli oper- ators, ˆI=   1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1   , ˆX=   1 0 0 0 0 1 0 0 0 0−1 0 0 0 0−1   , ˆY=   1 0 0 0 0−1 0 0 0 0 1 0 0 0 0−1   , ˆZ...

  6. [6]

    Data Reuploading Model Configuration In all data reuploading circuit simulations in the main text, circuits are initialised on the ground state,|0⟩, and measured in theZbasis

    Simulation Details a. Data Reuploading Model Configuration In all data reuploading circuit simulations in the main text, circuits are initialised on the ground state,|0⟩, and measured in theZbasis. Each trainable blockW l(θ) is implemented as a sequence of three single-qubit rota- tions: a Z-rotation byθ i, followed by a Y-rotation by θi+1, and another Z-...

  7. [7]

    Specifically, we compare Pauli-twirled amplitude damping with Clifford- twirled amplitude damping, using the same experimental setup described in Fig

    Gradient Distributions under Twirled Amplitude Damping To complement the analysis in the main text, we ex- amine the effect of twirled amplitude damping noise on gradient magnitudes during training. Specifically, we compare Pauli-twirled amplitude damping with Clifford- twirled amplitude damping, using the same experimental setup described in Fig. 5. TABL...

  8. [8]

    Biased Pauli Noise In this section, we extend our investigation beyond the twirled amplitude noise considered in the main text, fo- cusing instead on the effects of biased Pauli noise chan- nels on supervised learning performance. Here, biased refers to the non-uniformity of the noise; specifically, noise that acts along a single Pauli axis (X,Y, orZ), as...

  9. [9]

    Specifically, rather than relaxing from the excited state|1⟩to the ground state 15 (a) (b) FIG

    VQE: Reversing Directional Noise To further explore the sensitivity of variational quan- tum algorithms to the structure of noise, we consider a non-physical variant of amplitude damping in which the direction of decay is reversed. Specifically, rather than relaxing from the excited state|1⟩to the ground state 15 (a) (b) FIG. 6. Effect of biased Pauli noi...

  10. [10]

    Preskill, Quantum Computing in the NISQ era and beyond, Quantum2, 79 (2018), arXiv:1801.00862 [quant- ph]

    J. Preskill, Quantum Computing in the NISQ era and beyond, Quantum2, 79 (2018), arXiv:1801.00862 [quant- ph]

    Pith/arXiv arXiv 2018

  11. [11]

    Cerezo, A

    M. Cerezo, A. Arrasmith, R. Babbush, S. C. Ben- jamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, and P. J. Coles, Variational Quan- tum Algorithms, Nature Reviews Physics3, 625 (2021), arXiv:2012.09265 [quant-ph]

    Pith/arXiv arXiv 2021

  12. [12]

    Tilly, H

    J. Tilly, H. Chen, S. Cao, D. Picozzi, K. Setia, Y. Li, E. Grant, L. Wossnig, I. Rungger, G. H. Booth, and J. Tennyson, The Variational Quantum Eigensolver: A review of methods and best practices, Physics Reports 16 986, 1 (2022), arXiv:2111.05176 [quant-ph]

    Pith/arXiv arXiv 2022

  13. [13]

    M. P. Harrigan, K. J. Sung, M. Neeley, K. J. Satzinger, F. Arute, K. Arya, J. Atalaya, J. C. Bardin, R. Barends, S. Boixo, M. Broughton, B. B. Buckley, D. A. Buell, B. Burkett, N. Bushnell, Y. Chen, Z. Chen, B. Chiaro, R. Collins, W. Courtney, S. Demura, A. Dunsworth, D. Eppens, A. Fowler, B. Foxen, C. Gidney, M. Giustina, R. Graff, S. Habegger, A. Ho, S....

    Pith/arXiv arXiv 2021

  14. [14]

    Amaro, M

    D. Amaro, M. Rosenkranz, N. Fitzpatrick, K. Hirano, and M. Fiorentini, A case study of variational quantum algorithms for a job shop scheduling problem, EPJ Quan- tum Technology9, 5 (2022), arXiv:2109.03745 [quant- ph]

    Pith/arXiv arXiv 2022

  15. [16]

    Kandala, A

    A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, Hardware- efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets, Nature549, 242 (2017), arXiv:1704.05018 [quant-ph]

    Pith/arXiv arXiv 2017

  16. [17]

    Kokail, C

    C. Kokail, C. Maier, R. van Bijnen, T. Brydges, M. K. Joshi, P. Jurcevic, C. A. Muschik, P. Silvi, R. Blatt, C. F. Roos, and P. Zoller, Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model, Nature569, 355 (2019), arXiv:1810.03421 [quant-ph]

    Pith/arXiv arXiv 2019

  17. [18]

    Arute, K

    F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, S. Boixo, M. Broughton, B. B. Buck- ley, D. A. Buell, B. Burkett, N. Bushnell, Y. Chen, Z. Chen, B. Chiaro, R. Collins, W. Courtney, S. De- mura, A. Dunsworth, D. Eppens, E. Farhi, A. Fowler, B. Foxen, C. Gidney, M. Giustina, R. Graff, S. Habeg- ger, M. P. Harrigan, A. Ho, S. Hong, T. Huan...

    Pith/arXiv arXiv 2020

  18. [19]

    Huang, X

    K. Huang, X. Cai, H. Li, Z.-Y. Ge, R. Hou, H. Li, T. Liu, Y. Shi, C. Chen, D. Zheng, K. Xu, Z.-B. Liu, Z. Li, H. Fan, and W.-H. Fang, Variational Quantum Compu- tation of Molecular Linear Response Properties on a Su- perconducting Quantum Processor, The Journal of Phys- ical Chemistry Letters13, 9114 (2022), arXiv:2201.02426 [quant-ph]

    Pith/arXiv arXiv 2022

  19. [20]

    L. Zhao, J. Goings, K. Wright, J. Nguyen, J. Kim, S. Johri, K. Shin, W. Kyoung, J. I. Fuks, J.-K. K. Rhee, and Y. M. Rhee, Orbital-optimized pair-correlated electron simulations on trapped-ion quantum computers, npj Quantum Information9, 60 (2023), arXiv:2212.02482 [quant-ph]

    Pith/arXiv arXiv 2023

  20. [21]

    N. E. Belaloui, A. Tounsi, R. A. Khamadja, M. M. Louamri, A. Benslama, D. E. B. Neira, and M. T. Rouabah, Ground State Energy Estimation on Current Quantum Hardware Through The Variational Quan- tum Eigensolver: A Comprehensive Study (2024), arXiv:2412.02606 [quant-ph]

    Pith/arXiv arXiv 2024

  21. [22]

    Z. Han, C. Lyu, Y. Zhou, J. Yuan, J. Chu, W. Nuerbolati, H. Jia, L. Nie, W. Wei, Z. Yang, L. Zhang, Z. Zhang, C.- K. Hu, L. Hu, J. Li, D. Tan, A. Bayat, S. Liu, F. Yan, and D. Yu, Multi-Level Variational Spectroscopy using a Programmable Quantum Simulator, Physical Review Research6, 013015 (2024), arXiv:2306.02110 [quant-ph]

    Pith/arXiv arXiv 2024

  22. [23]

    Havlicek, A

    V. Havlicek, A. D. C´ orcoles, K. Temme, A. W. Harrow, A. Kandala, J. M. Chow, and J. M. Gambetta, Super- vised learning with quantum enhanced feature spaces, Nature567, 209 (2019), arXiv:1804.11326 [quant-ph]

    Pith/arXiv arXiv 2019

  23. [24]

    Fontana, N

    E. Fontana, N. Fitzpatrick, D. M. Ramo, R. Duncan, and I. Rungger, Evaluating the noise resilience of vari- ational quantum algorithms, Physical Review A104, 022403 (2021), arXiv:2011.01125 [quant-ph]

    Pith/arXiv arXiv 2021

  24. [25]

    Singkanipa and D

    P. Singkanipa and D. A. Lidar, Beyond unital noise in variational quantum algorithms: Noise-induced bar- ren plateaus and limit sets, Quantum9, 1617 (2025), arXiv:2402.08721 [quant-ph]

    Pith/arXiv arXiv 2025

  25. [26]

    J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Bab- bush, and H. Neven, Barren plateaus in quantum neural network training landscapes, Nature Communications9, 10.1038/s41467-018-07090-4 (2018)

    doi:10.1038/s41467-018-07090-4 2018

  26. [27]

    Ragone, B

    M. Ragone, B. N. Bakalov, F. Sauvage, A. F. Kemper, C. O. Marrero, M. Larocca, and M. Cerezo, A Lie Al- gebraic Theory of Barren Plateaus for Deep Parame- terized Quantum Circuits, Nature Communications15, 7172 (2024), arXiv:2309.09342 [quant-ph]

    Pith/arXiv arXiv 2024

  27. [28]

    E. R. Anschuetz and B. T. Kiani, Quantum variational algorithms are swamped with traps, Nature Communica- tions13, 10.1038/s41467-022-35364-5 (2022)

    doi:10.1038/s41467-022-35364-5 2022

  28. [29]

    E. R. Anschuetz, A Unified Theory of Quantum Neu- ral Network Loss Landscapes (2025), arXiv:2408.11901 [quant-ph]

    Pith/arXiv arXiv 2025

  29. [30]

    L. J. Henderson, K. Beer, S. Karuvade, R. Gupta, A. White, and S. Shrapnel, Quantum advantage without exponential concentration: Trainable kernels for symmetry-structured data (2025), arXiv:2509.14337 [quant-ph]

    arXiv 2025

  30. [31]

    C.-Y. Park, M. Kang, and J. Huh, Hardware-efficient ansatz without barren plateaus in any depth (2024), arXiv:2403.04844 [quant-ph]

    Pith/arXiv arXiv 2024

  31. [32]

    Cincio, K

    L. Cincio, K. Rudinger, M. Sarovar, and P. J. Coles, Ma- chine learning of noise-resilient quantum circuits (2021), arXiv:2007.01210 [quant-ph]

    Pith/arXiv arXiv 2021

  32. [33]

    Y. Du, T. Huang, S. You, M.-H. Hsieh, and 17 D. Tao, Quantum circuit architecture search for varia- tional quantum algorithms, npj Quantum Information 8, 10.1038/s41534-022-00570-y (2022), arXiv:2010.10217 [quant-ph]

    Pith/arXiv arXiv 2022

  33. [34]

    Temme, S

    K. Temme, S. Bravyi, and J. M. Gambetta, Error mitiga- tion for short-depth quantum circuits, Physical Review Letters119, 180509 (2017), arXiv:1612.02058 [quant-ph]

    Pith/arXiv arXiv 2017

  34. [35]

    van den Berg, Z

    E. van den Berg, Z. K. Minev, A. Kandala, and K. Temme, Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors, Na- ture Physics19, 1116 (2023), arXiv:2201.09866 [quant- ph]

    Pith/arXiv arXiv 2023

  35. [36]

    R. S. Gupta, E. van den Berg, M. Takita, D. Riste, K. Temme, and A. Kandala, Probabilistic error cancellation for dynamic quantum circuits (2023), arXiv:2310.07825 [quant-ph]

    Pith/arXiv arXiv 2023

  36. [37]

    R. S. Gupta, S. Karuvade, K. Beer, L. J. Hender- son, and S. Shrapnel, Characterizing noisy quantum computation with imperfectly addressed errors (2025), arXiv:2508.03261 [quant-ph]

    Pith/arXiv arXiv 2025

  37. [38]

    L. C. G. Govia, S. Majumder, S. V. Barron, B. Mitchell, A. Seif, Y. Kim, C. J. Wood, E. J. Pritchett, S. T. Merkel, and D. C. McKay, Bounding the systematic er- ror in quantum error mitigation due to model violation (2024), arXiv:2408.10985 [quant-ph]

    Pith/arXiv arXiv 2024

  38. [39]

    Y. Quek, D. S. Fran¸ ca, S. Khatri, J. J. Meyer, and J. Eis- ert, Exponentially tighter bounds on limitations of quan- tum error mitigation, Nature Physics20, 1648 (2024), arXiv:2210.11505 [quant-ph]

    Pith/arXiv arXiv 2024

  39. [40]

    Hashim, R

    A. Hashim, R. K. Naik, A. Morvan, J.-L. Ville, B. Mitchell, J. M. Kreikebaum, M. Davis, E. Smith, C. Iancu, K. P. O’Brien, I. Hincks, J. J. Wallman, J. Emerson, and I. Siddiqi, Randomized compiling for scalable quantum computing on a noisy superconduct- ing quantum processor, Physical Review X11, 041039 (2021), arXiv:2010.00215 [quant-ph]

    Pith/arXiv arXiv 2021

  40. [41]

    Layden, B

    D. Layden, B. Mitchell, and K. Siva, Theory of quan- tum error mitigation for non-Clifford gates (2025), arXiv:2403.18793 [quant-ph]

    arXiv 2025

  41. [42]

    D¨ ur, M

    W. D¨ ur, M. Hein, J. I. Cirac, and H.-J. Briegel, Stan- dard forms of noisy quantum operations via depolariza- tion, Physical Review A72, 052326 (2005), arXiv:quant- ph/0507134

    arXiv 2005

  42. [43]

    Emerson, R

    J. Emerson, R. Alicki, and K. Zyczkowski, Scalable Noise Estimation with Random Unitary Operators, Journal of Optics B: Quantum and Semiclassical Optics7, S347 (2005), arXiv:quant-ph/0503243

    Pith/arXiv arXiv 2005

  43. [44]

    Dankert, R

    C. Dankert, R. Cleve, J. Emerson, and E. Livine, Ex- act and Approximate Unitary 2-Designs: Constructions and Applications, Physical Review A80, 012304 (2009), arXiv:quant-ph/0606161

    Pith/arXiv arXiv 2009

  44. [45]

    Schuld, R

    M. Schuld, R. Sweke, and J. J. Meyer, The effect of data encoding on the expressive power of variational quan- tum machine learning models, Physical Review A103, 10.1103/PhysRevA.103.032430 (2021), arXiv:2008.08605 [quant-ph]

    Pith/arXiv arXiv 2021

  45. [46]

    S. Wang, E. Fontana, M. Cerezo, K. Sharma, A. Sone, L. Cincio, and P. J. Coles, Noise-induced barren plateaus in variational quantum algorithms, Nature Communica- tions12, 10.1038/s41467-021-27045-6 (2021)

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

  46. [47]

    N. A. Nemkov, E. O. Kiktenko, and A. K. Fedorov, Fourier expansion in variational quantum algorithms, Physical Review A108, 10.1103/physreva.108.032406 (2023)

    doi:10.1103/physreva.108.032406 2023

  47. [48]

    Holmes, K

    Z. Holmes, K. Sharma, M. Cerezo, and P. J. Coles, Connecting ansatz expressibility to gradient magnitudes and barren plateaus, PRX Quantum3, 010313 (2022), arXiv:2101.02138 [quant-ph]

    Pith/arXiv arXiv 2022

  48. [49]

    S. Wang, P. Czarnik, A. Arrasmith, M. Cerezo, L. Cincio, and P. J. Coles, Can Error Mitigation Improve Trainabil- ity of Noisy Variational Quantum Algorithms?, Quantum 8, 1287 (2024), arXiv:2109.01051 [quant-ph]

    Pith/arXiv arXiv 2024

  49. [50]

    Okumura and M

    S. Okumura and M. Ohzeki, Fourier coefficient of param- eterized quantum circuits and barren plateau problem (2023), arXiv:2309.06740 [quant-ph]

    arXiv 2023

  50. [51]

    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 quantum processor, Nature Communications5, 4213 (2014), arXiv:1304.3061 [quant-ph]

    Pith/arXiv arXiv 2014

  51. [52]

    A. A. Mele, A. Angrisani, S. Ghosh, S. Khatri, J. Eisert, D. S. Fran¸ ca, and Y. Quek, Noise-induced shallow circuits and absence of barren plateaus (2024), arXiv:2403.13927 [quant-ph]

    Pith/arXiv arXiv 2024

  52. [53]

    Aliferis and J

    P. Aliferis and J. Preskill, Fault-tolerant quantum com- putation against biased noise, Physical Review A78, 10.1103/PhysRevA.78.052331 (2008), arXiv:0710.1301 [quant-ph]

    Pith/arXiv arXiv 2008

  53. [54]

    D. K. Tuckett, S. D. Bartlett, S. T. Flammia, and B. J. Brown, Fault-tolerant thresholds for the surface code in excess of 5% under biased noise, Physical Review Letters124, 10.1103/PhysRevLett.124.130501 (2020), arXiv:1907.02554 [quant-ph]

    Pith/arXiv arXiv 2020

This paper was first reviewed by deepseek-v4-flash on August 4, 2026.