Pith. sign in

REVIEW 4 major objections 5 minor 70 references

Arbitrary state preparation in quantum harmonic oscillators using neural networks

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

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

Pith's one-line read Neural networks can generate, in one forward pass, the laser pulses that prepare arbitrary quantum states of a harmonic oscillator coupled to an auxiliary qubit, reaching average fidelities above 99.9% for qubit states and 97% for qutrits.

desk verdict A promising amortized-control paper that overclaims by hiding its per-state post-processing behind a 'single forward pass' headline, but the failure-mode analysis is genuinely good. read the letter →

arxiv 2502.04598 v5 pith:7OUQUFGB submitted 2025-02-07 quant-ph physics.optics

Nicolas Parra-A , Vladimir Vargas-Calderón , Herbert Vinck-Posada This is my paper · ORCID
classification quant-phphysics.optics
keywords statepreparationquantumharmonicoscillatorquditneuralnetworkcontrolcompositepulsesJaynes-Cummingsmodelfidelity
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

This paper claims that a neural network can replace per-target optimization in quantum state preparation: given any target state of a harmonic oscillator, a single forward pass outputs the amplitudes, phases, and total duration of a sequence of rectangular pulses applied to the oscillator and an auxiliary qubit, leaving the oscillator in the target state. The authors argue this makes state preparation fast and scalable, since the expensive cost is paid once at training time over Haar-random target states rather than for each new state. On random test sets they report average fidelities of 99.9% for qubit states (with $N=7$ pulses) and 97% for qutrits ($N=9$ pulses), and preliminary 92% for $n=4$ qudits. The paper also documents a narrow region on the Bloch sphere where fidelity collapses, traces it to the network's use of $\arctan(\langle X\rangle/\langle Y\rangle)$ which cannot distinguish two quadrants at $\phi=\pi/4$ and $5\pi/4$, and shows that a post-processing step over nearby states almost eliminates the region.

What carries the argument

The central object is the feed-forward neural network $f_\eta:\mathbb{R}^{n^2-1}\to\mathbb{R}^{4N+1}$ mapping expectation values of an $SU(n)$ basis in the target state to the parameters of a composite pulse sequence (amplitudes $\zeta$, $\xi$ and phases $\phi$, $\varphi$ for each of $N$ pulses, plus total time $T$). The dynamics are generated by a resonant Jaynes–Cummings-type Hamiltonian (Eq. 1) with drivings on both the harmonic oscillator and the auxiliary qubit; the composite-pulse ansatz (Eq. 3) provides controllability through repetition. Training minimizes average infidelity over Haar-random target states with an amplitude-penalty regularization that, together with a computational-basis truncation $n_{\mathrm{comp}}=6$, is meant to prevent leakage above the $n$ target levels. The failure analysis hinges on the function $\arctan(\langle X\rangle/\langle Y\rangle)$ being multi-valued when $\langle X\rangle=\langle Y\rangle$, so the network cannot distinguish the two quadrants and develops a discontinuity.

What would settle it

Run the trained pulse sequences with a larger computational basis, say $n_{\mathrm{comp}}=20$, and monitor the population outside the first $n$ levels; if the norm of the projected prepared state (Eq. 9) departs from 1 by an amount larger than the reported infidelity for any target state, the claimed fidelities are truncation artifacts. An experimental version would measure the harmonic-oscillator populations after the sequence and verify that only the first $n$ levels are occupied.

Watch

Extended reading notes

Core claim

The authors claim that control parameters for arbitrary state preparation in a harmonic oscillator coupled to an auxiliary qubit can be generated by a trained neural network in a single forward pass, eliminating per-instance optimization. Given a target state, the network outputs the amplitudes and phases of $N$ rectangular pulses applied to the oscillator and the qubit, plus the total preparation time; the oscillator is left in the target state after tracing out the qubit. For qubit states with $N=7$ pulses the average fidelity exceeds 99.9%, for qutrits with $N=9$ pulses it is 97%, and for $n=4$ qudits short experiments give 92% with $N=10$. The paper also identifies a narrow region on the Bloch sphere where fidelity drops abruptly, explains it via the quadrant ambiguity of $\arctan(\langle X\rangle/\langle Y\rangle)$ when $\langle X\rangle=\langle Y\rangle$ at $\phi=\pi/4$ and $5\pi/4$, and shows a post-processing step that removes this region, restoring fidelity above 99.8% over almost the entire sphere.

Load-bearing premise

The reported fidelities assume that a six-level computational basis and the amplitude-penalty regularization $\lambda=0.8$ keep population from leaking above the $n$ target levels of the harmonic oscillator, so the simulated dynamics match the real infinite-dimensional oscillator; this convergence check is performed only for $n=2$ and $n=3$.

Editorial extensions

If this is right

  • With a trained network, preparing a target state requires only a single forward pass (plus, in the qubit case, an optional post-processing filter), so the cost per state is inference time rather than an iterative per-state optimization.
  • For qubit targets, seven-pulse sequences give average fidelities above 99.9% over Haar-random states, with individual states reaching 99.999%; for qutrits, nine-pulse sequences give 97%, and preliminary $n=4$ runs give 92% with ten pulses.
  • The fidelity of preparation degrades as the target state's average number of excitations grows, and higher-dimensional qudits are harder; the authors attribute this to the larger Hilbert space and point to richer network architectures as the path forward.
  • A narrow region on the Bloch sphere ($\theta\in(0,0.9)\pi$, $\phi\in(0.25,0.3)\pi$) where fidelity drops abruptly is explained by the network modelling pulse phases with $\arctan(\langle X\rangle/\langle Y\rangle)$, which cannot distinguish the quadrants at $\phi=\pi/4$ and $5\pi/4$; the proposed post-processing of nearby states restores fidelity above 99.8% over almost the whole sphere.
  • Because the method uses rectangular pulses, it is experimentally feasible in platforms where nanosecond rectangular pulses are available (e.g., superconducting resonators coupled to qubits), not in platforms with picosecond timescales.

Reading between the lines

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

  • Inference: the arctangent-type quadrant ambiguity found for qubits is likely to recur for higher-dimensional qudits, because the $SU(n)$ input basis will generically contain points where two expectation values coincide; the $SO(n)$-rotation post-processing sketched in the paper is a natural test.
  • Inference: the regularization weight $\lambda=0.8$ was fixed without systematic optimization, and the authors note smaller values could improve high-excitation states; scanning $\lambda$ against fidelity for $n=3$ states with high occupation is a cheap extension that could push qutrit fidelity above 97%.
  • Inference: an alternative input representation that avoids ratio-based features, such as feeding complex amplitudes directly or using a basis with no crossing expectation values, could remove the failure region at the source rather than patching it with post-processing.
  • Inference: if the single-pass approach scales with improved architectures, it turns state preparation into an on-demand subroutine suitable for quantum machine learning and variational algorithms, where rapid re-encoding of changing target states is a bottleneck.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper proposes a neural-network-based method for preparing arbitrary states of a harmonic oscillator (HO) coupled to an auxiliary qubit. The network takes expectation values of SU(n) generators for the target state as input and outputs parameters for a sequence of rectangular pulses applied to both the HO and the qubit. Training is done on Haar-random target states using simulated Jaynes-Cummings dynamics with a truncated HO basis and an amplitude-penalty regularization. The authors report high average fidelities for qubit and qutrit targets, analyze a low-fidelity region on the Bloch sphere, and introduce a post-processing step that selects neighboring states for targets whose raw fidelity is below a threshold. The abstract claims higher fidelities than the body and asserts that controls are obtained from a single forward pass.

Significance. If the method worked as claimed, it would be a valuable amortized alternative to per-instance quantum optimal control: a neural network would map a target state directly to control pulses, avoiding expensive optimization at runtime. The paper builds on a rigorous controllability result (Pinna and Panati), uses a clean SU(n)-basis encoding, and includes a systematic analysis of a fidelity-drop region, which is a useful diagnostic. However, the central 'single forward pass' claim is contradicted by the paper's own post-processing protocol, and the fidelity numbers in the abstract do not match the body. As presented, the significance is therefore not supported; the method is a neural-network-initialized local search rather than the claimed direct mapping.

major comments (4)
  1. [Abstract; §III.D] The abstract reports average fidelities of 99.99% (qubit), 99.5% (qutrit), and 98.9% (n=4), but the body reports average fidelities of 99.9% for qubit states with seven pulses, 97% for qutrit states with nine pulses, and 92% for n=4 in a 'short experiment' (§III.D). These numbers are not reconciled anywhere in the paper, and the abstract's values appear to correspond to a different or unstated protocol. This direct contradiction must be resolved before the results can be assessed.
  2. [Abstract; §II; §III.F] The central claim that control parameters are obtained 'directly from a single forward pass' and that the framework 'eliminates the need for per-instance optimization' (Abstract, §II) is contradicted by the post-processing protocol in §III.F. For any target whose raw fidelity is below 99.7%, the protocol samples 10 randomly rotated neighboring states, evaluates each candidate against a 99.8% fidelity threshold using a fidelity oracle, and selects the best sequence. This is per-instance search requiring multiple forward passes and an oracle; the reported 99.9% qubit average is obtained after this post-processing (Fig. 8c), not by a single forward pass. The novelty claim as stated is therefore not supported by the implemented method.
  3. [§III.B; §III.D; Abstract] The convergence analysis of the computational basis size ncomp is performed only for n=2 and n=3 (§III.B), but the abstract claims high-fidelity preparation for qudit states with n=4. The only n=4 result in the body is the sentence in §III.D reporting 92% fidelity from 'short experiments', which is far below the abstract's 98.9%. Because the leakage risk is central to whether the truncated simulation faithfully represents the physical oscillator, the absence of a convergence check for n=4 undermines the qudit claim and must be addressed.
  4. [§IV; Eq. (8)] The regularization strength λ=0.8 is acknowledged in §IV to have been chosen without 'adequate optimization', and the paper states that smaller values were avoided for fear of exciting higher levels. This parameter directly controls the trade-off between pulse amplitude and leakage beyond the n target levels. Since the truncation convergence check is limited to low n, the simulated fidelities for higher-dimensional qudits rest on an unvalidated assumption about this trade-off; the authors should at least provide a scan over λ for n=4 and quantify leakage into levels above n.
minor comments (5)
  1. [Appendix A] The text says 'full-forward neural network'; the standard term is 'feed-forward neural network'.
  2. [Eq. (9)] The formula for the leaked-state operator \tilde{\rho}_{\rm prepared} is notationally confusing; the projector onto the high-lying HO subspace should be defined explicitly, and the convention for partial traces should be stated clearly.
  3. [Eq. (8)] The cost function is written as C = 1 - E[F - λ\sum(ζ_n^2+ξ_n^2)], which makes the sign of the penalty term look wrong; rewriting as C = 1 - E[F] + λ E[\sum(ζ_n^2+ξ_n^2)] would be clearer.
  4. [Fig. 5 and Eq. (10)] The Bloch-sphere plots would benefit from an explicit statement of which axis corresponds to which spherical angle (θ and ϕ), since the text defines them only in Eq. (10) and the figure caption is terse.
  5. [References] Reference [44] is incomplete: it lists only authors, a year, and an arXiv number; the full title and journal information should be provided.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the central claim is an out-of-sample neural-network prediction grounded by an external controllability theorem.

full rationale

The derivation is not circular. The controllability premise is imported from an external theorem, Pinna and Panati (Ref. [1]), not from the authors' prior work, and no uniqueness claim from the present authors is invoked. The neural-network training in Eq. (8) minimizes average infidelity over Haar-random target states, and the reported fidelities in Sec. III.D and Fig. 4 are evaluated on validation sets sampled from the same distribution but distinct from training; hence the evaluation is a genuine out-of-sample test, not a fit to the reported quantities. The ncomp truncation in Sec. III.B is checked by convergence of the dynamics as n_prepared increases, so the choice of ncomp=6 is an empirical modeling assumption rather than a quantity that is predicted from itself. The post-processing in Sec. III.F does undermine the abstract's "single forward pass" language, because poorly behaved targets are prepared by an oracle-guided search over 10 random neighboring states, and the 99.9% average is reported after that search; but this is an inconsistency or overclaim between the abstract and the implemented protocol, not a circular derivation, because the post-processing is an additional selection step whose success is not guaranteed by construction. The regularization choice lambda=0.8 is acknowledged in Sec. IV as not optimally chosen; that is a correctness risk, not circularity. Accordingly, no step reduces to its inputs by definition or by a self-citation chain.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on several hand-picked hyperparameters (lambda, ncomp, N, post-processing thresholds) and on a controllability theorem from the literature. No new physical entities are introduced.

free parameters (4)
  • lambda = 0.8
    Regularization weight in the cost function, chosen by hand because it yields good performance (Section III).
  • ncomp = 6
    Computational basis truncation size chosen from convergence analysis for qubit and qutrit; used for all results including n=4 without re-validation.
  • N (number of pulses) = 7 for qubit, 9 for qutrit, 10 for n=4 short experiment
    Selected empirically; the paper shows fidelity improves with N but does not provide a stopping rule.
  • post-processing thresholds = 99.7% threshold, 99.8% neighbor threshold, 10 neighbors, epsilon=0.004
    Ad hoc values used in the fidelity-repair step (Section III.F).
assumptions (5)
  • domain assumption The driven Jaynes-Cummings system is completely controllable (Pinna and Panati).
    Cited [1]; used to claim that any target state can be prepared with time-dependent controls, but the paper does not prove piecewise-constant pulses inherit this.
  • domain assumption The rotating wave approximation and exact resonance (detunings zero) are valid for the physical platform.
    Used to write Hamiltonian (1); not justified for the nanosecond-pulse superconducting platform.
  • ad hoc to paper Truncating the oscillator to ncomp=6 levels and adding a pulse-amplitude penalty sufficiently captures the physical dynamics without leakage above n levels.
    Central modeling assumption in Section III.B; no rigorous bound, only a convergence heuristic.
  • ad hoc to paper The neural network trained on Haar-random states generalizes to the full state space.
    Standard ML assumption; the paper itself finds a generalization failure region (Fig. 5).
  • domain assumption The initial state is |0,0>, the ground state.
    Justified for low-temperature systems; the paper notes this cannot prepare states with lower mean excitation.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Arbitrary state preparation in quantum harmonic oscillators using neural networks." pith.science (2026). https://pith.science/paper/7OUQUFGB

@misc{pith2026250204598,
  author       = {Pith},
  title        = {Pith review of: Arbitrary state preparation in quantum harmonic oscillators using neural networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7OUQUFGB}},
  note         = {Machine review of arXiv:2502.04598}
}
read the original abstract

Preparing quantum states is a fundamental task in various quantum algorithms. In particular, state preparation in quantum harmonic oscillators (HOs) is crucial for the manipulation of qudits and the implementation of high-dimensional algorithms. In this work, we develop a general methodology for quantum state preparation in an HO coupled to an auxiliary qubit, guaranteeing that any target state is physically preparable. Both the qubit and the HO are driven by two lasers with time-dependent phase modulation. The modulation times and phase values are generated by a neural network whose input is the desired target state. In contrast to conventional quantum control approaches, this framework eliminates the need for per-instance optimization of the control protocol. Instead, the control parameters required to prepare an arbitrary quantum state of the HO are obtained directly from a single forward pass through the neural network. Specifically, we present results for preparing arbitrary qubit, qutrit, and qudit (n=4) states in the HO, achieving average fidelities of 99.99%, 99.5%, and 98.9%, respectively, across random target states.

Figures

Figures reproduced from arXiv: 2502.04598 by the authors.

Figure 1
Figure 1. FIG. 1. Scheme of the proposed methodology. The target [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Average preparation infidelity as a function of the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Trajectory of the state in the HO when attempting [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Preparation infidelity using the proposed neural net [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 4
Figure 4. Figure 4: fig. 4. It is expected that when attempting to prepare [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Base-10 logarithm of the infidelity on the Bloch [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Inputs and outputs of the neural network as a function of the azimuthal angle [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Comparison between the pulse phases predicted by [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Front view of the Bloch sphere colored by the base-10 logarithm of the infidelity. Panel a) corresponds to the fidelities [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Base-10 logarithm of the infidelity as a function of the [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

70 extracted references · 48 canonical work pages

  1. [1]

    Pinna and G

    L. Pinna and G. Panati, Approximate controllability of the jaynes-cummings dynamics, Journal of Mathematical Physics59(2018)

    work page 2018

  2. [2]

    Rosenkranz, E

    M. Rosenkranz, E. Brunner, G. Marin-Sanchez, N. Fitzpatrick, S. Dilkes, Y. Tang, Y. Kikuchi, and M. Benedetti, Quantum state preparation for multivari- ate functions (2024), arXiv:2405.21058 [quant-ph]

    arXiv 2024

  3. [3]

    Mohseni, A

    M. Mohseni, A. Scherer, K. G. Johnson, O. Wertheim, M. Otten, N. A. Aadit, K. M. Bresniker, K. Y. Cam- sari, B. Chapman, S. Chatterjee, G. A. Dagnew, A. Es- posito, F. Fahim, M. Fiorentino, A. Khalid, X. Kong, B. Kulchytskyy, R. Li, P. A. Lott, I. L. Markov, R. F. McDermott, G. Pedretti, A. Gajjar, A. Silva, J. Sorebo, P. Spentzouris, Z. Steiner, B. Toros...

    arXiv 2024

  4. [4]

    Altman, K

    E. Altman, K. R. Brown, G. Carleo, L. D. Carr, E. Dem- ler, C. Chin, B. DeMarco, S. E. Economou, M. A. Eriks- son, K.-M. C. Fu, M. Greiner, K. R. Hazzard, R. G. Hulet, A. J. Koll´ ar, B. L. Lev, M. D. Lukin, R. Ma, X. Mi, S. Misra, C. Monroe, K. Murch, Z. Nazario, K.-K. Ni, A. C. Potter, P. Roushan, M. Saffman, M. Schleier- Smith, I. Siddiqi, R. Simmonds,...

    2021

  5. [5]

    C. W. Bauer, Z. Davoudi, A. B. Balantekin, T. Bhat- tacharya, M. Carena, W. A. de Jong, P. Draper, A. El-Khadra, N. Gemelke, M. Hanada, D. Kharzeev, H. Lamm, Y.-Y. Li, J. Liu, M. Lukin, Y. Meurice, C. Monroe, B. Nachman, G. Pagano, J. Preskill, E. Ri- naldi, A. Roggero, D. I. Santiago, M. J. Savage, I. Sid- diqi, G. Siopsis, D. Van Zanten, N. Wiebe, Y. Ya...

    2023

  6. [6]

    Cerezo, G

    M. Cerezo, G. Verdon, H.-Y. Huang, L. Cincio, and P. J. Coles, Challenges and opportunities in quantum machine learning, Nature Computational Science2, 567 (2022)

    2022

  7. [7]

    F. A. Gonz´ alez, V. Vargas-Calder´ on, and H. Vinck- Posada, Classification with quantum measurements, Journal of the Physical Society of Japan90, 044002 (2021)

    work page 2021

  8. [8]

    Brearley and S

    P. Brearley and S. Laizet, Quantum algorithm for solv- ing the advection equation using hamiltonian simulation, Phys. Rev. A110, 012430 (2024)

    2024

Show all 70 references
  1. [9]

    Krovi, Improved quantum algorithms for linear and nonlinear differential equations, Quantum7, 913 (2023)

    H. Krovi, Improved quantum algorithms for linear and nonlinear differential equations, Quantum7, 913 (2023)

    2023

  2. [10]

    Fomichev, K

    S. Fomichev, K. Hejazi, M. S. Zini, M. Kiser, J. Fraxanet, P. A. M. Casares, A. Delgado, J. Huh, A.-C. Voigt, J. E. Mueller, and J. M. Arrazola, Initial state preparation for quantum chemistry on quantum computers, PRX Quan- tum5, 040339 (2024)

    2024

  3. [11]

    Bauer, S

    B. Bauer, S. Bravyi, M. Motta, and G. K.-L. Chan, Quantum algorithms for quantum chemistry and quan- tum materials science, Chemical Reviews120, 12685 (2020)

    2020

  4. [12]

    Couteau, S

    C. Couteau, S. Barz, T. Durt, T. Gerrits, J. Huwer, R. Prevedel, J. Rarity, A. Shields, and G. Weihs, Appli- cations of single photons in quantum metrology, biology and the foundations of quantum physics, Nature Reviews Physics5, 354 (2023)

    2023

  5. [13]

    Li and Z

    Y. Li and Z. Ren, Quantum metrology with ann-qubitw superposition state under noninteracting and interacting operations, Phys. Rev. A107, 012403 (2023)

    2023

  6. [14]

    Dooley, W

    S. Dooley, W. J. Munro, and K. Nemoto, Quantum metrology including state preparation and readout times, inQuantum Information and Measurement (QIM) 2017 (Optica Publishing Group, 2017) p. QW3A.5

    2017

  7. [15]

    J. S. Kollath-B¨ onig, L. Dellantonio, L. Giannelli, T. Schmit, G. Morigi, and A. S. Sørensen, Fast storage of photons in cavity-assisted quantum memories, Physical Review Applied22, 10.1103/physrevapplied.22.044038 (2024)

    2024 doi

  8. [16]

    S. R. Hasan, M. Z. Chowdhury, M. Saiam, and Y. M. Jang, Quantum communication systems: Vision, proto- cols, applications, and challenges, IEEE Access11, 15855 (2023)

    2023

  9. [17]

    Rojan, D

    K. Rojan, D. M. Reich, I. Dotsenko, J.-M. Raimond, C. P. Koch, and G. Morigi, Arbitrary-quantum-state preparation of a harmonic oscillator via optimal control, Phys. Rev. A90, 023824 (2014)

    2014

  10. [18]

    Volya and P

    D. Volya and P. Mishra, State preparation on quantum computers via quantum steering, IEEE Transactions on Quantum Engineering5, 1–14 (2024)

    2024

  11. [19]

    W. Cai, J. Han, L. Hu, Y. Ma, X. Mu, W. Wang, Y. Xu, Z. Hua, H. Wang, Y. P. Song, J.-N. Zhang, C.-L. Zou, and L. Sun, High-efficiency arbitrary quantum operation on a high-dimensional quantum system, Phys. Rev. Lett. 127, 090504 (2021)

    2021

  12. [20]

    A. B. Magann, C. Arenz, M. D. Grace, T.-S. Ho, R. L. Kosut, J. R. McClean, H. A. Rabitz, and M. Sarovar, From pulses to circuits and back again: A quantum op- timal control perspective on variational quantum algo- rithms, PRX Quantum2, 010101 (2021)

    2021

  13. [21]

    Porotti, A

    R. Porotti, A. Essig, B. Huard, and F. Marquardt, Deep Reinforcement Learning for Quantum State Preparation with Weak Nonlinear Measurements, Quantum6, 747 (2022)

    2022

  14. [22]

    Khalid, C

    I. Khalid, C. A. Weidner, E. A. Jonckheere, S. G. Schirmer, and F. C. Langbein, Sample-efficient model- based reinforcement learning for quantum control, Phys. Rev. Res.5, 043002 (2023)

    2023

  15. [23]

    B. T. Torosov and N. V. Vitanov, Composite pulses with errant phases, Phys. Rev. A100, 023410 (2019)

    2019

  16. [24]

    Shi, J.-H

    Z.-C. Shi, J.-H. Wang, C. Zhang, J. Song, and Y. Xia, Universal composite pulses for robust quantum state en- gineering in four-level systems, Phys. Rev. A109, 022441 (2024)

    2024

  17. [25]

    Zylberman and F

    J. Zylberman and F. Debbasch, Efficient quantum state preparation with walsh series, Phys. Rev. A109, 042401 (2024)

    2024

  18. [26]

    Iaconis, S

    J. Iaconis, S. Johri, and E. Y. Zhu, Quantum state preparation of normal distributions using matrix prod- uct states, npj Quantum Information10, 15 (2024)

    2024

  19. [27]

    M. Zhou, F. A. C´ ardenas-L´ opez, S. Dominique, and X. Chen, Optimal control for open quantum system in circuit quantum electrodynamics (2024), arXiv:2412.20149 [quant-ph]

    2024 arXiv

  20. [28]

    C. K. Law and J. H. Eberly, Arbitrary control of a quan- tum electromagnetic field, Phys. Rev. Lett.76, 1055 11 (1996)

    1996

  21. [29]

    Vogel, V

    K. Vogel, V. M. Akulin, and W. P. Schleich, Quantum state engineering of the radiation field, Phys. Rev. Lett. 71, 1816 (1993)

    1993

  22. [30]

    Y. R. Sanders, G. H. Low, A. Scherer, and D. W. Berry, Black-box quantum state preparation without arithmetic, Phys. Rev. Lett.122, 020502 (2019)

    2019

  23. [31]

    Bausch, Fast Black-Box Quantum State Preparation, Quantum6, 773 (2022)

    J. Bausch, Fast Black-Box Quantum State Preparation, Quantum6, 773 (2022)

    2022

  24. [32]

    T. M. L. de Veras, L. D. da Silva, and A. J. da Silva, Double sparse quantum state preparation, Quantum In- formation Processing21, 204 (2022)

    2022

  25. [33]

    Ramacciotti, A

    D. Ramacciotti, A. I. Lefterovici, and A. F. Rotundo, Simple quantum algorithm to efficiently prepare sparse states, Phys. Rev. A110, 032609 (2024)

    2024

  26. [34]

    Luo and X

    M. Luo and X. Wang, Universal quantum computation with qudits, Science China: Physics, Mechanics and As- tronomy57, 1712 (2014)

    2014

  27. [35]

    Ringbauer, M

    M. Ringbauer, M. Meth, L. Postler, R. Stricker, R. Blatt, P. Schindler, and T. Monz, A universal qudit quantum processor with trapped ions, Nature Physics18, 1053 (2022), arXiv:2109.06903

    2022 arXiv

  28. [36]

    W. Chen, J. Gan, J.-N. Zhang, D. Matuskevich, and K. Kim, Quantum computation and simulation with vi- brational modes of trapped ions, Chinese Physics B30, 060311 (2021)

    2021

  29. [37]

    Vargas-Calder´ on, N

    V. Vargas-Calder´ on, N. Parra-A., H. Vinck-Posada, and F. A. Gonz´ alez, Many-qudit representation for the travelling salesman problem optimisation, Journal of the Physical Society of Japan90, 114002 (2021), https://doi.org/10.7566/JPSJ.90.114002

    2021 doi

  30. [38]

    Goswami, P

    K. Goswami, P. Schmelcher, and R. Mukherjee, Qudit- based scalable quantum algorithm for solving the integer programming problem (2025), arXiv:2508.13906 [quant- ph]

    2025 arXiv

  31. [39]

    Cozzolino, B

    D. Cozzolino, B. Da Lio, D. Bacco, and L. K. Oxenløwe, High-dimensional quantum communi- cation: Benefits, progress, and future challenges, Advanced Quantum Technologies2, 1900038 (2019), https://onlinelibrary.wiley.com/doi/pdf/10.1002/qute.201900038

    2019 doi

  32. [40]

    A. M. Bloch, R. W. Brockett, and C. Rangan, Fi- nite controllability of infinite-dimensional quantum sys- tems, IEEE Transactions on Automatic Control55, 1797 (2010)

    2010

  33. [41]

    B. W. Shore, Two-state coherent excitation, inManip- ulating Quantum Structures Using Laser Pulses(Cam- bridge University Press, 2011) pp. 97–136

    2011

  34. [42]

    Kavokin, J

    A. Kavokin, J. J. Baumberg, G. Malpuech, and F. P. Laussy,Microcavities(Oxford University Press, 2007) dOI: 10.1093/acprof:oso/9780199228942.001.0001

    2007

  35. [43]

    J. J. Garc ´ ıa Ripoll,Quantum Information and Quantum Optics with Superconducting Circuits(Cambridge Uni- versity Press, 2022)

    2022

  36. [44]

    Wang, H.-Y

    Z.-W. Wang, H.-Y. Ma, Y.-A. Yan, L.-A. Wu, and Z.-M. Wang, (2025), arXiv:2508.20377 [quant-ph]

    2025 arXiv

  37. [45]

    training

    (ℏ= 1): ˆH=g(ˆaˆσ+ + ˆa† ˆσ−) +ζ(e iϕ ˆσ− +e −iϕ ˆσ+) +ξ(e iφˆa+e−iφˆa†) + ∆c ˆn+ ∆ωeg ˆσz 2 ,(1) where ˆais the HO annihilation operator (ˆa † is the cre- ation operator), ˆσ+ and ˆσ− are the raising and lowering operators of the qubit,gis the oscillator-qubit interac- tion c...

  38. [46]

    I. A. Bocanegra-Garay, L. Hern´ andez-S´ anchez, I. Ramos- Prieto, F. Soto-Eguibar, and H. M. Moya-Cessa, Invari- ant approach to the driven jaynes-cummings model, Sci- Post Physics16, 007 (2024)

    2024

  39. [47]

    M. H. Levitt, Composite pulses, Progress in Nuclear Magnetic Resonance Spectroscopy18, 61 (1986)

    1986

  40. [48]

    Plesch and i

    M. Plesch and i. c. v. Brukner, Quantum-state prepara- tion with universal gate decompositions, Phys. Rev. A 83, 032302 (2011)

    2011

  41. [49]

    Pfeifer,The Lie Algebras su(N)(Birkh¨ auser Basel, Basel, 2003) pp

    W. Pfeifer,The Lie Algebras su(N)(Birkh¨ auser Basel, Basel, 2003) pp. 16,108

    2003

  42. [50]

    M. V. Narkhede, P. P. Bartakke, and M. S. Sutaone, A review on weight initialization strategies for neural net- works, Artificial Intelligence Review55, 291 (2022)

    2022

  43. [51]

    O. D. Matteo, Understanding the haar measure,https: //pennylane.ai/qml/demos/tutorial_haar_measure (2021), date Accessed: 2024-12-13

    2021

  44. [52]

    J. P. Palao, R. Kosloff, and C. P. Koch, Protecting co- herence in optimal control theory: State-dependent con- straint approach, Phys. Rev. A77, 063412 (2008)

    2008

  45. [53]

    Ndong, C

    M. Ndong, C. Koch, and D. S. and, Time opti- mization and state-dependent constraints in the quantum optimal control of molecular orienta- tion, Journal of Modern Optics61, 857 (2014), https://doi.org/10.1080/09500340.2013.860200

    2014

  46. [54]

    D’Alessandro,Introduction to quantum control and dynamics, Chapman & Hall/CRC applied mathematics & nonlinear science (Taylor & Francis Ltd, Hoboken, NJ, 2007)

    D. D’Alessandro,Introduction to quantum control and dynamics, Chapman & Hall/CRC applied mathematics & nonlinear science (Taylor & Francis Ltd, Hoboken, NJ, 2007)

    2007

  47. [55]

    T. Dong, J. Lin, Y. Zhou, C. Gu, P. Yao, and L. Xu, Noise-like square pulses in a linear-cavity npr mode- locked yb-doped fiber laser, Optics & Laser Technology 136, 106740 (2021)

    2021

  48. [56]

    Tong, T.-J

    L.-Y. Tong, T.-J. Li, Q.-B. Zhu, M. Liu, Z.-R. Zhang, and Z.-C. Luo, Intelligent multi-parameter control of a rectangular pulse in a passively mode-locked fiber laser, Opt. Express32, 43214 (2024)

    2024

  49. [57]

    Huang, B

    L. Huang, B. Li, D. Jia, and C. Ge, Generation of a switchable and tunable rectangular pulse and multi-pulse with different peak powers at the l-band, Appl. Opt.63, 4245 (2024)

    2024

  50. [58]

    We have also split the Hilbert space of the HO into two: the firstnlevels, and the rest of the space up ton comp

  51. [59]

    Bravyi and A

    S. Bravyi and A. Kitaev, Universal quantum computa- tion with ideal clifford gates and noisy ancillas, Phys. Rev. A71, 022316 (2005)

    2005

  52. [60]

    of Virginia, Bootstrap estimates of confidence intervals (n.d.), accessed: 2025-01-29

    U. of Virginia, Bootstrap estimates of confidence intervals (n.d.), accessed: 2025-01-29

    2025

  53. [61]

    Sharma and A

    P. Sharma and A. Singh, Era of deep neural networks: A review, in2017 8th International Conference on Comput- ing, Communication and Networking Technologies (ICC- CNT)(2017) pp. 1–5

    2017

  54. [62]

    D. M. van Egmond and U. Reinosa, Su(n) cartan-weyl bases and color factors (2021), arXiv:2104.12139 [hep-th]

    2021 arXiv

  55. [63]

    C. D. Mladenova and I. M. Mladenov, About parametric representations of so(n) matrices and plane rotations, AIP Conference Proceedings1487, 280 (2012), https://pubs.aip.org/aip/acp/article- pdf/1487/1/280/11586729/280 1 online.pdf

    2012

  56. [64]

    You and Y.-M

    X. You and Y.-M. He, Developing the quantum-dot single-photon sources with excellent performance by coupling asymmetric microcavity, Phys. Rev. Res.7, L012016 (2025)

    2025

  57. [65]

    Meher and S

    N. Meher and S. Sivakumar, A review on quantum in- formation processing in cavities, The European Physical Journal Plus137, 985 (2022)

    2022

  58. [66]

    Shi, J.-T

    Z.-C. Shi, J.-T. Ding, Y.-H. Chen, J. Song, Y. Xia, X. Yi, and F. Nori, Supervised learning for robust quantum con- trol in composite-pulse systems, Phys. Rev. Appl.21, 044012 (2024)

    2024

  59. [67]

    Kokaew, T

    W. Kokaew, T. Chotibut, and A. Chantasri, Optimal control for state preparation in a noisy environment via the most-likely path, inAPS March Meeting Abstracts, 12 APS Meeting Abstracts, Vol. 2022 (2022) p. S33.009

    2022

  60. [68]

    Chen and H.-S

    C.-C. Chen and H.-S. Goan, Effects of initial system- environment correlations on open-quantum-system dy- namics and state preparation, Phys. Rev. A93, 032113 (2016)

    2016

  61. [69]

    Norambuena, M

    A. Norambuena, M. Mattheakis, F. J. Gonz´ alez, and R. Coto, Physics-informed neural networks for quantum control, Phys. Rev. Lett.132, 010801 (2024)

    2024

  62. [70]

    ARBITRAR Y ST A TE PREP ARA TION IN QUANTUM HARMONIC OSCILLA TORS USING NEURAL NETWORKS

    S. Sun, L.-C. Shih, and Y.-C. Cheng, Efficient quantum simulation of open quantum system dynamics on noisy quantum computers, Physica Scripta99, 035101 (2024). Appendix A: Neural network In this work, we consider a full-forward neural network, which results from the consecutiv...

    2024

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.