Pith. sign in

REVIEW 4 major objections 6 minor 59 references

Qualitative differences in the robust controllability of model two-qubit systems

T0 review · 4 major / 6 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 Two look-alike two-qubit systems have very different robust-control behaviour.

desk verdict Useful numerical case study on robust two-qubit control, but a mismatched Hamiltonian definition and an overclaimed conclusion need fixing before it is citable. read the letter →

arxiv 2502.04102 v2 pith:D7KPHTBL submitted 2025-02-06 quant-ph

Anirban Dey , Mattias T. Johnsson , Daniel Burgarth This is my paper · ORCID
classification quant-ph
keywords quantumcontrolrobustcontrollabilitytwo-qubitsystemsparameteruncertaintyensembletimescalinggradientascentpulseengineeringmodifiedfidelity
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 asks whether two superficially similar two-qubit systems, each with one continuous parameter written $\omega$ and known only to lie in $[1,2]$, can be controlled robustly despite that parameter uncertainty. The first system, A, is proved robustly controllable by a standard algebraic argument that builds the needed operations from repeated commutators of the drift and control terms, and optimizing its control pulses behaves well. The second system, B, resists that proof, so the authors test it numerically by discretizing $\omega$ into $N$ sample values and searching for a single pulse that works for all of them. The numerics indicate that B is also robustly controllable at error $10^{-3}$, but the minimum control time only plateaus after many more samples, and B shows no improvement when given more time or when the fidelity is modified to penalize parameter sensitivity. The practical point is that two apparently similar devices can have very different robustness behaviour, so controllability on paper does not predict how hard robust gates will be to realize.

What carries the argument

The carrying device is the finite-ensemble approximation to a continuous parameter. The unknown parameter $\omega$ is replaced by $N$ discrete values, the system is embedded as a block-diagonal ensemble $\bar H_d=\bigoplus_{n=1}^N H_d(\omega_n)$, and controllability of the ensemble is certified by two Lie-algebraic conditions: each individual system must be fully controllable, and no two systems may be Lie-related, so a single pulse can drive all copies to the same unitary. The scaling argument then uses Duhamel's bound $\|U_\omega(t)-U_\sigma(t)\le t\,\|H_d(\omega)-H_d(\sigma)\|$: if the minimal control time $T_\epsilon(N)$ grows more slowly than linearly in $N$, the worst-case error between neighbouring grid points shrinks as $N$ grows, which is taken as evidence for robust controllability of the continuous family. A second mechanism is the modified fidelity $f'=f-\alpha|\partial f/\partial\omega|$, whose analytic gradient with respect to $\omega$ is computed through the eigendecomposition of each time slice, and which is meant to suppress the sharp error peaks that appear between optimized grid points.

What would settle it

Run a much wider numerical search for System B, using many random initial pulses for $N=20$ and $N=30$ and targeting error $10^{-4}$, and ask whether the apparent plateau in $T_\epsilon(N)$ survives. If a pulse beats $10^{-4}$ or $T_\epsilon(N)$ keeps growing linearly with $N$, the inference of continuous-parameter robust controllability fails; if no search beats the $10^{-3}$ plateau, that supports the paper's conclusion.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is a qualitative gap in robust controllability between two model two-qubit Hamiltonians that have the same control dimension and the same unknown parameter range. System A, with drift $\omega X\otimes I + X\otimes X + Y\otimes Y + Z\otimes Z$ and control $Z\otimes I$, is demonstrably robustly controllable over a compact interval with $\omega_0\omega_1>0$, and its numerically optimized pulses improve predictably as the control time grows. System B, with drift $\omega(X\otimes X + I\otimes X) + Z\otimes I + Y\otimes Y + Z\otimes Z$ and control $X\otimes I$, cannot be settled by the same theoretical scheme because the $\omega$-dependent part of the drift commutes with the control, so there is no way to invert the drift or generate its commutators. Discretizing $\omega$ into $N$ equally spaced points and optimizing one pulse for the ensemble, the authors find that System B becomes robustly controllable for $N\ge 10$ with errors below $10^{-3}$ over $\omega\in[1,2]$, whereas System A already plateaus at $N=3$. The qualitative difference is that System A's worst-case error falls monotonically as control time increases and improves with the modified fidelity $f'=f-\alpha|\partial f/\partial\omega|$, while System B's worst-case error stays roughly constant and the same penalty gives no improvement; the authors conclude that both systems are robustly controllable but that robust control of B is qualitatively harder.

Load-bearing premise

The conclusion that System B is robustly controllable over the whole continuous range rests on assuming that the numerically observed plateau in the minimum control time is the true minimum and not just the best a local optimizer could find.

Editorial extensions

If this is right

  • If System B is robustly controllable as claimed, then a single control pulse can implement a fixed gate across the whole parameter interval, but only after a much longer pulse and a finer parameter grid than System A requires.
  • For System A, extra control time and gradient-penalty re-optimization are reliable robustness levers; for System B, neither lever helps, so any practical robust-control protocol for B must look elsewhere for improvement.
  • The numerical plateau diagnostic, combining sublinear $T_\epsilon(N)$ scaling with inter-sample error suppression, becomes a general test for continuous-parameter robust controllability when theoretical proofs are unavailable.
  • The qualitative difference observed for CNOT and for a generic two-qubit unitary is the same, so the conclusion is not an artifact of a particular target gate.

Reading between the lines

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

  • Inference: if the plateau for System B is a genuine feature of the optimization landscape and not a local-optimizer artefact, then the minimum control time for continuous-parameter robust control of B may grow at least linearly with the desired accuracy, implying an intrinsic robustness cost that no pulse-shaping trick can remove.
  • Inference: the likely structural cause is that in System B the uncertain parameter enters the drift in a direction that commutes with the control; the same obstruction should appear in any system where the unknown parameter multiplies a Hamiltonian piece that commutes with all controls, giving a simple design rule for parameter placement.
  • Inference: a direct test would be to apply a global or many-seed optimization search to System B at larger $N$ and over a wider parameter interval, since the paper's search was local and could in principle have missed shorter control pulses that would change the scaling conclusion.
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 / 6 minor

Summary. This paper studies robust approximate controllability of two two-qubit systems with a single unknown parameter ω in the drift Hamiltonian and a single control field. System A, previously shown to be robustly controllable within an interval, is used as a benchmark. For System B, the paper shows that the Lie-algebraic polynomial-approximation argument used for System A cannot be directly applied, then discretizes ω into an ensemble and uses GRAPE in QuTiP to find a common pulse. It infers robust controllability from the scaling of the minimal control time with the number of discretization points and introduces a modified fidelity with a gradient penalty α|∂f/∂ω| to improve robustness. The authors report that System B is robustly controllable but qualitatively harder: its Tε(N) plateaus more slowly, the worst-case error does not improve with control time, and the modified fidelity does not improve the between-grid-point errors.

Significance. The paper addresses a real question—how to assess robust controllability when the unknown parameter is continuous—and offers a concrete numerical protocol with a novel penalty term and an analytic gradient derivation in Appendix A. The comparison of two systems with different Lie-algebraic structure is a useful case study, and the authors are careful to cite Ref. [11] for System A rather than re-derive it. However, the central numerical claim is not yet fully supported: the System B Hamiltonian is specified inconsistently, the structural conditions for ensemble controllability are asserted without proof, and the inference from local optimization to continuous robust controllability is stronger than the evidence warrants. These issues are fixable, but they are load-bearing.

major comments (4)
  1. [Eq. (4) and Sec. II, System B] System B is defined by two different drift Hamiltonians: Eq. (4) gives Hd(ω)=ω(X⊗I+I⊗X)+Z⊗I+Y⊗Y+Z⊗Z with Hc=X⊗I, whereas the System B paragraph of Sec. II defines Hd(ω)=ω(X⊗X+I⊗X)+Z⊗I+Y⊗Y+Z⊗Z with the same Hc. The numerical section never states which of these two Hamiltonians was used in the QuTiP simulations, so Figs. 1–3 and 5 are not tied to a unique reproducible model. The definitions are not equivalent in any obvious way: under conjugation by X⊗I, the term I⊗X is mapped to X⊗X, so the δ-pulse computation and the obstruction in Sec. II apply literally only to the Sec. II Hamiltonian. Please state explicitly which Hamiltonian was used in every simulation, or prove and state a unitary equivalence between the two models and keep the analysis consistent.
  2. [Sec. III B] Section III B states that System B 'exhibits the two key properties'—full controllability of H(ω) for each fixed ω and pairwise non-Lie-relatedness of H(ω) and H(ω′) for ω≠ω′—but neither property is proved or referenced. These conditions are the sufficient conditions from Refs. [37,38,42] under which the finite-N ensemble is controllable, and they are not self-evident for a drift with an unknown multiplicative parameter. Without a proof or citation, the numerical search cannot be grounded in the ensemble-controllability framework that the paper invokes.
  3. [Sec. III B / Fig. 1 / Sec. V] Fig. 1 and the surrounding discussion in Sec. III B infer continuous robust controllability from the observed plateau of Tε(N) for System B. This inference is valid only if the plotted Tε(N) are true minimum control times. GRAPE is a local optimizer, and the plateau at N≥10 could be an artifact of the optimizer failing to locate better pulses as the ensemble dimension grows; if the true Tε(N) grew at least linearly, Duhamel's bound Eq. (6) would not imply any continuous-limit guarantee. The manuscript acknowledges the difficulty of the continuous limit in Sec. III, but the concluding statement in Sec. V that the numerical approach 'confirms that both systems are robustly controllable' goes beyond the evidence. Please add evidence of global optimality (e.g., many random initial guesses, a global search for moderate N) or explicitly restrict the claim to the discretized ensemble.
  4. [Sec. IV / Appendix A] Sec. IV introduces the modified fidelity f′=f−α|∂f/∂ω|, but it does not specify which fidelity f is being used. The numerical method in Sec. III A defines the phase-sensitive fidelity fSU in Eq. (7), while Sec. IV and Appendix A define and differentiate the phase-insensitive fPSU in Eq. (17). The paper never states whether the α≠0 optimizations used fSU, fPSU, or both, nor whether the analytical gradient in Eq. (16) was evaluated with the same fidelity that entered the optimization. Because the qualitative conclusion of Sec. IV—that the penalty improves System A but not System B—could depend on this choice, the fidelity convention must be fixed for the comparison to be meaningful.
minor comments (6)
  1. [Sec. I, Sec. III B, Sec. IV, Fig. 3] There are several typographical errors: 'understod' should be 'understood' and 'mthods' should be 'methods' in Sec. I; 'rboust' should be 'robust' in Sec. III B; 'derivar-tion', 'withinin', 'ilustrated', and 'grouo' appear in Sec. IV and should be 'derivation', 'within', 'illustrated', and 'group'; and 'approximatley' in the Fig. 3 caption should be 'approximately'.
  2. [Sec. III A, Eq. (7)] The fidelity fSU in Eq. (7) is called an 'average phase-sensitive fidelity', but the expression is written for a single target and a single evolution operator; if an ensemble average is intended, the notation should reflect the sum over the N discretized ω values.
  3. [Fig. 2 caption] The caption states that for N=14 the error lies below 10^-3 for all ω∈[1,2]; since the curves are evaluated on a finite sample of ω values, the wording should be 'for all sampled ω' to avoid implying an exhaustive continuous sweep.
  4. [Sec. III B] The sentence claiming that CNOT and a generic two-qubit unitary are 'sufficient' target operations for assessing two-qubit robust controllability is stronger than the presented evidence warrants; since the numerical results are target-specific, this claim should be softened or justified.
  5. [Sec. IV] The choice of the penalty weight α and the number of gradient-reduction points n is not discussed; a brief description of how these values were selected, and of how sensitive the reported qualitative differences are to them, would strengthen the comparison.
  6. [Sec. III A] The numerical section does not list the QuTiP parameters used to produce Figs. 1–5, such as the number of pulse segments, the iteration count, and the stopping tolerance; these details are needed for reproducibility of the central numerical results.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: System A's theory is reproduced rather than assumed, System B's robust-controllability claim rests on direct numerical error results, and the finite-N-to-continuous extrapolation is flagged as difficult by the paper itself.

full rationale

The derivation chain is not circular. System A's robust controllability is argued from an explicit Lie-algebraic construction in Sec. II (steps I–VI), not merely imported as a conclusion; Ref. [11], which shares an author, is used for the construction and scaling criterion, but the criterion is restated via Duhamel's bound Eq. (6), giving it independent logical content. System B's central claim is empirical: Fig. 1 shows T_epsilon(N) plateauing for N >= 10, Fig. 2 shows N=14 pulses keeping error below 10^-3 for all omega in [1,2], and Figs. 3 and 5 display the qualitative failure to improve with time or the modified fidelity. Eq. (9) introduces a gradient penalty; alpha and n are chosen hyperparameters, not fitted to the target conclusion, so calling the resulting degradation 'no improvement' is not a prediction forced by construction. The paper itself flags the weakest step: Sec. III says 'it is difficult to determine whether this scheme works in the continuous limit' and later 'numerical results do not guarantee existence of an optimized pulse that can achieve arbitrarily low error'; this is an honest limitation, not a circular equivalence. The Eq. (4)/Sec. II discrepancy in System B's drift definition is a reproducibility bug, not a circularity: no equation reduces to its own input. Accordingly, no circular step is exhibited.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The paper's argument rests on standard controllability theorems and on one unproved structural assumption specific to System B. The modified fidelity introduces two hand-chosen hyperparameters, alpha and n. No new physical entities are postulated.

free parameters (2)
  • alpha penalty weight = 0.1 for System A; 0.2 and 1.0 for System B
    Hand-selected in Sec. IV to make the modified fidelity work; no systematic selection rule is given, and the choice affects whether the method shows improvement.
  • n gradient-reduction points = 2 for System A; 2 and 8 for System B
    Number of omega points at which |df/domega| is penalized; chosen ad hoc in Sec. IV and varied only for System B.
assumptions (6)
  • standard math Lie-algebra rank criterion (LARC) characterizes full controllability of finite-dimensional bilinear quantum systems.
    Invoked in Sec. II and Sec. III A as the criterion for individual and ensemble controllability.
  • standard math Quantum recurrence theorem allows effective simulation of the negative drift Hamiltonian for finite-dimensional systems.
    Invoked in Sec. II, especially in the System A construction, and in the introduction.
  • standard math Trotter and commutator expansion formulas, Eq. (1) and Eq. (2), approximate sums and commutators of Hamiltonians.
    Used throughout the theoretical controllability analysis in Sec. II.
  • standard math Duhamel bound Eq. (6): ||U_omega(t) - U_sigma(t)|| <= t ||H_d(omega) - H_d(sigma)||.
    The bridge from finite-N discretization to continuous-parameter robust controllability relies on this bound and on the scaling of T_epsilon(N) in Sec. III.
  • domain assumption The two sufficient conditions for ensemble controllability, individual full controllability and pairwise non-Lie-relatedness, from Refs. [37,38,42] apply to the discretized system.
    Adopted from the literature to justify ensemble controllability in Sec. III; assumed applicable to the block-diagonal ensemble.
  • ad hoc to paper For System B, each H(omega) is fully controllable and H_omega and H_omega0 are not mutually Lie-related for omega not equal to omega0.
    Stated without proof in Sec. III B; necessary for the finite-ensemble argument to apply.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Qualitative differences in the robust controllability of model two-qubit systems." pith.science (2026). https://pith.science/paper/D7KPHTBL

@misc{pith2026250204102,
  author       = {Pith},
  title        = {Pith review of: Qualitative differences in the robust controllability of model two-qubit systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/D7KPHTBL}},
  note         = {Machine review of arXiv:2502.04102}
}
read the original abstract

The precise implementation and manipulation of quantum gates is key to extracting advantages from future quantum technologies. Achieving this requires very accurate control over the quantum system. If one has complete knowledge about a Hamiltonian, accurate manipulation of the system is possible. However, in real scenarios, there will often be some uncertainty in the parameters of the Hamiltonian, which makes full control of the system either difficult or impossible. In this paper we consider two model Hamiltonians with a continuous parameter that is partly unknown. We assess robust controllability against this parameter uncertainty using existing theoretical frameworks and take a numerical route by discretizing the unknown parameter in the cases where we cannot predict controllability. Furthermore, we introduce a penalty term into the fidelity function to optimize control pulses, enhancing robustness against the influence of parameter fluctuations. Within our framework, we analyze the qualitative differences in the robust controllability of the two systems.

Figures

Figures reproduced from arXiv: 2502.04102 by the authors.

Figure 1
Figure 1. FIG. 1. The figure shows how the minimum control time [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The figure shows how an optimized pulse for system [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) System A. (b) System B. The above figure illustrates how worst-case error behaves for system A and system B [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The figure above compares errors produced by the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The figure above compares errors produced by the [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

59 extracted references · 56 canonical work pages

  1. [11]

    Bocchieri and A

    P. Bocchieri and A. Loinger. Quantum recurrence theo- rem. Phys. Rev., 107:337–338, 1957

    work page 1957

  2. [1]

    Full controllability is characterized by the LARC criterion

    Each system H(ωn)(t) in the system is individually fully controllable. Full controllability is characterized by the LARC criterion

    work page

  3. [2]

    All Hamiltonians H(ωk)(t) and H(ωj )(t) are not mutually Lie-related. Given two pairs ( A, B) ∈ g and ( A′, B′) ∈ g′ for any two arbitrary Lie-algebras g and g′, if there exists a Lie- algebra isomorphism ϕ : g → g′ such that ϕ(A) = A′ and ϕ(B) = B′, then two pairs ( A, B) and ( A′, B′) are Lie-related. While the first condition guarantees the implementa-...

    work page

  4. [3]

    Preskill

    J. Preskill. Quantum computing in the nisq era and be- yond. Quantum, 2:79, 2018

    work page 2018

  5. [4]

    C. A. Weidner, E. A. Reed, J. Monroe, Sheller. B, S. O’Neil, E. Maas, E. A. Jonckheere, F. C. Langbein, and S. Schirmer. Robust quantum control in closed and open systems: Theory and practice. Automatica, 172:111987, 2025

    work page 2025

  6. [5]

    Werninghaus, D

    M. Werninghaus, D. J. Egger, F. Roy, S. Machnes, F. K. Wilhelm, and S. Filipp. Leakage reduction in fast super- conducting qubit gates via optimal control. npj Quant. Inf., 7(1):14, 2021

    work page 2021

  7. [6]

    C P. Koch, U. Boscain, T. Calarco, G. Dirr, S. Filipp, S. J. Glaser, R. Kosloff, S. Montangero, T. S-Herbr¨ uggen, D. Sugny, and F. K. Wilhelm. Quantum optimal control in quantum technologies. strategic report on current sta- tus, visions and goals for research in europe. EPJ Quant. Tech., 9(1):19, 2022

    work page 2022

  8. [7]

    Poggi, Gabriele De Chiara, Steve Campbell, and Anthony Kiely

    Pablo M. Poggi, Gabriele De Chiara, Steve Campbell, and Anthony Kiely. Universally robust quantum control. Phys. Rev. Lett., 132:193801, May 2024

    work page 2024

Show all 59 references
  1. [8]

    Krantz, M

    P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gus- tavsson, and W. D. Oliver. A quantum engineer’s guide to superconducting qubits. App. Phys. Rev., 6(2):021318, 06 2019

    2019

  2. [9]

    Stefanatos and E

    D. Stefanatos and E. Paspalakis. A shortcut tour of quan- tum control methods for modern quantum technologies. EPL, 132(6):60001, 2021

    2021

  3. [10]

    W. Dong, F. Zhuang, S. E. Economou, and E. Barnes. Doubly geometric quantum control. PRX Quant. , 2:030333, 2021

    2021

  4. [12]

    L. S. Schulman. Note on the quantum recurrence theo- rem. Phys. Rev. A, 18:2379–2380, 1978

    1978

  5. [13]

    Sakai, A

    R. Sakai, A. Soeda, M. Murao, and D. Burgarth. Robust controllability of two-qubit hamiltonian dynamics. Phys. Rev. A, 100:042305, 2019

    2019

  6. [14]

    Majumder, L

    S. Majumder, L. Andreta de Castro, and K. R. Brown. Real-time calibration with spectator qubits. npj Quan- tum Information, 6(1):19, 2020

    2020

  7. [15]

    Y. Baum, M. Amico, S. Howell, M. Hush, M. Liuzzi, P. Mundada, T. Merkh, A. R.R. Carvalho, and M. J. Biercuk. Experimental deep reinforcement learning for error-robust gate-set design on a superconducting quan- tum computer. PRX Quant., 2:040324, 2021

    2021

  8. [16]

    White, C.D

    G.A.L. White, C.D. Hill, and L.C.L. Hollenberg. Perfor- mance optimization for drift-robust fidelity improvement of two-qubit gates. Phys. Rev. Appl., 15:014023, 2021

    2021

  9. [17]

    Riesebos, B

    L. Riesebos, B. Bondurant, and K. R. Brown. Univer- sal graph-based scheduling for quantum systems. IEEE Micro, 41(5):57–65, 2021

    2021

  10. [18]

    H. Ball, M. J. Biercuk, A. R. R. Carvalho, J. Chen, M. Hush, L. A. De Castro, L. Li, P. J. Liebermann, H. J. Slatyer, C. Edmunds, V. F., C. Hempel, and A. Milne. Software tools for quantum control: improving quantum computer performance through noise and error suppres- sion. Q...

    2021

  11. [19]

    S. S. Ivanov, B. T. Torosov, and N. V. Vitanov. High- fidelity quantum control by polychromatic pulse trains. Phys. Rev. Lett., 129:240505, 2022

    2022

  12. [20]

    Z. Zhou, R. Sitler, Y. Oda, K. Schultz, and G. Quiroz. Quantum crosstalk robust quantum control. arXiv, 2208.05978 [quant-ph], 2022

    2022 arXiv

  13. [21]

    K. N. Smith et al. Programming physical quantum sys- tems with pulse-level control. Front. in Phys., 10, 2022

    2022

  14. [22]

    Semola, L

    R. Semola, L. Moro, D. Bacciu, and E. Prati. Deep re- inforcement learning quantum control on ibmq platforms and qiskit pulse. In IEEE Int. Conf. on QCE, pages 759– 762, 2022

    2022

  15. [23]

    Acharya et al

    R. Acharya et al. Suppressing quantum errors by scaling a surface code logical qubit. Nature, 614(7949):676–681, 2023

    2023

  16. [24]

    Arute et al

    F. Arute et al. Observation of separated dynamics of charge and spin in the fermi-hubbard model. arXiv, 2010.07965 [quant-ph], 2020

    2010 arXiv

  17. [25]

    Wittler, F

    N. Wittler, F. Roy, K. Pack, M. Werninghaus, A. S. Roy, D. J. Egger, S. Filipp, F. K. Wilhelm, and S. Machnes. Integrated tool set for control, calibration, and charac- terization of quantum devices applied to superconducting qubits. Phys. Rev. Appl., 15:034080, 2021

    2021

  18. [26]

    Kelly et al

    J. Kelly et al. Scalable in situ qubit calibration during repetitive error detection. Phys. Rev. A, 94:032321, 2016

    2016

  19. [27]

    Kelly, P

    J. Kelly, P. O’Malley, M. Neeley, Hartmut N., and John M. Martinis. Physical qubit calibration on a directed acyclic graph. arXiv:quant-ph, 1803.03226, 2018

    2018 arXiv

  20. [28]

    Huang, T

    C. Huang, T. Wang, F. Wu, D. Ding, Qi Ye, L. Kong, F. Zhang, X. Ni, Z. Song, Y. Shi, H.-H. Zhao, C. Deng, and J. Chen. Quantum instruction set design for perfor- mance. Phys. Rev. Lett., 130:070601, 2023

    2023

  21. [29]

    L. Lao, P. Murali, M. Martonosi, and D. Browne. De- signing calibration and expressivity-efficient instruction sets for quantum computing. In Proc. of the 48th Ann. Int. Symp. on Comp. Arch., ISCA ’21, pages 846–859. IEEE Press, 2021

    2021

  22. [30]

    Y. Xu, G. Huang, J. Balewski, A. Morvan, K. Nowrouzi, D. I. Santiago, R. K. Naik, B. Mitchell, and I. Siddiqi. Automatic qubit characterization and gate optimization with qubic. ACM Trans. on Quant. Comp., 4(1), 2022

    2022

  23. [31]

    Lishman and F

    J. Lishman and F. Mintert. Trapped-ion entangling gates robust against qubit frequency errors. Phys. Rev. Res., 2:033117, 2020

    2020

  24. [32]

    Bermudez, P

    A. Bermudez, P. O. Schmidt, M. B. Plenio, and A. Ret- zker. Robust trapped-ion quantum logic gates by con- tinuous dynamical decoupling. Phys. Rev. A, 85:040302, 2012

    2012

  25. [33]

    Shapira, S

    Y. Shapira, S. Cohen, N. Akerman, A. Stern, and R. Oz- eri. Robust two-qubit gates for trapped ions using spin- dependent squeezing. Phys. Rev. Lett., 130:030602, Jan 2023

    2023

  26. [34]

    Shapira, R

    Y. Shapira, R. Shaniv, T. Manovitz, N. Akerman, and R. Ozeri. Robust entanglement gates for trapped-ion qubits. Phys. Rev. Lett., 121:180502, 2018

    2018

  27. [35]

    C. H. Valahu, I. Apostolatos, S. Weidt, and W. K Hensinger. Quantum control methods for robust entan- glement of trapped ions. J. Phys. B: Atomic, Molecular and Optical Physics, 55(20):204003, 2022

    2022

  28. [36]

    Beauchard, J.-M

    K. Beauchard, J.-M. Coron, and P. Rouchon. Controlla- bility issues for continuous-spectrum systems and ensem- ble controllability of bloch equations. Comm. in Math. Phys., 296(2):525–557, 2010. 10

    2010

  29. [37]

    Allg¨ ower, V

    F. Allg¨ ower, V. Blondel, and U. Helmke. Control the- ory: Mathematical perspectives on complex networked systems. Oberwolfach Rep, 9(1):p. 674, 2012

    2012

  30. [39]

    Turinici, V

    G. Turinici, V. Ramakhrishna, B. Li, and H. Rabitz. Op- timal discrimination of multiple quantum systems: con- trollability analysis. J. Phys. A: Math. Gen, 37(1):273, 2004

    2004

  31. [40]

    G. Dirr, U. Helmke, and F. R¨ uppel. Accessibility of bi- linear networks of systems: control by interconnections. Math. of Control, Signals, and Systems, 28(2):14, 2016

    2016

  32. [41]

    Kurniawan, G

    I. Kurniawan, G. Dirr, and U. Helmke. Controllabil- ity aspects of quantum dynamics:a unified approach for closed and open systems. IEEE Trans. on Aut. Cont., 57(8):1984–1996, 2012

    1984

  33. [42]

    Li and N

    Jr-S. Li and N. Khaneja. Ensemble control of bloch equa- tions. IEEE Trans. on Aut. Cont., 54(3):528–536, 2009

    2009

  34. [43]

    Li and N

    Jr-S. Li and N. Khaneja. Control of inhomogeneous quan- tum ensembles. Phys. Rev. A, 73:030302, 2006

    2006

  35. [44]

    Belhadj, J

    M. Belhadj, J. Salomon, and G. Turinici. Ensemble con- trollability and discrimination of perturbed bilinear con- trol systems on connected, simple, compact lie groups. Eu. J. Cont., 22:23–29, 2015

    2015

  36. [45]

    Ge, R.-B Wu, and H

    X. Ge, R.-B Wu, and H. Rabitz. The optimization landscape of hybrid quantum–classical algorithms: From quantum control to nisq applications. Annual Reviews in Control, 54:314–323, 2022

    2022

  37. [46]

    Arenz, B

    C. Arenz, B. Russell, D. Burgarth, and H. Rabitz. The roles of drift and control field constraints upon quantum control speed limits. NJP, 19(10):103015, 2017

    2017

  38. [47]

    Khaneja, T

    N. Khaneja, T. Reiss, C. Kehlet, T Schulte-Herbr¨ uggen, and S. J. Glaser. Optimal control of coupled spin dy- namics: design of nmr pulse sequences by gradient ascent algorithms. Journal of Magnetic Resonance, 172(2):296– 305, 2005

    2005

  39. [48]

    Benjamin and J

    R. Benjamin and J. A. Jonathan. Implementing quan- tum logic gates with gradient ascent pulse engineering: principles and practicalities. Phil. Trans. R. Soc. A., 370:4636–4650, 2012

    2012

  40. [49]

    Johansson, P.D

    J.R. Johansson, P.D. Nation, and F. Nori. Qutip 2: A python framework for the dynamics of open quantum sys- tems. Computer Physics Communications, 184(4):1234– 1240, 2013

    2013

  41. [50]

    Johansson, P.D

    J.R. Johansson, P.D. Nation, and F. Nori. Qutip: An open-source python framework for the dynamics of open quantum systems. Computer Physics Communications, 183(8):1760–1772, 2012

    2012

  42. [51]

    de Fouquieres, S

    P. de Fouquieres, S. G. Schirmer, S. J. Glaser, and Ilya Kuprov. Second order gradient ascent pulse engineering. Journal of Magnetic Resonance, 212(2):412–417, 2011

    2011

  43. [52]

    Chowdhury, Matt C.J

    Farhan T. Chowdhury, Matt C.J. Denton, Daniel C. Bonser, and Daniel R. Kattnig. Quantum control of radical-pair dynamics beyond time-local optimization. PRX Quantum, 5:020303, Apr 2024

    2024

  44. [53]

    Liu and Jorge Nocedal

    Dong C. Liu and Jorge Nocedal. On the limited memory bfgs method for large scale optimization. Mathematical Programming, 45(1):503–528, 1989

    1989

  45. [54]

    Nocedal and S

    J. Nocedal and S. J. Wright. Numerical optimization. Springer New York, 2006

    2006

  46. [55]

    C. G. Broyden. The convergence of a class of double-rank minimization algorithms 1. general considerations. IMA Journal of Applied Mathematics, 6(1):76–90, 03 1970

    1970

  47. [56]

    Fletcher

    R. Fletcher. A new approach to variable metric algo- rithms. The Computer Journal, 13(3):317–322, 01 1970

    1970

  48. [57]

    D. F. Shanno. Conditioning of quasi-newton methods for function minimization. Mathematics of Computation, 24(111):647–656, 2024/06/11/ 1970

    2024

  49. [58]

    A family of variable-metric methods derived by variational means

    Donald Goldfarb. A family of variable-metric methods derived by variational means. Mathematics of Computa- tion, 24(109):23–26, 2024/06/11/ 1970

    2024

  50. [59]

    Machnes, U

    S. Machnes, U. Sander, S. J. Glaser, P. de Fouqui` eres, A. Gruslys, S. Schirmer, and T. Schulte-Herbr¨ uggen. Comparing, optimizing, and benchmarking quantum- control algorithms in a unifying programming framework. Phys. Rev. A, 84:022305, 2011

    2011

  51. [60]

    Schulte-Herbr¨ uggen, A

    T. Schulte-Herbr¨ uggen, A. Sp¨ orl, N. Khaneja, and S. J. Glaser. Optimal control-based efficient synthesis of build- ing blocks of quantum algorithms: A perspective from network complexity towards time complexity. Phys. Rev. A, 72:042331, 2005. Appendix A: Calculation of the...

    2005

Pith tools

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