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Efficient re-sampling in quasi-probability decompositions

T0 review · 3 major / 3 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read This paper introduces a reweighting strategy for quasi-probability decompositions that reuses samples from one reference circuit to estimate expectation values at many nearby parameter settings, cutting circuit evaluations in fidelity and q

desk verdict Reweighting QPDs across parameter shifts is a sound and potentially useful idea, but the paper's error analysis doesn't match the estimator used in the numerical QGT experiments. read the letter →

arxiv 2608.02075 v1 pith:TT5Q2QXS submitted 2026-08-03 quant-ph

Sara Santos , Stefan Woerner , Vincenzo Savona , Julien Gacon This is my paper · ORCID
classification quant-ph PACS 03.67.-a
keywords quasi-probabilitydecompositioncircuitknittingimportancesamplingfidelityestimationquantumgeometrictensorSPSAvariationalalgorithmssamplereuse
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper's central claim is that when two parameterized quantum circuits share the same decomposition basis and the target's support lies inside the reference's, samples drawn once from a reference quasi-probability decomposition (QPD) can be reweighted via self-normalized importance sampling to estimate expectation values at other parameter settings, without running new circuits. If correct, this tames the exponential sampling overhead of QPDs in regimes where many related expectation values are needed at nearby parameters. The authors demonstrate the method on fidelity estimation between variational states and on the real part of the quantum geometric tensor via SPSA, showing under realistic noise fewer circuit executions than compute-uncompute or Hadamard-test approaches. A sympathetic reader would care because variational algorithms routinely need many such evaluations at nearby points.

What carries the argument

The central object is the quasi-probability decomposition (QPD), which expresses a quantum channel $U$ as $U = \sum_i a_i u_i$, with real coefficients summing to 1 and sampling overhead $\gamma = \sum |a_i|$. The decomposition is chosen with angle-independent local channels so that the same sampled channels can serve multiple parameter values. The reweighted estimator uses self-normalized importance sampling with weights $w_i = \left| \frac{a_i(\theta')}{a_i(\theta)} \right|$, and the variance indicator $\chi$ (Eq. 23) tells when sample reuse is efficient. The support-inclusion condition $\xi' \subset \xi$ is the gate that makes the reweighted estimator unbiased.

What would settle it

Choose a target parameter $\theta'$ outside the reference support, where $a_i(\theta)=0$ but $a_i(\theta')$ is nonzero for some channel in a single CRZ QPD; the reweighted estimator then has bias equal to $\sum_{i \in \xi'\setminus \xi} a_i(\theta') \mathrm{tr}(O u_i)$. A direct numerical check of this bias, or a scan of $\chi$ over the SPSA displacement set for a 3-qubit layered ansatz, would settle whether the claimed variance bound holds.

Watch

Extended reading notes

Core claim

Quasi-probability decompositions express difficult gates as signed mixtures of local channels, but sampling overhead $\gamma$ grows exponentially with the number of cut gates. The paper shows that for a family of circuits $U(\theta)$ sharing the same decomposition basis, a sample from a reference QPD can be reused for a target $U(\theta')$ as long as the target's support is contained in the reference's. The reweighted estimator is unbiased under that support-inclusion condition, and its variance is controlled by $\chi(\theta,\theta') = \sum_i \frac{|a_i(\theta')|^2}{\gamma |a_i(\theta)|}$. For the CRZ decomposition with angle-independent channels, parameters within an $\ell_\infty$ neighborhood of the reference sati

Load-bearing premise

The method requires that the target QPD's support lies inside the reference QPD's support (and $\chi \le 1$ for variance control); for the SPSA application this is assumed for all target fidelities and is justified only by a numerical example with two CRZ gates, not by a proof.

Editorial extensions

If this is right

  • Fidelity between U(theta)|0> and U(theta+h1)|0> can be estimated by sampling only the reference QPD; the root-mean-square error scales as O(gamma/sqrt(M)).
  • The number of circuit evaluations for SPSA-based QGT estimation drops from 4KN (compute-uncompute) or 8KN (Hadamard test) to at most M, independent of the number of SPSA samples K.
  • Under realistic hardware noise, the shallow QPD circuits give lower relative QGT error than compute-uncompute at equal circuit-execution budget, with the advantage growing as CNOT error rates increase.
  • A parameter-independent decomposition of CRZ enables reweighting; the standard optimal decomposition with angle-dependent channels cannot be reweighted in this way.
  • The same reweighting framework applies to any variational algorithm that needs many expectation values at nearby parameter configurations, such as variational time evolution and kernel methods.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The chi criterion is more informative than comparing gamma alone: the paper shows parameter points with gamma < gamma_r but chi > 1, so support overlap, not just overhead, determines whether reuse is efficient. A natural next step is choosing the reference point to minimize variance across a whole parameter family.
  • If reweighting is combined with adaptive reference selection, the method might extend to parameter trajectories in variational time evolution, where consecutive states are close; this is not demonstrated in the paper.
  • The paper's numerical support for the required support-inclusion condition rests on a two-CRZ example, so a testable extension is to check chi <= 1 over the full SPSA displacement set for larger ansatze with more layers and qubits.
  • Because the classical weight recomputation costs up to M x n_c per parameter set but is parallelizable, the practical bottleneck may shift from quantum circuits to classical post-processing as M grows.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 3 minor

Summary. The paper introduces a reweighting strategy for quasi-probability decompositions (QPDs) that reuses samples from a single reference parameter setting to estimate expectation values at nearby parameter settings, using self-normalized importance sampling. The authors derive variance formulas for the reweighted estimator, introduce a factor χ that controls the variance, and apply the method to fidelity estimation via a compressed Hadamard test and to SPSA-based estimation of the real part of the quantum geometric tensor (QGT). Numerical simulations on a 3-qubit layered ansatz with noiseless and noisy Qiskit backends are used to support the claim that the QPD-based approach outperforms compute–uncompute and Hadamard-test methods under realistic noise.

Significance. If the theoretical guarantees are made fully rigorous, the idea of reusing QPD samples across a family of parameterized circuits is a genuinely useful contribution to circuit knitting and to variational quantum algorithms that require many nearby fidelity evaluations. The paper contains a concrete QPD decomposition with angle-independent channels, explicit variance formulas (Eqs. (19)–(23)), and numerical comparisons under a fixed circuit-execution budget, which are strengths. However, two load-bearing points need attention: the support-inclusion/χ≤1 condition is only numerically illustrated for two CRZ gates, and the self-normalized estimator actually used in the QGT protocol is not covered by the χ-based variance bound used in the error analysis.

major comments (3)
  1. [Section III-A1 and Fig. 5] The SPSA application requires that for every target fidelity in Eq. (29) the reference QPD satisfies ξ'⊆ξ and χ≤1. The choice of θ+2h1 is justified only by the numerical two-CRZ-gate example in Fig. 5; no proof is given that the CRZ QPD of Eq. (8) has this property for arbitrary θ, h, and number of gates. Since the total χ factorizes over gates, a per-gate proof would suffice, but it is missing. If a target parameter falls outside the reference support, Eq. (21) shows the estimator is biased and Eq. (22) no longer bounds the error. This condition is load-bearing for the central claim that a single reference QPD can estimate all 4K SPSA fidelity terms.
  2. [Section III-1 and Appendix D] The χ-based variance guarantee (Eqs. (22)–(23)) is derived for the un-normalized reweighted estimator, while the QGT protocol uses the self-normalized estimator (24) and (30). For self-normalized estimators the finite-sample bias is O(1/M) and the variance differs from Eq. (22); the paper only states asymptotic unbiasedness. Appendix D's ε_F comes from Appendix B, which analyzes the un-normalized estimator (33) and the bias-corrected fidelity estimator (40), not the estimator used in Fig. 6. The theoretical error scaling of the QGT results is therefore not directly supported. The authors should either provide a finite-sample bias/variance analysis for Eq. (30) or use the un-normalized estimator with the bias correction (40), in which case the χ bound would apply.
  3. [Section III-1, text near Eq. (24)] The statement 'the normalization condition Σ_i p̂_i w_i = 1 holds only in expectation' is not correct in general: E[Σ_i p̂_i w_i] = Σ_i p_i w_i = γ'/γ, not unity. This suggests a confusion between the un-normalized estimator of Eq. (19), the sample version of Eq. (22), and the self-normalized estimator of Eq. (24). The definitions and the variance formulas should be attached consistently to the estimator actually used in the numerics.
minor comments (3)
  1. [Fig. 4] In Fig. 4(b), the horizontal axis is γ, but since h varies, each point corresponds to a different target state; a brief explanation of the relationship between h and γ would help the reader interpret the RMSE-vs-γ scaling.
  2. [Appendix C] The sentence 'if the qubit remains in |0⟩ or |1⟩ at measurement, then ⟨Z⟩=1 or −1' should be clarified: this statement applies after the final Hadamard gate, with the pre-Hadamard state being |+⟩ or |−⟩. As written, it appears to contradict the preceding sentence.
  3. [Eqs. (39)–(40) and Fig. 4] The unbiased fidelity estimator F^⋆ is introduced but it is not stated whether Fig. 4 reports F̂ or F^⋆. Since the unbiased correction is not used in the QGT implementation, the text should explicitly say which estimator is used in each numerical result.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the reweighting estimator, variance criterion chi, and QGT protocol are derived algebraically from the QPD expansion and standard importance sampling; numerical claims are simulations, not fitted predictions.

full rationale

The central derivation (Eqs. 19-23) follows by direct algebra: the target QPD is re-expanded in the reference basis with weights w_i = |a'_i/a_i|, the support condition (20) makes Eq. (21) unbiased, and variance Eq. (22) is a standard multinomial calculation. Eq. (23) defines chi as a ratio of expansion coefficients; it is not fitted from data. No parameter is extracted from fidelity or QGT outputs and then renamed a prediction. The CR_Z QPD is taken from an external reference [22], and the choice of angle-independent channels is motivated by the reweighting condition, not by the conclusion. The SPSA estimator is cited from prior work [36]; that is a normal use of an existing method, not a self-citation chain that forces the result. The paper is transparent about assumptions: the support-inclusion requirement xi' subset of xi is stated in Eq. (20), and the practical validity of the reference choice theta+2h*1 is supported by a numerical example (Fig. 5) rather than a theorem; this is an assumption and a scalability limitation acknowledged in Section IV, not a circular step. The manuscript also explicitly flags the finite-sample bias of the self-normalized estimator: 'In practice, the reweighted estimator U' is biased at finite sample size... Self-normalized importance sampling estimators are often employed in such cases as variance reduction methods, yielding a comparatively smaller variance, while remaining asymptotically unbiased [41].' The skeptic's concern that Appendix D's error analysis inherits epsilon_F from the unnormalized estimator and does not bound the O(1/M) self-normalization bias is a legitimate correctness/robustness risk, but it does not make any claim reduce to its input. No uniqueness theorem or load-bearing self-citation is invoked. The numerical comparisons are simulations with equal execution budgets; they are evidence, not derivations forced by definition. Verdict: no meaningful circularity.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. The reweighting method is a statistical technique built on standard importance sampling. The main axioms are the validity of the CRZ decomposition, the layered ansatz structure, the realism of Qiskit fake backends, and standard statistical results.

free parameters (1)
  • SPSA perturbation step h = 0.1
    Chosen by hand for all numerics; controls the bias-variance tradeoff of the SPSA estimator and the size of the reweighting region. Not fitted, but a free hyperparameter.
assumptions (5)
  • domain assumption The CRZ QPD decomposition (8) with angle-independent channels u_i is valid and has gamma as given in (10).
    Derived in the paper from known RZZ/RZ QPDs; no machine-checked proof, but algebraically plausible.
  • domain assumption The state-encoding ansatz U(theta) factors into layers R_l(theta_l) W_l with R_l(theta_l+delta)=R_l(theta_l)R_l(delta), allowing the compressed Hadamard test.
    Assumed for the fidelity estimation setting; holds for typical layered ansaetze.
  • standard math Self-normalized importance sampling is asymptotically unbiased and has the variance properties cited from Owen [41].
    Standard statistical result used without proof.
  • domain assumption Qiskit fake backends Manila and Toronto provide realistic hardware noise models.
    The empirical claim of outperforming CU under noise rests on these noise models.
  • standard math The multinomial sampling distribution of QPD channels [40] underlies variance calculations.
    Standard result used in Appendix B.

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Pith. "Pith review of Efficient re-sampling in quasi-probability decompositions." pith.science (2026). https://pith.science/paper/TT5Q2QXS

@misc{pith2026260802075,
  author       = {Pith},
  title        = {Pith review of: Efficient re-sampling in quasi-probability decompositions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TT5Q2QXS}},
  note         = {Machine review of arXiv:2608.02075}
}
read the original abstract

Near-term quantum devices are limited by noise and hardware constraints, motivating algorithmic approaches that trade circuit complexity for increased sampling overhead. Quasi-probability decompositions (QPDs), for example, allow replacing non-local operations by multiple circuits with local operations, but the associated sampling overhead generally scales exponentially and limits their practicality. In this work, we introduce a reweighting strategy for QPDs for circuits with the same variational structure across parameter settings, reusing samples and thereby reducing the sampling overhead. We first demonstrate this approach by estimating fidelities between parameterized quantum states, a key primitive in variational time evolution and quantum kernel methods. Importantly, this setup allows controlling the exponential QPD sampling overhead while preserving the structure of the state-encoding ansatz. We then apply the method to estimate the real part of the quantum geometric tensor using the simultaneous perturbation stochastic approximation and find that, in the presence of realistic hardware noise, our method outperforms other standard estimation techniques. These results highlight the potential of reweighting strategies to extend the applicability of QPD-based methods in variational quantum algorithms.

Figures

Figures reproduced from arXiv: 2608.02075 by the authors.

Figure 1
Figure 1. Hadamard test circuit for computing the real and imaginary parts of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Decomposition of the compressed Hadamard test circuit: (a) each [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Schematic representation of a layered ansatz with 3 qubits. This ansatz [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Numerical results for the RMSE of the fidelity estimator, averaged [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: Comparison of γ and χ of the QPD for two CRZ gates, parameterized by the pairs (θ1, θ2). The red points (±θr, ±θr) represent the reference an￾gles. By symmetry, all pairs (±θr, ±θr) lead to the same γr = γ(±θr, ±θr) and χ, and, thus, the same resulting plot. The shaded…
Figure 6
Figure 6. Figure 6: Numerical results for the estimation of the real part of the QGT of a 3-qubit system described by the layered ansatz illustrated in Fig. 3 with [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: QPDs for (a) the RZZ (−θ/2) and (b) the RZ (θ/2) gates. Empty wires represent the identity operation, S = √ Z, and measurements are in the computational basis. in ⟨Z⟩ i , we analyze Rˆ (the same results apply to Jˆ). The estimator reads Rˆ = γ X i∈ξ pˆi sgn(ai)⟨Z⟩i(2ˆq…

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Reference graph

Works this paper leans on

42 extracted references

  1. [1]

    R. P. Feynman,Simulating physics with computers. International Journal of Theoretical Physics, 1982

    1982

  2. [2]

    Programmable simulations of molecules and materials with reconfigurable quantum processors,

    N. Maskara, S. Ostermann, J. Shee, M. Kalinowski, A. McClain Gomez, R. Araiza Bravo, D. S. Wang, A. I. Krylov, N. Y . Yao, M. Head-Gordon, M. D. Lukin, and S. F. Yelin, “Programmable simulations of molecules and materials with reconfigurable quantum processors,”Nature Physics, vol. 21, no. 2, pp. 289–297, 2025

    2025

  3. [3]

    Nonadiabatic molecular quantum dynamics with quantum computers,

    P. J. Ollitrault, G. Mazzola, and I. Tavernelli, “Nonadiabatic molecular quantum dynamics with quantum computers,”Physical Review Letters, vol. 125, p. 260511, 2020

    2020

  4. [4]

    Universal quantum simulators,

    S. Lloyd, “Universal quantum simulators,”Science, vol. 273, pp. 1073– 1078, 1996

    1996

  5. [5]

    Quantum algorithms for electronic structure calculations: Particle–hole Hamiltonian and optimized wave-function expansions,

    P. K. Barkoutsos, J. F. Gonthier, I. Sokolov, N. Moll, G. Salis, A. Fuhrer, M. Ganzhorn, D. J. Egger, M. Troyer, A. Mezzacapo, S. Filipp, and I. Tavernelli, “Quantum algorithms for electronic structure calculations: Particle–hole Hamiltonian and optimized wave-function expansions,” Physical Review A, vol. 98, p. 022322, 2018

    2018

  6. [6]

    A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem,

    E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda, “A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem,”Science, vol. 292, no. 5516, pp. 472–475, 2001

    2001

  7. [7]

    Quantum approximate optimization algorithm: Performance, mechanism, and im- plementation on near-term devices,

    L. Zhou, S.-T. Wang, S. Choi, H. Pichler, and M. D. Lukin, “Quantum approximate optimization algorithm: Performance, mechanism, and im- plementation on near-term devices,”Physical Review X, vol. 10, no. 2, p. 021067, 2020

    2020

  8. [8]

    Quantum approximate optimization of non-planar graph problems on a planar superconducting processor,

    M. P. Harrigan, K. J. Sung, M. Neeley, K. J. Satzinger, F. Arute, K. Arya, and et al., “Quantum approximate optimization of non-planar graph problems on a planar superconducting processor,”Nature Physics, vol. 17, no. 3, pp. 332–336, 2021

    2021

Show all 42 references
  1. [9]

    Optimization by decoded quantum interferometry,

    S. P. Jordan, N. Shutty, M. Wootters, A. Zalcman, A. Schmidhuber, and et al., “Optimization by decoded quantum interferometry,”Nature, vol. 646, no. 8086, pp. 831–836, 2025

    2025

  2. [10]

    A quantum processor based on coherent transport of entangled atom arrays,

    D. Bluvstein, H. Levine, G. Semeghini, and et al., “A quantum processor based on coherent transport of entangled atom arrays,”Nature, vol. 604, no. 7906, pp. 451–456, 2022

    2022

  3. [11]

    Logical quantum processor based on reconfigurable atom arrays,

    D. Bluvstein, S. J. Evered, A. A. Geim, and et al., “Logical quantum processor based on reconfigurable atom arrays,”Nature, vol. 626, pp. 58–65, 2024

    2024

  4. [12]

    Universal control of a six-qubit quantum processor in silicon,

    S. G. J. Philips, M. A. Broome, T. Marquardt, and et al., “Universal control of a six-qubit quantum processor in silicon,”Nature, vol. 609, no. 7929, pp. 919–924, 2022

    2022

  5. [13]

    Generation of genuine entanglement up to 51 superconducting qubits,

    S. Cao, B. Wu, J. Pan, and et al., “Generation of genuine entanglement up to 51 superconducting qubits,”Nature, vol. 619, no. 7971, pp. 738– 742, 2023

    2023

  6. [14]

    Advanced CMOS manufacturing of superconducting qubits on 300 mm wafers,

    J. Van Damme, S. Massar, R. Acharya, and et al., “Advanced CMOS manufacturing of superconducting qubits on 300 mm wafers,”Nature, vol. 634, no. 8032, pp. 74–79, 2024

    2024

  7. [15]

    Demonstration of the trapped-ion quantum-ccd computer architecture,

    J. M. Pino, J. Dreiling, C. Figgatt, and et al., “Demonstration of the trapped-ion quantum-ccd computer architecture,”Nature, vol. 592, no. 7853, pp. 209–213, 2021

    2021

  8. [16]

    Experimental entanglement of four particles,

    C. A. Sackett, D. Kielpinski, B. E. King, and et al., “Experimental entanglement of four particles,”Nature, vol. 404, no. 6775, pp. 256– 259, 2000

    2000

  9. [17]

    Realization of the Cirac–Zoller controlled-NOT quantum gate,

    F. Schmidt-Kaler, H. H ¨affner, M. Riebe, and et al., “Realization of the Cirac–Zoller controlled-NOT quantum gate,”Nature, vol. 422, pp. 408– 411, 2003

    2003

  10. [18]

    Implementation of the Deutsch–Jozsa algorithm on an ion-trap quantum computer,

    S. Gulde, M. Riebe, G. P. T. Lancaster, C. Becher, J. Eschner, H. H¨affner, F. Schmidt-Kaler, I. L. Chuang, and R. Blatt, “Implementation of the Deutsch–Jozsa algorithm on an ion-trap quantum computer,”Nature, vol. 421, pp. 48–50, 2003

    2003

  11. [19]

    Scaling the ion trap quantum processor,

    C. Monroe and J. Kim, “Scaling the ion trap quantum processor,” Science, vol. 339, no. 6124, pp. 1164–1169, 2013

    2013

  12. [20]

    Quantum supremacy using a programmable superconducting processor,

    F. Arute, K. Arya, R. Babbush, and et al, “Quantum supremacy using a programmable superconducting processor,”Nature, vol. 574, no. 7779, pp. 505–510, 2019

    2019

  13. [21]

    Evidence of scaling advantage for the quantum approximate optimization algorithm on a classically intractable problem,

    R. Shaydulin, C. Li, S. Chakrabarti, M. DeCross, D. Herman, and et al., “Evidence of scaling advantage for the quantum approximate optimization algorithm on a classically intractable problem,”Science Advances, vol. 10, no. 22, p. eadm6761, 2024

    2024

  14. [22]

    Constructing a virtual two-qubit gate by sampling single-qubit operations,

    K. Mitarai and K. Fujii, “Constructing a virtual two-qubit gate by sampling single-qubit operations,”New Journal of Physics, vol. 23, no. 2, p. 023021, 2021

    2021

  15. [23]

    Circuit knitting with classical commu- nication,

    C. Piveteau and D. Sutter, “Circuit knitting with classical commu- nication,”IEEE Transactions on Information Theory, vol. 70, no. 4, pp. 2734–2745, 2024

    2024

  16. [24]

    Error mitigation for short- depth quantum circuits,

    K. Temme, S. Bravyi, and J. M. Gambetta, “Error mitigation for short- depth quantum circuits,”Physical Review Letters, vol. 119, no. 18, p. 180509, 2017

    2017

  17. [25]

    Quasiprobability decomposi- tions with reduced sampling overhead,

    C. Piveteau, D. Sutter, and S. Woerner, “Quasiprobability decomposi- tions with reduced sampling overhead,”npj Quantum Information, vol. 8, no. 1, p. 12, 2022

    2022

  18. [26]

    Combining quantum processors with real-time classical communication,

    A. Carrera Vazquez, C. Tornow, D. Rist `e, and et al., “Combining quantum processors with real-time classical communication,”Nature, vol. 636, pp. 75–79, 2024

    2024

  19. [27]

    Theory of variational quantum simulation,

    X. Yuan, S. Endo, Q. Zhao, Y . Li, and S. C. Benjamin, “Theory of variational quantum simulation,”Quantum, vol. 3, p. 191, 2019

    2019

  20. [28]

    Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution,

    M. Motta, C. Sun, A. T. K. Tan, and et al., “Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution,”Nature Physics, vol. 16, no. 2, pp. 205–210, 2020

    2020

  21. [29]

    Variational quantum simulation of general processes,

    S. Endo, J. Sun, Y . Li, S. C. Benjamin, and X. Yuan, “Variational quantum simulation of general processes,”Physical Review Letters, vol. 125, no. 1, p. 010501, 2020

    2020

  22. [30]

    Real- and imaginary-time evolution with compressed quantum circuits,

    S.-H. Lin, R. Dilip, A. G. Green, A. Smith, and F. Pollmann, “Real- and imaginary-time evolution with compressed quantum circuits,”PRX Quantum, vol. 2, no. 1, p. 010342, 2021

    2021

  23. [31]

    An efficient quantum algorithm for the time evolution of parameterized circuits,

    S. Barison, F. Vicentini, and G. Carleo, “An efficient quantum algorithm for the time evolution of parameterized circuits,”Quantum, vol. 5, p. 512, 2021

    2021

  24. [32]

    Stochastic approxima- tion of variational quantum imaginary time evolution,

    J. Gacon, C. Zoufal, G. Carleo, and S. Woerner, “Stochastic approxima- tion of variational quantum imaginary time evolution,” in2023 IEEE International Conference on Quantum Computing and Engineering (QCE), vol. 03, pp. 129–139, IEEE, 2023

    2023

  25. [33]

    Variational quantum time evolution without the quantum geometric tensor,

    J. Gacon, J. Nys, R. Rossi, S. Woerner, and G. Carleo, “Variational quantum time evolution without the quantum geometric tensor,”Physical Review Research, vol. 6, p. 013143, 2024

    2024

  26. [34]

    Quantum natural gradient,

    J. Stokes, J. Izaac, N. Killoran, and G. Carleo, “Quantum natural gradient,”Quantum, vol. 4, p. 269, 2020

    2020

  27. [35]

    Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer,

    D. Wierichs, C. Gogolin, and M. Kastoryano, “Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer,” Physical Review Research, vol. 2, p. 043246, 2020

    2020

  28. [36]

    Simultaneous Pertur- bation Stochastic Approximation of the Quantum Fisher Information,

    J. Gacon, C. Zoufal, G. Carleo, and S. Woerner, “Simultaneous Pertur- bation Stochastic Approximation of the Quantum Fisher Information,” Quantum, vol. 5, p. 567, 2021

    2021

  29. [37]

    Quantum measurements and the abelian stabilizer prob- lem,

    A. Y . Kitaev, “Quantum measurements and the abelian stabilizer prob- lem,” inProceedings of the 1st Annual International Conference on Quantum Communication, Computing and Measurement, pp. 181–188, Springer, 1997

    1997

  30. [38]

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information. Cambridge University Press, 10th anniversary edition ed., 2010

    2010

  31. [39]

    Predicting many properties of a quantum system from very few measurements,

    H.-Y . Huang, R. Kueng, and J. Preskill, “Predicting many properties of a quantum system from very few measurements,”Nature Physics, vol. 16, pp. 1050–1057, 2020

    2020

  32. [40]

    Evans, N

    M. Evans, N. Hastings, and B. Peacock,Statistical Distributions. New York: John Wiley & Sons, 3 ed., 2000

    2000

  33. [41]

    A. B. Owen,Monte Carlo theory, methods and examples. 2013. [Online]. Available: https://artowen.su.domains/mc/

    2013

  34. [42]

    Qiskit: An open-source framework for quantum computing,

    Qiskit Community, “Qiskit: An open-source framework for quantum computing,” 2017. [Online]. Available: https://qiskit.org/

    2017

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