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REVIEW 5 major objections 4 minor 1 cited by

Machine-Learning-Assisted Pulse Design for State Preparation in a Noisy Environment

T0 review · 5 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper proposes noise-aware machine-learning pulse design for arbitrary qubit state preparation, reporting that a single model with environmental parameters as input features outperforms noise-blind control and generalizes to unseen…

desk verdict A plausible crossover between DRL and SL for noise-aware pulse design, but the DRL reward is unspecified and the policy state drops non-Markovian bath memory, so the claim needs revision before it can be trusted. read the letter →

arxiv 2508.20377 v1 pith:2HKH3MHE submitted 2025-08-28 quant-ph

Zhao-Wei Wang , Hong-Yang Ma , Yun-An Yan , Lian-Ao Wu , Zhao-Ming Wang This is my paper · ORCID
classification quant-ph
keywords quantumstatepreparationcontroldeepreinforcementlearningsupervisednon-Markovianenvironmentnoisesuppressionopensystemspulsedesign
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 asks whether a quantum control policy can be made noise-aware by feeding the environment's parameters directly into the neural network that chooses control pulses. Using arbitrary qubit-to-qubit state preparation in a two-level system coupled to a bosonic bath, it trains Deep Reinforcement Learning (DRL) and Supervised Learning (SL) models under three conditions: ignoring noise, incorporating noise parameters only in the simulation, and encoding noise parameters as input features. It reports that noise-aware models achieve higher test-set fidelity than noise-unaware models, and that a single feature-encoded model performs about as well as separately retrained per-environment models, including on environment parameters not seen in training. It also reports a regime split: DRL outperforms SL in weak or absent noise, while SL is more stable and outperforms DRL in strong noise. If correct, this gives a practical rule for choosing the learning method by noise level and for replacing many environment-specific controllers with one general network.

What carries the argument

The load-bearing object is the state vector $s = [P_{\mathrm{ini}}^1,\ldots,P_{\mathrm{ini}}^4,P_{\mathrm{tar}}^1,\ldots,P_{\mathrm{tar}}^4,\Gamma,\gamma,T]$, built by compressing the current and target density matrices into four POVM probabilities each and appending the bath parameters. This vector is the input on which both the DRL policy and the SL classifier act; at each step the simulator evolves the density matrix with the non-Markovian quantum-state-diffusion master equation under a Lorentz-Drude spectral density. The claim that Case 3 works rests on this vector carrying enough information to choose the next pulse.

What would settle it

Train a Case-3 DRL model with bath frequencies $\gamma$ at or above a moderate value, then test it at a strongly non-Markovian value such as $\gamma = 0.1$, and compare its average fidelity with a per-environment Case-2 model trained at $\gamma = 0.1$ using the same QSD simulator; if the Case-3 model falls clearly below the Case-2 model, the sufficiency of $s$ and the generalization claim fail in the non-Markovian regime.

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Extended reading notes

Core claim

The central claim is that incorporating the bath parameters $\Gamma$, $\gamma$, and $T$ into the training loop—either as fixed inputs to the simulation (Case 2) or as explicit input features to the network (Case 3)—yields higher average state-preparation fidelity than a model trained without any noise information (Case 1). For the same neural network architecture, the DRL models outperform SL models in noise-free or weakly noisy settings, while SL models retain higher fidelity when noise is strong; the crossing point is the paper's main comparative finding. The paper further claims that a Case-3 model trained over a range of environmental parameters can design pulses for unseen parameter values, so that one network acts as a universal controller across the covered noise regime.

Load-bearing premise

The network's input contains only the current-state and target-state measurement probabilities plus the three bath parameters, with no information about the bath's memory, so the whole scheme assumes this short vector is enough to choose the optimal next pulse even in the non-Markovian regime.

Editorial extensions

If this is right

  • A single Case-3 network replaces the need to retrain a policy for each new set of environmental parameters within the covered range.
  • Noise-aware training pays off most when noise is strong, because the fidelity gap between Case-1 and Cases-2/3 grows with $\Gamma$, $\gamma$, and $T$.
  • In low-noise or noise-free devices, DRL-trained pulses should be preferred; in high-noise devices, SL-trained pulses should be preferred.
  • SL models are more stable and faster at inference time, with smaller average step counts, while DRL models are more time-consuming and show more scattered design times.
  • The comparison is made with identical network architectures, so the reported differences are attributed to the learning algorithms and the input encoding rather than to model capacity.

Reading between the lines

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

  • The near-equal performance of Case 2 and Case 3 suggests the practical advantage of encoding environment parameters as features is logistical (one model for many environments) rather than a fidelity gain; an engineering rule would be to use Case 3 for deployment across many environments and Case 2 when inference speed matters.
  • The sufficiency of $s$ is the most exposed assumption: adding bath-memory observables to the state, or using a recurrent policy, is a direct test of whether the method extends deeper into the non-Markovian regime.
  • The same training recipe could be applied to other spectral densities, such as Ohmic or sub-Ohmic baths; the QSD equations would change but the input-encoding idea would not.
  • Because the action set and step duration are discrete, the policies are approximate optimal controllers; allowing continuous pulse amplitudes or adaptive time steps could reveal how much fidelity is lost to discretization.
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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

5 major / 4 minor

Summary. The paper trains DRL and SL agents to design piecewise-constant control pulses for arbitrary qubit-to-qubit state preparation in a two-level system coupled to a bosonic bath, using a non-Markovian QSD master equation. Three training strategies are compared: a noise-unaware model (Case 1), models trained for fixed environmental parameters that enter only the simulator (Case 2), and a single model that receives the environmental parameters as input features (Case 3). On a held-out test set of 242 state-preparation tasks, the authors report that noise-aware models outperform the noise-unaware baseline, that the Case 3 network generalizes across environmental parameters, and that DRL is superior in weak-noise environments while SL is more stable and more accurate in strong-noise environments.

Significance. If the central comparison withstands scrutiny, the paper offers useful evidence that environment-aware training can improve quantum control fidelity in a non-Markovian open-system setting, and that a single network with environmental parameters as input features can replace multiple separately trained controllers. The use of a held-out test set, a noise-unaware baseline, and explicit hyperparameter tables are strengths. However, the DRL reward function is never specified, the agent's observation is memoryless despite non-Markovian dynamics, the auxiliary-equation derivation in Appendix A contains apparent inconsistencies, and the main fidelity comparison lacks statistical uncertainty. These gaps leave the central DRL-versus-SL crossover claim only partially supported.

major comments (5)
  1. [Sec. 3.1, Eq. (8)] The DRL reward rt is never defined in the text or appendices. Eq. (8) uses rt as the immediate reward in the loss, but there is no statement of how rt is computed from fidelity, step count, or task completion. The reward determines the trained policy and is essential for reproducing the DRL/SL comparison. Please give the exact reward function for all three cases and state how terminal rewards are handled.
  2. [Sec. 2.2, Eqs. (2)-(3), Fig. 1] The observation s = [P^1_ini, ..., P^4_tar, Gamma, gamma, T] is not a sufficient statistic for optimal action selection in the non-Markovian dynamics used by the simulator. Eqs. (2)-(3) contain auxiliary operators O_z and O_w that are convolutions with bath correlation functions and therefore carry memory of the entire past control history, while the loop in Fig. 1 re-encodes only rho_n. Unless the authors prove that the reduced density matrix plus fixed bath parameters determines the future evolution, the trained policies are restricted to a memoryless policy class. The claim of optimal pulse sequences and the DRL/SL crossover in Fig. 3 may therefore be artifacts of this restricted observation, and the low-gamma regime emphasized in Sec. 2.1 is precisely where memory effects are largest. Please quantify the effect by augmenting s with O_z, O_w, or a finite action history, and re-running the comparison.
  3. [Appendix A, Eqs. (A.8)-(A.9), (A.12)] The derivation of the auxiliary equations is not internally consistent. In Eq. (A.9) the derivative dO_w/dt commutes with O_z rather than O_w, and the subtracted derivative terms are not the appropriate w* derivatives. In addition, Eq. (A.12) claims single-exponential decay for the correlation functions, which is not true for the Bose-Einstein occupation appearing in Eqs. (A.4)-(A.5) for the Lorentz-Drude spectrum at finite temperature. Since Eqs. (2)-(3) are obtained from these equations and drive all reported fidelities, the numerical results need either a corrected derivation or an explicit statement of the single-pole approximation together with an error estimate.
  4. [Fig. 3 and Table 1] Fig. 3 shows only single point estimates of the test-set average fidelity, with no error bars, no number of independent training runs, and no confidence intervals. The DRL/SL differences and the Case (2)/(3) differences in Table 1 are often around 0.01 in fidelity, so the crossover claims require statistical uncertainty estimates. Please add repeated-run means with standard errors or otherwise quantify the variability.
  5. [Sec. 4, Case (3)] The claimed generalization to unseen environmental parameters is not auditable because the training grid for Case (3) is not specified. The text and Fig. 3 distinguish hollow points as unseen parameters, but they do not give the set of (Gamma, gamma, T) combinations used in training. Please state the training grid explicitly and report the held-out points separately, including whether the unseen points lie inside or outside the convex hull of the training parameters.
minor comments (4)
  1. [Sec. 2.1, Eq. (1)] The symbols O_z(t) and O_w(t) are used in Eq. (1) without a non-circular definition; the text says they are convolutions of O_z and O_w, but the reader would benefit from a one-line identification with the noise-averaged operators M[O] and M[Q] from Eq. (A.11).
  2. [Sec. 3.1 and Table B.2] The epsilon-greedy description is inconsistent with the hyperparameter table: standard DQN uses a decreasing exploration probability epsilon, while the text says epsilon increases from 0 to slightly below 1 as the probability of choosing the currently most advantageous action. Clarify the convention, and state whether validation and test use epsilon=1 for greedy action selection or epsilon=0.
  3. [Eqs. (5), (7), and Tables B.2-B.3] The symbol alpha is used for the discount factor in Eq. (5) and for the learning rate in the hyperparameter tables, while gamma is used both for the bath characteristic frequency and for the reward discount factor in Table B.2. Please rename the learning rate and the discount factor to avoid these collisions.
  4. [Fig. 4] The action-sequence panels do not label the step index on the horizontal axis, and the mapping between the action labels on the vertical axis and the pairs (J, phi) of the action set is not given. Adding this information would make the pulse sequences reproducible.

Circularity Check

0 steps flagged · score 2.0 of 10

No circularity found; held-out evaluation and independent derivation keep the central claim non-tautological.

full rationale

The paper's central comparison is not circular. The DRL and SL models are evaluated on a held-out test set of 242 tasks, separate from the 700 training tasks, and against a noise-unaware baseline (Case 1). The fidelity used in rewards and evaluation is computed from the QSD master equation, with no test-set labels or environment parameters used to retune the models after training. Case (3) is additionally tested on environmental parameters not seen during training, so the generalization claim is not forced by construction. The master equation (1)-(3) is derived in Appendix A from the QSD ansatz, and although prior work [53] is cited, the derivation is reproduced in the paper, making the environment model self-contained rather than an imported black box. The paper also cites its own prior SL work [46] for the SL training strategy and for the statement that SL Case (2) behaves similarly to DRL, but the present paper independently trains SL models and reports corresponding results in Fig. 3, so this self-citation is not load-bearing. The DRL/SL performance crossover is an empirical outcome of the experiments, not a consequence of either algorithm's objective being defined in terms of the other's output. No fitted parameter is renamed as a prediction: the environment parameters are either fixed simulation inputs, input features, or held-out test conditions, and the models are never fit to the test fidelities they are asked to predict. The concern raised in the skeptic pass, that the reinforcement-learning state omits the bath-memory operators O_z and O_w and therefore solves only a partially observable MDP, is a modeling limitation or correctness risk, not a circularity: the policies are still learned and evaluated against a consistent, externally specified dynamical model. Overall, the derivation chain is not self-referential; the central claims rest on independent held-out simulation experiments.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

All three machine-learned controllers are evaluated on simulated fidelities that come from the QSD master equation. The paper introduces no new physical entity; the free parameters are choices about the control horizon, action discretization, and neural network training. The most fragile modeling assumptions are the sufficiency of the POVM state encoding and the weak-coupling closure of the QSD equations.

free parameters (7)
  • h (transverse field / Zeeman splitting in Eq. 4)
    Appears in Hs(t)=J(t)sigma_z+h sigma_x but no numerical value is given; it fixes the timescale of the pulse dynamics.
  • Total evolution time Ttot=2*pi and step dt=pi/5
    Hand-chosen control horizon and step size, giving N=10 steps.
  • Action discretization: J in {0,...,8}, phi in {pi, pi/2, pi/4}
    Hand-chosen discrete action set of 27 controls.
  • Fidelity threshold F_threshold = 0.999 = 0.999
    Termination threshold used during training and evaluation.
  • SL local-optimality filter
    The rule that removes samples whose fidelity does not increase; the threshold and concrete criterion are not specified.
  • DRL reward function r_t
    The instantaneous reward r_t is never defined, only the discounted cumulative R in Eq. (5); training cannot be reproduced without it.
  • Environmental parameter grid for Case (3) training
    Appendix C mentions 'all combinations of environmental parameters' but the ranges and grid spacing are not stated.
assumptions (6)
  • domain assumption The QSD-based non-Markovian master equation (Eq. 1) with Lorentz-Drude bath and the weak-coupling closure in Eqs. (2)-(3) correctly describes the system dynamics.
    All fidelity computations rely on this dynamics; the derivation in Appendix A is sketched and contains apparent typos in Eqs. (A.8)-(A.9).
  • domain assumption The finite-temperature bath is initialized in a thermal state and the Lorentz-Drude spectral density is appropriate for the target physical systems.
    The environment model is assumed from the start in Section 2.1; no justification for the specific spectral density is provided beyond standard usage.
  • ad hoc to paper The control state s = [POVM(rho_ini), POVM(rho_tar), Gamma, gamma, T] is a sufficient statistic for optimal action selection.
    This is the key non-Markovian assumption identified in the weakest_assumption field; it enters Section 2.2 and Fig. 1.
  • domain assumption The control Hamiltonian Hs(t)=J(t)sigma_z+h sigma_x with discrete, non-negative J and discrete phi is sufficient to drive arbitrary qubit states with high fidelity.
    Controllability of the chosen pulse family is not proven; the paper relies on the action set being expressive enough.
  • domain assumption Weak system-bath coupling justifies replacing noise-dependent operators O and Q by noise-independent averages.
    Used in Appendix A to derive the master equation; validity at the strongest couplings tested (Gamma up to 0.4) is not checked.
  • standard math The Pauli-4 POVM encoding is informationally complete for a single qubit.
    The paper cites Ref. [85] for the Pauli-4 POVM; the basis state |l> is not defined, though the method is standard.

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Pith. "Pith review of Machine-Learning-Assisted Pulse Design for State Preparation in a Noisy Environment." pith.science (2026). https://pith.science/paper/2HKH3MHE

@misc{pith2026250820377,
  author       = {Pith},
  title        = {Pith review of: Machine-Learning-Assisted Pulse Design for State Preparation in a Noisy Environment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2HKH3MHE}},
  note         = {Machine review of arXiv:2508.20377}
}
read the original abstract

High-precision quantum control is essential for quantum computing and quantum information processing. However, its practical implementation is challenged by environmental noise, which affects the stability and accuracy of quantum systems. In this paper, using machine learning techniques we propose a quantum control approach that incorporates environmental factors into the design of control schemes, improving the control fidelity in noisy environments. Specifically, we investigate arbitrary quantum state preparation in a two-level system coupled to a bosonic bath. We use both Deep Reinforcement Learning (DRL) and Supervised Learning (SL) algorithms to design specific control pulses that mitigate the noise. These two neural network (NN) based algorithm both have the advantage that the well trained NN can output the optimal pulse sequence for any environmental parameters. Comparing the performance of these two algorithms, our results show that DRL is more effective in low-noise environments due to its strong optimization capabilities, while SL provides greater stability and performs better in high-noise conditions. These findings highlight the potential of machine learning techniques to enhance the quantum control fidelity in practical applications.

Figures

Figures reproduced from arXiv: 2508.20377 by the authors.

Figure 1
Figure 1. Design flow chart of control trajectory in Case (3). Input the control task’s initial [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. The validation set average fidelity F¯ of the model trained by the DRL algorithm as a function of training epoch under Case (1) and Case (2). The maximum training epoch is 10000, and the model effect is verified on the validation set every 200 epoch. when the noise becomes stronger (Γ = 0.1), the model trained by Case (2) strategy exhibits superior noise resistance. Note that the SL algorithms have the same conclusi… view at source ↗
Figure 3
Figure 3. The test set average fidelity F¯ of the model trained by the DRL and SL algo￾rithms as a function of different environmental parameters: (a) Γ (γ = 4, T = 10); (b) γ (Γ = 0.1, T = 10); and (c) T (Γ = 0.1, γ = 4) for three cases. The hollow data points represent the test results of environmental parameters that the model has not seen during the training process. 13 [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Comparison of the control action sequences generated by the DRL and SL models [PITH_FULL_IMAGE:figures/full_fig_p016_4.png]
Figure 5
Figure 5. Figure 5: The distribution of the fidelities F versus design time of the DRL and SL algorithms in Case (2) and Case (3) based on the test set. Γ = 0.1,γ = 4 and T = 10. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_5.png]

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Reference graph

Works this paper leans on

87 extracted references · 76 canonical work pages · cited by 1 Pith paper

  1. [1]

    Quantum Computation and Quantum Information: 10th Anniversary Edition

    Michael A Nielsen and Isaac L Chuang. Quantum Computation and Quantum Information: 10th Anniversary Edition . Cambridge University Press, Cambridge, UK, 10th anniversary edition edition, 2010

    2010

  2. [2]

    Quantum state prepa- ration with optimal circuit depth: Implementations and applications

    Xiao-Ming Zhang, Tongyang Li, and Xiao Yuan. Quantum state prepa- ration with optimal circuit depth: Implementations and applications. Phys. Rev. Lett. , 129:230504, Nov 2022

    2022

  3. [3]

    Quantum computation: Algorithms and applications

    Chien-Hung Cho, Chih-Yu Chen, Kuo-Chin Chen, Tsung-Wei Huang, Ming-Chien Hsu, Ning-Ping Cao, Bei Zeng, Seng-Ghee Tan, and Ching- Ray Chang. Quantum computation: Algorithms and applications. Chin. J. Phys. , 72:248–269, 2021

    2021

  4. [4]

    Quantum communications, volume 2

    Gianfranco Cariolaro. Quantum communications, volume 2. Springer, 2015

    2015

  5. [5]

    High-dimensional quantum communication: benefits, progress, and future challenges

    Daniele Cozzolino, Beatrice Da Lio, Davide Bacco, and Leif Katsuo Ox- enløwe. High-dimensional quantum communication: benefits, progress, and future challenges. Adv. Quantum Technol., 2(12):1900038, 2019

    2019

  6. [6]

    Perfect function transfer and interference effects in interacting boson lattices

    Lian-Ao Wu, Adam Miranowicz, XiangBin Wang, Yu-xi Liu, and Franco Nori. Perfect function transfer and interference effects in interacting boson lattices. Phys. Rev. A , 80:012332, Jul 2009

    2009

  7. [7]

    Sarandy, and Lian-Ao Wu

    Zhao-Ming Wang, Marcelo S. Sarandy, and Lian-Ao Wu. Almost exact state transfer in a spin chain via pulse control.Phys. Rev. A, 102:022601, Aug 2020

    2020

  8. [8]

    When does reinforcement learning stand out in quantum con- trol? a comparative study on state preparation

    Xiao-Ming Zhang, Zezhu Wei, Raza Asad, Xu-Chen Yang, and Xin Wang. When does reinforcement learning stand out in quantum con- trol? a comparative study on state preparation. NPJ Quantum Inform. , 5(1):85, 2019

    work page 2019

Show all 87 references
  1. [9]

    Deep reinforcement learning for universal quan- tum state preparation via dynamic pulse control

    Run-Hong He, Rui Wang, Shen-Shuang Nie, Jing Wu, Jia-Hui Zhang, and Zhao-Ming Wang. Deep reinforcement learning for universal quan- tum state preparation via dynamic pulse control. EPJ Quantum Tech- nol., 8(1):29, 2021. 26

    2021

  2. [10]

    Quantum circuits for amplification of kerr nonlinearity via quadrature squeezing

    Monika Bartkowiak, Lian-Ao Wu, and Adam Miranowicz. Quantum circuits for amplification of kerr nonlinearity via quadrature squeezing. J. Phys. B: At. Mol. Opt. Phys , 47(14):145501, 2014

    2014

  3. [11]

    van de Kamp, Ryan J

    Marko Toroˇ s, Thomas W. van de Kamp, Ryan J. Marshman, M. S. Kim, Anupam Mazumdar, and Sougato Bose. Relative acceleration noise mitigation for nanocrystal matter-wave interferometry: Applications to entangling masses via quantum gravity. Phys. Rev. Res. , 3:023178, Jun 2021

    2021

  4. [12]

    Materials challenges and oppor- tunities for quantum computing hardware.Science, 372(6539):eabb2823, 2021

    Nathalie P De Leon, Kohei M Itoh, Dohun Kim, Karan K Mehta, Tracy E Northup, Hanhee Paik, BS Palmer, Nitin Samarth, Sorawis Sangtawesin, and David W Steuerman. Materials challenges and oppor- tunities for quantum computing hardware.Science, 372(6539):eabb2823, 2021

    2021

  5. [13]

    Almost-exact state transfer by leakage-elimination- operator control in a non-markovian environment

    Zhao-Ming Wang, Feng-Hua Ren, Da-Wei Luo, Zhan-Yuan Yan, and Lian-Ao Wu. Almost-exact state transfer by leakage-elimination- operator control in a non-markovian environment. Phys. Rev. A , 102:042406, Oct 2020

    2020

  6. [14]

    Brun, R¨ udiger Schack, and Timothy P

    Adriano Barenco, Todd A. Brun, R¨ udiger Schack, and Timothy P. Spiller. Effects of noise on quantum error correction algorithms. Phys. Rev. A, 56:1177–1188, Aug 1997

    1997

  7. [15]

    Claudia Benedetti, Fabrizio Buscemi, Paolo Bordone, and Matteo G. A. Paris. Dynamics of quantum correlations in colored-noise environments. Phys. Rev. A , 87:052328, May 2013

    2013

  8. [16]

    Paladino, Y

    E. Paladino, Y. M. Galperin, G. Falci, and B. L. Altshuler. 1/f noise: Implications for solid-state quantum information quantum information. Rev. Mod. Phys. , 86:361–418, Apr 2014

    2014

  9. [17]

    Quantum correlations dynamics and deco- herence of a three-qubit system subject to classical environmental noise

    Martin Tchoffo, Lionel Tenemeza Kenfack, Georges Collince Fouokeng, and Lukong Cornelius Fai. Quantum correlations dynamics and deco- herence of a three-qubit system subject to classical environmental noise. Eur. Phys. J. Plus , 131:1–18, 2016

    2016

  10. [18]

    Smolin and David P

    John A. Smolin and David P. DiVincenzo. Five two-bit quantum gates are sufficient to implement the quantum fredkin gate. Phys. Rev. A , 53:2855–2856, Apr 1996. 27

    1996

  11. [19]

    DiVincenzo

    David P. DiVincenzo. Two-bit gates are universal for quantum compu- tation. Phys. Rev. A , 51:1015–1022, Feb 1995

    1995

  12. [20]

    Booth, and Jonathan Tennyson

    Jules Tilly, Hongxiang Chen, Shuxiang Cao, Dario Picozzi, Kanav Setia, Ying Li, Edward Grant, Leonard Wossnig, Ivan Rungger, George H. Booth, and Jonathan Tennyson. The variational quantum eigensolver: A review of methods and best practices. Physics Reports, 986:1–128,

  13. [21]

    Quantum error correction: an introductory guide

    Joschka Roffe. Quantum error correction: an introductory guide. Con- temp. Phys. , 60(3):226–245, 2019

    2019

  14. [22]

    Theory of quantum error- correcting codes

    Emanuel Knill and Raymond Laflamme. Theory of quantum error- correcting codes. Phys. Rev. A , 55:900–911, Feb 1997

    1997

  15. [23]

    Perfect quantum error correcting code

    Raymond Laflamme, Cesar Miquel, Juan Pablo Paz, and Wojciech Hu- bert Zurek. Perfect quantum error correcting code. Phys. Rev. Lett. , 77:198–201, Jul 1996

    1996

  16. [24]

    A. R. Calderbank and Peter W. Shor. Good quantum error-correcting codes exist. Phys. Rev. A , 54:1098–1105, Aug 1996

    1996

  17. [25]

    Khodjasteh and D

    K. Khodjasteh and D. A. Lidar. Fault-tolerant quantum dynamical decoupling. Phys. Rev. Lett. , 95:180501, Oct 2005

    2005

  18. [26]

    Nonperturbative dynamical decoupling with random control

    Jun Jing, C Allen Bishop, and Lian-Ao Wu. Nonperturbative dynamical decoupling with random control. Sci. Rep., 4(1):6229, 2014

    2014

  19. [27]

    Protectability of ibmq qubits by dynamical decoupling technique

    Arturo Mena L´ opez and Lian-Ao Wu. Protectability of ibmq qubits by dynamical decoupling technique. Symmetry, 15(1):62, 2022

    2022

  20. [28]

    Neural-network- designed pulse sequences for robust control of singlet-triplet qubits

    Xu-Chen Yang, Man-Hong Yung, and Xin Wang. Neural-network- designed pulse sequences for robust control of singlet-triplet qubits. Phys. Rev. A , 97:042324, Apr 2018

    2018

  21. [29]

    Composite pulses for robust universal control of singlet– triplet qubits

    Xin Wang, Lev S Bishop, JP Kestner, Edwin Barnes, Kai Sun, and S Das Sarma. Composite pulses for robust universal control of singlet– triplet qubits. Nat. Commun. , 3(1):997, 2012. 28

    2012

  22. [30]

    Lidar, and Lorenza Viola

    Kaveh Khodjasteh, Daniel A. Lidar, and Lorenza Viola. Arbitrarily accurate dynamical control in open quantum systems. Phys. Rev. Lett. , 104:090501, Mar 2010

    2010

  23. [31]

    Automated syn- thesis of dynamically corrected quantum gates

    Kaveh Khodjasteh, Hendrik Bluhm, and Lorenza Viola. Automated syn- thesis of dynamically corrected quantum gates. Phys. Rev. A, 86:042329, Oct 2012

    2012

  24. [32]

    C. Wan, M. Scala, G. W. Morley, ATM. A. Rahman, H. Ulbricht, J. Bateman, P. F. Barker, S. Bose, and M. S. Kim. Free nano-object ramsey interferometry for large quantum superpositions. Phys. Rev. Lett., 117:143003, Sep 2016

    2016

  25. [33]

    Panos Aliferis and Andrew W. Cross. Subsystem fault tolerance with the bacon-shor code. Phys. Rev. Lett. , 98:220502, May 2007

    2007

  26. [34]

    Fowler, Matteo Mariantoni, John M

    Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland. Surface codes: Towards practical large-scale quantum compu- tation. Phys. Rev. A , 86:032324, Sep 2012

    2012

  27. [35]

    Non- perturbative dynamical decoupling control: A spin-chain model

    Zhao-Ming Wang, Lian-Ao Wu, Jun Jing, Bin Shao, and Ting Yu. Non- perturbative dynamical decoupling control: A spin-chain model. Phys. Rev. A, 86:032303, Sep 2012

    2012

  28. [36]

    Todd Green, Hermann Uys, and Michael J. Biercuk. High-order noise filtering in nontrivial quantum logic gates. Phys. Rev. Lett., 109:020501, Jul 2012

    2012

  29. [37]

    DiVincenzo, and Hendrik Bluhm

    Pascal Cerfontaine, Tim Botzem, David P. DiVincenzo, and Hendrik Bluhm. High-fidelity single-qubit gates for two-electron spin qubits in gaas. Phys. Rev. Lett. , 113:150501, Oct 2014

    2014

  30. [38]

    Control of quan- tum phenomena: past, present and future

    Constantin Brif, Raj Chakrabarti, and Herschel Rabitz. Control of quan- tum phenomena: past, present and future. New J. Phys. , 12(7):075008, jul 2010

    2010

  31. [39]

    Universal quantum control through deep reinforcement learning

    Murphy Yuezhen Niu, Sergio Boixo, Vadim N Smelyanskiy, and Hartmut Neven. Universal quantum control through deep reinforcement learning. NPJ Quantum Inf. , 5(1):33, 2019. 29

    2019

  32. [40]

    Vamvoudakis, and Jayadev Vijayan

    Anthony Siming Chen, Guido Herrmann, Kyriakos G. Vamvoudakis, and Jayadev Vijayan. Learning-based quantum control for optimal pure state manipulation. IEEE Contr. Sys. Lett. , 8:1319–1324, 2024

    2024

  33. [41]

    Z.-J. Chen, H. Huang, L. Sun, Q.-X. Jie, J. Zhou, Z. Hua, Y. Xu, W. Wang, G.-C. Guo, C.-L. Zou, L. Sun, and X.-B. Zou. Robust and optimal control of open quantum systems. Sci. Adv. , 11(9):eadr0875, 2025

    2025

  34. [42]

    Gonz´ alez, and Ra´ ul Coto

    Ariel Norambuena, Marios Mattheakis, Francisco J. Gonz´ alez, and Ra´ ul Coto. Physics-informed neural networks for quantum control.Phys. Rev. Lett., 132:010801, Jan 2024

    2024

  35. [43]

    Robust control of uncertain quan- tum systems based on physics-informed neural networks and sampling learning

    Kai Zhang, Qi Yu, and Sen Kuang. Robust control of uncertain quan- tum systems based on physics-informed neural networks and sampling learning. IEEE Trans. Artif. Intell. , pages 1–12, 2025

    2025

  36. [44]

    Learning robust and high-precision quantum controls

    Re-Bing Wu, Haijin Ding, Daoyi Dong, and Xiaoting Wang. Learning robust and high-precision quantum controls. Phys. Rev. A , 99:042327, Apr 2019

    2019

  37. [45]

    Yi, and Franco Nori

    Zhi-Cheng Shi, Jun-Tong Ding, Ye-Hong Chen, Jie Song, Yan Xia, X.X. Yi, and Franco Nori. Supervised learning for robust quantum control in composite-pulse systems. Phys. Rev. Appl. , 21:044012, Apr 2024

    2024

  38. [46]

    Adaptive denoising quantum state preparation in a dynamic environment

    Zhao-Ming Wang and Tuo-Zhi Chen. Adaptive denoising quantum state preparation in a dynamic environment. Phys. Rev. Res. , 6:043195, Nov 2024

    2024

  39. [47]

    Realizing a deep reinforcement learn- ing agent for real-time quantum feedback

    Kevin Reuer, Jonas Landgraf, Thomas F¨ osel, James O’Sullivan, Liberto Beltr´ an, Abdulkadir Akin, Graham J Norris, Ants Remm, Michael Ker- schbaum, Jean-Claude Besse, et al. Realizing a deep reinforcement learn- ing agent for real-time quantum feedback. Nat. Commun. , 14(1):7...

    2023

  40. [48]

    V. A. Mikhailov and N. V. Troshkin. Non-markovian dynamics of a two- level system in a bosonic bath and a gaussian fluctuating environment with finite correlation time. Phys. Rev. A , 103:012208, Jan 2021. 30

    2021

  41. [49]

    Studying light-harvesting models with superconducting circuits

    Anton Potoˇ cnik, Arno Bargerbos, Florian AYN Schr¨ oder, Saeed A Khan, Michele C Collodo, Simone Gasparinetti, Yves Salath´ e, Ce- lestino Creatore, Christopher Eichler, Hakan E T¨ ureci, et al. Studying light-harvesting models with superconducting circuits. Nat. Commun. , 9(...

    2018

  42. [50]

    Strong coupling of a single electron in silicon to a microwave photon

    Xiao Mi, JV Cady, DM Zajac, PW Deelman, and Jason R Petta. Strong coupling of a single electron in silicon to a microwave photon. Science, 355(6321):156–158, 2017

    2017

  43. [51]

    Observation of non-markovian micromechanical brownian motion

    Simon Groeblacher, A Trubarov, N Prigge, GD Cole, M Aspelmeyer, and J Eisert. Observation of non-markovian micromechanical brownian motion. Nat. Commun. , 6(1):7606, 2015

    2015

  44. [52]

    Lajos Di´ osi and Walter T. Strunz. The non-markovian stochastic schr¨ odinger equation for open systems. Phys. Lett. A , 235(6):569–573, 1997

    1997

  45. [53]

    Quantum state transmission through a spin chain in finite- temperature heat baths

    Zhao-Ming Wang, Feng-Hua Ren, Da-Wei Luo, Zhan-Yuan Yan, and Lian-Ao Wu. Quantum state transmission through a spin chain in finite- temperature heat baths. J. Phys. A: Math. Theor. , 54(15):155303, mar 2021

    2021

  46. [54]

    From coherent motion to localization: Ii

    Haobin Wang and Michael Thoss. From coherent motion to localization: Ii. dynamics of the spin-boson model with sub-ohmic spectral density at zero temperature. Chem. Phys. , 370(1):78–86, 2010. Dynamics of molecular systems: From quantum to classical

    2010

  47. [55]

    Analytic representations of bath correlation functions for ohmic and superohmic spectral densities using simple poles

    Gerhard Ritschel and Alexander Eisfeld. Analytic representations of bath correlation functions for ohmic and superohmic spectral densities using simple poles. J. Chem. Phys. , 141(9), 2014

    2014

  48. [56]

    Non-markovian evolution of the density operator in the presence of strong laser fields

    Christoph Meier and David J Tannor. Non-markovian evolution of the density operator in the presence of strong laser fields. J. Chem. Phys. , 111(8):3365–3376, 1999

    1999

  49. [57]

    Coherent manipulation of coupled electron spins in semiconductor quantum dots

    Jason R Petta, Alexander Comstock Johnson, Jacob M Taylor, Ed- ward A Laird, Amir Yacoby, Mikhail D Lukin, Charles M Marcus, Micah P Hanson, and Arthur C Gossard. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science, 309(5744):2180–2184, 2005. 31

    2005

  50. [58]

    Notch filtering the nuclear environment of a spin qubit

    Filip K Malinowski, Frederico Martins, Peter D Nissen, Edwin Barnes, Lukasz Cywi´ nski, Mark S Rudner, Saeed Fallahi, Geoffrey C Gardner, Michael J Manfra, Charles M Marcus, et al. Notch filtering the nuclear environment of a spin qubit. Nat. Nanotechnol., 12(1):16–20, 2017

    2017

  51. [59]

    Brunner, Y.-S

    R. Brunner, Y.-S. Shin, T. Obata, M. Pioro-Ladri` ere, T. Kubo, K. Yoshida, T. Taniyama, Y. Tokura, and S. Tarucha. Two-qubit gate of combined single-spin rotation and interdot spin exchange in a double quantum dot. Phys. Rev. Lett. , 107:146801, Sep 2011

    2011

  52. [60]

    Enhancing the coherence of a spin qubit by operating it as a feedback loop that controls its nuclear spin bath

    Hendrik Bluhm, Sandra Foletti, Diana Mahalu, Vladimir Umansky, and Amir Yacoby. Enhancing the coherence of a spin qubit by operating it as a feedback loop that controls its nuclear spin bath. Phys. Rev. Lett. , 105:216803, Nov 2010

    2010

  53. [61]

    Semiconductor quantum computation

    Xin Zhang, Hai-Ou Li, Gang Cao, Ming Xiao, Guang-Can Guo, and Guo-Ping Guo. Semiconductor quantum computation. Natl. Sci. Rev. , 6(1):32–54, 2019

    2019

  54. [62]

    Tunable phonon-induced steady-state coherence in a double-quantum-dot charge qubit

    Archak Purkayastha, Giacomo Guarnieri, Mark T Mitchison, Radim Filip, and John Goold. Tunable phonon-induced steady-state coherence in a double-quantum-dot charge qubit. NPJ Quantum Inf. , 6(1):27, 2020

    2020

  55. [63]

    Understanding machine learning: From theory to algorithms

    Shai Shalev-Shwartz and Shai Ben-David. Understanding machine learning: From theory to algorithms . Cambridge University Press, 2014

    2014

  56. [64]

    Reinforcement learning: An introduction

    Richard S Sutton and Andrew G Barto. Reinforcement learning: An introduction. MIT press, 2018

    2018

  57. [65]

    Q-learning

    Christopher JCH Watkins and Peter Dayan. Q-learning. Mach. Learn., 8:279–292, 1992

    1992

  58. [66]

    Human-level control through deep reinforcement learning

    Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Andrei A Rusu, Joel Veness, Marc G Bellemare, Alex Graves, Martin Riedmiller, An- dreas K Fidjeland, Georg Ostrovski, et al. Human-level control through deep reinforcement learning. Nature, 518(7540):529–533, 2015

    2015

  59. [67]

    Riedmiller

    Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Alex Graves, Ioan- nis Antonoglou, Daan Wierstra, and Martin A. Riedmiller. Playing atari with deep reinforcement learning. ArXiv, abs/1312.5602, 2013. 32

    2013 arXiv

  60. [68]

    Super- vised learning

    P´ adraig Cunningham, Matthieu Cord, and Sarah Jane Delany. Super- vised learning. In Machine learning techniques for multimedia: case studies on organization and retrieval , pages 21–49. Springer, 2008

    2008

  61. [69]

    A review of supervised machine learning algorithms

    Amanpreet Singh, Narina Thakur, and Aakanksha Sharma. A review of supervised machine learning algorithms. In 2016 3rd International Conference on Computing for Sustainable Global Development (INDIA- Com), pages 1310–1315. IEEE, 2016

    2016

  62. [70]

    Gradus, and Anthony J

    Tammy Jiang, Jaimie L. Gradus, and Anthony J. Rosellini. Supervised machine learning: A brief primer. Behav. Ther. , 51(5):675–687, 2020

    2020

  63. [71]

    Neural networks and deep learning , volume 25

    Michael A Nielsen. Neural networks and deep learning , volume 25. De- termination press San Francisco, CA, USA, 2015

    2015

  64. [72]

    Introduction to algorithms

    Thomas H Cormen, Charles E Leiserson, Ronald L Rivest, and Clifford Stein. Introduction to algorithms . MIT press, 2022

    2022

  65. [73]

    Chapter 6 - basics of decision-making in de- sign and management of biomass-based production chains

    S ¸ebnem Yılmaz Balaman. Chapter 6 - basics of decision-making in de- sign and management of biomass-based production chains. In S ¸ebnem Yılmaz Balaman, editor, Decision-Making for Biomass-Based Produc- tion Chains , pages 143–183. Academic Press, 2019

    2019

  66. [74]

    Solving the local- minimum problem in training deep learning machines

    James Ting-Ho Lo, Yichuan Gui, and Yun Peng. Solving the local- minimum problem in training deep learning machines. In Neural In- formation Processing: 24th International Conference, ICONIP 2017, Guangzhou, China, November 14-18, 2017, Proceedings, Part I 24 , pages 166–174. S...

    2017

  67. [75]

    On the omnipresence of spu- rious local minima in certain neural network training problems

    Constantin Christof and Julia Kowalczyk. On the omnipresence of spu- rious local minima in certain neural network training problems. Constr. Approx., 60(2):197–224, Oct 2024

    2024

  68. [76]

    Enhanced quan- tum state preparation via stochastic predictions of neural networks

    Chao-Chao Li, Run-Hong He, and Zhao-Ming Wang. Enhanced quan- tum state preparation via stochastic predictions of neural networks. Phys. Rev. A , 108:052418, Nov 2023

    2023

  69. [77]

    Negative log likelihood ratio loss for deep neural network classification

    Hengshuai Yao, Dong-lai Zhu, Bei Jiang, and Peng Yu. Negative log likelihood ratio loss for deep neural network classification. InProceedings of the Future Technologies Conference (FTC) 2019: Volume 1 , pages 276–282. Springer, 2020. 33

    2019

  70. [78]

    Pytorch: An imperative style, high-performance deep learning library

    Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Brad- bury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high-performance deep learning library. ArXiv, 32, 2019

    2019

  71. [79]

    Strunz, Lajos Di´ osi, Nicolas Gisin, and Ting Yu

    Walter T. Strunz, Lajos Di´ osi, Nicolas Gisin, and Ting Yu. Quantum trajectories for brownian motion. Phys. Rev. Lett. , 83:4909–4913, Dec 1999

    1999

  72. [80]

    Non-markovian quantum trajectories versus master equations: Finite-temperature heat bath

    Ting Yu. Non-markovian quantum trajectories versus master equations: Finite-temperature heat bath. Phys. Rev. A , 69:062107, Jun 2004

    2004

  73. [81]

    Dynamics of non-markovian open quantum systems

    In´ es de Vega and Daniel Alonso. Dynamics of non-markovian open quantum systems. Rev. Mod. Phys. , 89:015001, Jan 2017

    2017

  74. [82]

    Di´ osi, N

    L. Di´ osi, N. Gisin, and W. T. Strunz. Non-markovian quantum state diffusion. Phys. Rev. A , 58:1699–1712, Sep 1998

    1998

  75. [83]

    Clark, Maksims Volkovs, and Leandro Aolita

    Juan Carrasquilla, Di Luo, Felipe P´ erez, Ashley Milsted, Bryan K. Clark, Maksims Volkovs, and Leandro Aolita. Probabilistic simulation of quantum circuits using a deep-learning architecture. Phys. Rev. A , 104:032610, Sep 2021

    2021

  76. [84]

    Time-dependent variational principle for open quantum systems with artificial neural networks

    Moritz Reh, Markus Schmitt, and Martin G¨ arttner. Time-dependent variational principle for open quantum systems with artificial neural networks. Phys. Rev. Lett. , 127:230501, Dec 2021

    2021

  77. [85]

    Reconstructing quantum states with generative models

    Juan Carrasquilla, Giacomo Torlai, Roger G Melko, and Leandro Aolita. Reconstructing quantum states with generative models. Nat. Mach. Intell., 1(3):155–161, 2019

    2019

  78. [86]

    Di Luo, Zhuo Chen, Juan Carrasquilla, and Bryan K. Clark. Autoregres- sive neural network for simulating open quantum systems via a proba- bilistic formulation. Phys. Rev. Lett. , 128:090501, Feb 2022. 34

    2022

  79. [2022]

    The Variational Quantum Eigensolver: a review of methods and best practices

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.