pith. sign in

arxiv: 2503.20130 · v3 · submitted 2025-03-26 · 🪐 quant-ph

Energy shortcut of N-level quantum protocols by optimal control

C. L. Latune , M. B. Puthuveedu Shebeek , D. Sugny , S. Gu\'erin This is my paper

Pith reviewed 2026-05-22 23:36 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum optimal controlshortcut to adiabaticityenergy minimizationN-level systemsgeodesicsLandau-ZenerSTIRAProbust control
0
0 comments X

The pith

QOSTE achieves the same quantum transformations as STA protocols but at the lowest possible energy cost for N-level systems.

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

The paper introduces Quantum-Optimal-Shortcut-To-Energetics (QOSTE) as a method that matches the state changes of Shortcut-To-Adiabaticity (STA) protocols while using the smallest energy input. For general N-level quantum systems the controls are found with geometry and optimal-control methods, and the lowest energy cost equals the length of the geodesic traced in the rotating frame set by the original protocol. When control times are long the ratio of energy costs between STA and QOSTE grows quadratically with time. Benchmarks on the Landau-Zener qubit protocol and on three-level STIRAP show large energy reductions, and gradient optimization also yields robust QOSTE versions that beat STA on both energy and stability.

Core claim

QOSTE produces the same transformation as STA for a given protocol used in quantum technologies or thermodynamics, but at the lowest possible energy cost. In the general case of an N-level quantum system the minimal energy cost is determined by the length of the geodesic in the rotating frame given by the original protocol. For long control times the scaling of the ratio between the two energy costs of STA and QOSTE is quadratic in time.

What carries the argument

The length of the geodesic in the rotating frame defined by the original protocol, which fixes the minimal energy cost under optimal control.

If this is right

  • QOSTE controls produce the identical final states as STA but with lower energy expenditure.
  • The energy-cost ratio of STA to QOSTE scales quadratically with control time when times are long.
  • Landau-Zener and STIRAP examples exhibit drastic energy reductions relative to standard STA.
  • Gradient-based robust QOSTE protocols can exceed STA performance in both energy efficiency and robustness.

Where Pith is reading between the lines

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

  • The geodesic correspondence could be used to minimize dissipation in quantum heat engines or thermodynamic cycles.
  • The reported robustness-energy trade-off points to design rules for choosing protocols under experimental noise.
  • Direct verification of the quadratic scaling could be attempted in superconducting-qubit or trapped-ion platforms.

Load-bearing premise

The length of the geodesic in the rotating frame equals the minimal energy cost without hidden costs from frame transformations or unaccounted constraints in the N-level Hamiltonian.

What would settle it

An experiment that applies the derived QOSTE controls to an N-level system and measures an energy cost strictly larger than the geodesic length calculated from the rotating frame.

Figures

Figures reproduced from arXiv: 2503.20130 by C. L. Latune, D. Sugny, M. B. Puthuveedu Shebeek, S. Gu\'erin.

Figure 1
Figure 1. Figure 1: FIG. 1. Representation on the Bloch sphere of the excited [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Trajectories of the qubit state when driven re [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Plot of the average fidelity [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

We introduce an energetically-optimal method inspired from Shortcut-To-Adiabaticity (STA) processes, named Quantum-Optimal-Shortcut-To-Energetics (QOSTE). QOSTE produces the same transformation as STA for a given protocol used in quantum technologies or thermodynamics, but at the lowest possible energy cost. In the general case of a N- level quantum system, we derive the QOSTE controls using geometrical and optimal control tools, and show that the minimal energy cost is determined by the length of the geodesic in the rotating frame given by the original protocol. For long control times, the scaling of the ratio between the two energy costs of STA and QOSTE is quadratic in time. We benchmark our results with the Landau-Zener protocol for qubits and STIRAP for three-level systems. We observe a drastic reduction in energy with respect to standard STA methods. Finally, using gradient-based optimization algorithms and highlighting the emerging trade-off between robustness and energy cost, we design robust QOSTE outperforming STA both in robustness and energy efficiency.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces Quantum-Optimal-Shortcut-To-Energetics (QOSTE), a method that achieves the same state transformations as Shortcut-To-Adiabaticity (STA) protocols for N-level quantum systems but at minimal energy cost. It derives the QOSTE controls via geometrical and optimal control tools, asserts that the minimal energy equals the geodesic length in the rotating frame defined by the original protocol, reports quadratic scaling of the STA/QOSTE energy ratio for long times, benchmarks on Landau-Zener (qubits) and STIRAP (three-level), and designs a robust variant via gradient optimization that trades off robustness and energy.

Significance. If the central derivation holds without hidden costs from frame transformations, the result would offer a systematic route to lower-energy quantum control protocols with clear scaling advantages, directly relevant to quantum technologies and quantum thermodynamics; the benchmarks and robustness trade-off discussion add practical value.

major comments (2)
  1. [Abstract] Abstract and introduction: the central claim equates minimal lab-frame energy cost directly to the geodesic length in the rotating frame of the input protocol. This requires explicit demonstration that the time-dependent frame transformation introduces no additional energy contributions when the derived controls are substituted back into the original N-level Hamiltonian; the skeptic concern on unaccounted transformation effects is not addressed in the provided description of the derivation.
  2. [Abstract] Abstract: the reported quadratic scaling of the energy-cost ratio for long control times is stated without reference to a specific equation or theorem establishing the asymptotic behavior; the derivation steps using geometrical/optimal-control tools must be shown to produce this scaling independently of the particular protocol.
minor comments (2)
  1. [Abstract] Abstract provides no equations, error metrics, or numerical data despite claiming derivations and benchmarks; this makes independent verification of the geodesic-energy equivalence impossible from the summary alone.
  2. The manuscript should clarify whether the SU(N) geometry fully encodes all control constraints of the physical N-level Hamiltonian or if additional bounds appear in the lab frame.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed report and constructive suggestions. We address the two major comments below and will revise the manuscript to incorporate explicit demonstrations and references as requested.

read point-by-point responses

  1. Referee: [Abstract] Abstract and introduction: the central claim equates minimal lab-frame energy cost directly to the geodesic length in the rotating frame of the input protocol. This requires explicit demonstration that the time-dependent frame transformation introduces no additional energy contributions when the derived controls are substituted back into the original N-level Hamiltonian; the skeptic concern on unaccounted transformation effects is not addressed in the provided description of the derivation.

    Authors: We agree that an explicit verification is needed to confirm that the rotating-frame geodesic length directly gives the lab-frame energy without hidden contributions from the time-dependent transformation. In the revised manuscript we will add a dedicated derivation (likely as a new subsection or appendix) that starts from the rotating-frame controls, substitutes them into the original N-level Hamiltonian, and shows that any frame-induced terms are exactly canceled by the optimal-control construction, leaving the energy cost equal to the geodesic length. revision: yes

  2. Referee: [Abstract] Abstract: the reported quadratic scaling of the energy-cost ratio for long control times is stated without reference to a specific equation or theorem establishing the asymptotic behavior; the derivation steps using geometrical/optimal-control tools must be shown to produce this scaling independently of the particular protocol.

    Authors: We will add an explicit reference (new equation or theorem statement, supported by a short proof sketch) that derives the quadratic scaling of the STA/QOSTE energy ratio for large T directly from the geodesic property in the rotating frame. The argument relies only on the general properties of the SU(N) geometry and the optimal-control problem, not on the details of any specific protocol such as Landau-Zener or STIRAP; this will be placed in the main text or an appendix. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation uses optimal control to relate cost to geodesic length

full rationale

The abstract states that QOSTE controls are derived using geometrical and optimal control tools, with the result that minimal energy cost equals the geodesic length in the rotating frame of the input protocol. This is presented as an output of the optimal-control analysis rather than a definitional equivalence or fitted prediction. No self-citations, ansatzes smuggled via prior work, or renaming of known results are indicated in the provided text. The central claim retains independent content from the control-theoretic derivation and is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review based on abstract only; no explicit free parameters, axioms, or invented entities listed. The central claim rests on unstated assumptions about applicability of geometric optimal control to the rotating frame.

axioms (1)
  • domain assumption Geometrical and optimal control tools suffice to derive controls that achieve the geodesic length as minimal energy for any N-level system.
    Invoked in abstract as the basis for deriving QOSTE controls.

pith-pipeline@v0.9.0 · 5728 in / 1303 out tokens · 35682 ms · 2026-05-22T23:36:10.663909+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Symmetric $C_Z$ gate for ultracold neutral atoms based on counterdiabatic driving at Rydberg excitation

    quant-ph 2025-10 unverdicted novelty 6.0

    A counterdiabatic symmetric Rydberg-blockade CZ gate scheme for neutral atoms that reduces operation time versus prior adiabatic protocols, provides analytical pulse profiles, and avoids intrinsic single-qubit phase s...

Reference graph

Works this paper leans on

72 extracted references · 72 canonical work pages · cited by 1 Pith paper · 1 internal anchor

  1. [1]

    S. J. Glaser, U. Boscain, T. Calarco, C. P. Koch, W. K¨ ockenberger, R. Kosloff, I. Kuprov, B. Luy, S. Schirmer, T. Schulte-Herbr¨ uggen, D. Sugny, and F. K. Wilhelm, Training Schr¨ odinger’s cat: quantum optimal control, Eur. Phys. J. D69, 1 (2015)

    work page 2015

  2. [2]

    C. P. Koch, U. Boscain, T. Calarco, G. Dirr, S. Fil- ipp, S. J. Glaser, R. Kosloff, S. Montangero, T. Schulte- Herbr¨ uggen, D. Sugny, and F. K. Wilhelm, Quantum op- timal control in quantum technologies. strategic report on current status, visions and goals for research in eu- rope, EPJ Quantum Technology9, 19 (2022)

    work page 2022

  3. [3]

    C. Brif, R. Chakrabarti, and H. Rabitz, Control of quan- tum phenomena: past, present and future, New Journal of Physics12, 075008 (2010)

    work page 2010

  4. [4]

    Altafini and F

    C. Altafini and F. Ticozzi, Modeling and control of quan- tum systems: An introduction, IEEE Trans. Automat. Control57, 1898 (2012)

    work page 2012

  5. [5]

    Dong and I

    D. Dong and I. A. Petersen, Quantum control theory and applications: A survey, IET Control Theory A4, 2651 (2010)

    work page 2010

  6. [6]

    C. P. Koch, M. Lemeshko, and D. Sugny, Quantum con- trol of molecular rotation, Rev. Mod. Phys.91, 035005 (2019)

    work page 2019

  7. [7]

    Gu´ ery-Odelin, A

    D. Gu´ ery-Odelin, A. Ruschhaupt, A. Kiely, E. Tor- rontegui, S. Mart´ ınez-Garaot, and J. G. Muga, Short- cuts to adiabaticity: Concepts, methods, and applica- tions, Rev. Mod. Phys.91, 045001 (2019)

    work page 2019

  8. [8]

    Stefanatos and E

    D. Stefanatos and E. Paspalakis, A shortcut tour of quan- tum control methods for modern quantum technologies, Europhysics Letters132, 60001 (2021)

    work page 2021

  9. [9]

    Torrontegui, S

    E. Torrontegui, S. Ib´ a˜ nez, S. Mart´ ınez-Garaot, M. Mod- ugno, A. del Campo, D. Gu´ ery-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, Chapter 2 - shortcuts to adi- abaticity, inAdvances in Atomic, Molecular, and Opti- cal Physics, Advances In Atomic, Molecular, and Optical Physics, Vol. 62, edited by E. Arimondo, P. R. Berman, and C. C. Lin (Academi...

    work page 2013

  10. [10]

    C. W. Duncan, P. M. Poggi, M. Bukov, N. T. Zinner, and S. Campbell, Taming quantum systems: A tutorial for using shortcuts-to-adiabaticity, quan- tum optimal control, and reinforcement learning, arXiv 10.48550/arXiv.2501.16436 (2025), 2501.16436

    work page doi:10.48550/arxiv.2501.16436 2025

  11. [11]

    R. G. Unanyan, L. P. Yatsenko, K. Bergmann, and B. W. Shore, Laser-induced adiabatic atomic reorientation with control of diabatic losses, Opt. Commun.139, 48 (1997)

    work page 1997

  12. [12]

    Demirplak and S

    M. Demirplak and S. A. Rice, Adiabatic Population Transfer with Control Fields, J. Phys. Chem. A107, 9937 (2003)

    work page 2003

  13. [13]

    Demirplak and S

    M. Demirplak and S. A. Rice, Assisted Adiabatic Passage Revisited, J. Phys. Chem. A109, 6838 (2005)

    work page 2005

  14. [14]

    Demirplak and S

    M. Demirplak and S. A. Rice, On the consistency, ex- tremal, and global properties of counterdiabatic fields, J. Chem. Phys.129, 154111 (2008)

    work page 2008

  15. [15]

    M. V. Berry, Transitionless quantum driving, J. Phys. A: Math. Theor.42, 365303 (2009)

    work page 2009

  16. [16]

    Del Campo, Shortcuts to adiabaticity by counter- diabatic driving, Physical Review Letters111, 100502 (2013)

    A. Del Campo, Shortcuts to adiabaticity by counter- diabatic driving, Physical Review Letters111, 100502 (2013)

    work page 2013

  17. [18]

    Deng, Q.-h

    J. Deng, Q.-h. Wang, Z. Liu, P. H¨ anggi, and J. Gong, Boosting work characteristics and overall heat-engine performance via shortcuts to adiabaticity: Quantum and classical systems, Phys. Rev. E88, 062122 (2013)

    work page 2013

  18. [19]

    M. Beau, J. Jaramillo, and A. Del Campo, Scaling-Up Quantum Heat Engines Efficiently via Shortcuts to Adi- abaticity, Entropy18, 168 (2016)

    work page 2016

  19. [22]

    R. Dann, R. Kosloff, and P. Salamon, Quantum Finite- Time Thermodynamics: Insight from a Single Qubit En- gine, Entropy22, 1255 (2020)

    work page 2020

  20. [23]

    Dann and R

    R. Dann and R. Kosloff, Quantum signatures in the quan- tum Carnot cycle, New J. Phys.22, 013055 (2020)

    work page 2020

  21. [24]

    S. Deng, A. Chenu, P. Diao, F. Li, S. Yu, I. Coulamy, A. del Campo, and H. Wu, Superadiabatic quantum fric- tion suppression in finite-time thermodynamics, Sci. Adv. 4, 10.1126/sciadv.aar5909 (2018)

    work page doi:10.1126/sciadv.aar5909 2018

  22. [25]

    Kosloff and T

    R. Kosloff and T. Feldmann, Discrete four-stroke quan- tum heat engine exploring the origin of friction, Phys. Rev. E65, 055102 (2002)

    work page 2002

  23. [26]

    Feldmann and R

    T. Feldmann and R. Kosloff, Quantum four-stroke heat engine: Thermodynamic observables in a model with in- trinsic friction, Phys. Rev. E68, 016101 (2003)

    work page 2003

  24. [27]

    Feldmann and R

    T. Feldmann and R. Kosloff, Characteristics of the limit cycle of a reciprocating quantum heat engine, Phys. Rev. E70, 046110 (2004)

    work page 2004

  25. [28]

    N. N. Hegade, K. Paul, Y. Ding, M. Sanz, F. Albarr´ an- Arriagada, E. Solano, and X. Chen, Shortcuts to Adi- abaticity in Digitized Adiabatic Quantum Computing, Phys. Rev. Appl.15, 024038 (2021). 6

    work page 2021

  26. [29]

    Y.-H. Chen, W. Qin, X. Wang, A. Miranowicz, and F. Nori, Shortcuts to Adiabaticity for the Quantum Rabi Model: Efficient Generation of Giant Entangled Cat States via Parametric Amplification, Phys. Rev. Lett. 126, 023602 (2021)

    work page 2021

  27. [30]

    A. C. Santos, A. Nicotina, A. M. Souza, R. S. Sarthour, I. S. Oliveira, and M. S. Sarandy, Optimizing NMR quan- tum information processing via generalized transitionless quantum driving, Europhys. Lett.129, 30008 (2020)

    work page 2020

  28. [31]

    Liberzon,Calculus of variations and optimal control theory(Princeton University Press, Princeton, NJ, 2012) pp

    D. Liberzon,Calculus of variations and optimal control theory(Princeton University Press, Princeton, NJ, 2012) pp. xviii+235

    work page 2012

  29. [32]

    D’Alessandro,Introduction to quantum control and dynamics.(Applied Mathematics and Nonlinear Science Series

    D. D’Alessandro,Introduction to quantum control and dynamics.(Applied Mathematics and Nonlinear Science Series. Boca Raton, FL: Chapman, Hall/CRC., 2008)

    work page 2008

  30. [33]

    D. E. Kirk,Optimal control theory: an introduction (Courier Corporation, New York, 2004)

    work page 2004

  31. [34]

    L. S. Pontryagin, V. Boltianski, R. Gamkrelidze, and E. Mitchtchenko,The Mathematical Theory of Optimal Processes(John Wiley and Sons, New York, 1962)

    work page 1962

  32. [35]

    M. M. Lee and L. Markus,Foundations of Optimal Con- trol Theory(John Wiley and Sons, New York, 1967)

    work page 1967

  33. [36]

    Ansel, E

    Q. Ansel, E. Dionis, F. Arrouas, B. Peaudecerf, S. Gu´ erin, D. Gu´ ery-Odelin, and D. Sugny, Introduction to theoretical and experimental aspects of quantum op- timal control, Journal of Physics B: Atomic, Molecular and Optical Physics57, 133001 (2024)

    work page 2024

  34. [37]

    Boscain, M

    U. Boscain, M. Sigalotti, and D. Sugny, Introduction to the Pontryagin Maximum Principle for Quantum Opti- mal Control, PRX Quantum2, 030203 (2021)

    work page 2021

  35. [38]

    Bonnard and D

    B. Bonnard and D. Sugny,Optimal Control with Applica- tions in Space and Quantum Dynamics, AIMS on applied mathematics, Vol. 5 (American Institute of Mathemati- cal Sciences, Springfield, 2012)

    work page 2012

  36. [39]

    Dupont, G

    N. Dupont, G. Chatelain, L. Gabardos, M. Arnal, J. Billy, B. Peaudecerf, D. Sugny, and D. Gu´ ery-Odelin, Quantum state control of a bose-einstein condensate in an optical lattice, PRX Quantum2, 040303 (2021)

    work page 2021

  37. [40]

    Born and V

    M. Born and V. Fock, Beweis des Adiabatensatzes, Z. Phys.51, 165 (1928)

    work page 1928

  38. [41]

    A. d. Campo, J. Goold, and M. Paternostro, More bang for your buck: Super-adiabatic quantum engines, Sci. Rep.4, 1 (2014)

    work page 2014

  39. [42]

    Abah and M

    O. Abah and M. Paternostro, Shortcut-to-adiabaticity Otto engine: A twist to finite-time thermodynamics, Phys. Rev. E99, 022110 (2019)

    work page 2019

  40. [43]

    Hartmann, V

    A. Hartmann, V. Mukherjee, W. Niedenzu, and W. Lech- ner, Many-body quantum heat engines with shortcuts to adiabaticity, Phys. Rev. Res.2, 023145 (2020)

    work page 2020

  41. [44]

    Daems, S

    D. Daems, S. Gu´ erin, and N. J. Cerf, Quantum search by parallel eigenvalue adiabatic passage, Phys. Rev. A78, 042322 (2008)

    work page 2008

  42. [45]

    N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, Stimulated raman adiabatic passage in physics, chemistry, and beyond, Rev. Mod. Phys.89, 015006 (2017)

    work page 2017

  43. [46]

    A. E. Allahverdyan and Th. M. Nieuwenhuizen, Minimal work principle: Proof and counterexamples, Phys. Rev. E71, 046107 (2005)

    work page 2005

  44. [47]

    Albash, S

    T. Albash, S. Boixo, D. A. Lidar, and P. Zanardi, Quan- tum adiabatic Markovian master equations, New J. Phys. 14, 123016 (2012)

    work page 2012

  45. [48]

    J. P. Moutinho, M. Pezzutto, S. S. Pratapsi, F. F. da Silva, S. De Franceschi, S. Bose, A. T. Costa, and Y. Omar, Quantum Dynamics for Energetic Advantage in a Charge-Based Classical Full Adder, PRX Energy2, 033002 (2023)

    work page 2023

  46. [49]

    Energetics of Trapped-Ion Quantum Computation

    F. G´ ois, M. Pezzutto, and Y. Omar, Towards En- ergetic Quantum Advantage in Trapped-Ion Quantum Computation, arXiv 10.48550/arXiv.2404.11572 (2024), 2404.11572

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2404.11572 2024

  47. [50]

    Campbell and S

    S. Campbell and S. Deffner, Trade-Off Between Speed and Cost in Shortcuts to Adiabaticity, Phys. Rev. Lett. 118, 100601 (2017)

    work page 2017

  48. [51]

    Zheng, S

    Y. Zheng, S. Campbell, G. De Chiara, and D. Poletti, Cost of counterdiabatic driving and work output, Phys. Rev. A94, 042132 (2016)

    work page 2016

  49. [52]

    Torrontegui, I

    E. Torrontegui, I. Lizuain, S. Gonz´ alez-Resines, A. To- balina, A. Ruschhaupt, R. Kosloff, and J. G. Muga, En- ergy consumption for shortcuts to adiabaticity, Phys. Rev. A96, 022133 (2017)

    work page 2017

  50. [53]

    Tobalina, I

    A. Tobalina, I. Lizuain, and J. G. Muga, Vanishing effi- ciency of a speeded-up ion-in-Paul-trap Otto engine(a), Europhys. Lett.127, 20005 (2019)

    work page 2019

  51. [54]

    Funo, J.-N

    K. Funo, J.-N. Zhang, C. Chatou, K. Kim, M. Ueda, and A. del Campo, Universal Work Fluctuations During Shortcuts to Adiabaticity by Counterdiabatic Driving, Phys. Rev. Lett.118, 100602 (2017)

    work page 2017

  52. [55]

    del Campo, A

    A. del Campo, A. Chenu, S. Deng, and H. Wu, Friction- free quantum machines, inThermodynamics in the Quan- tum Regime: Fundamental Aspects and New Directions, edited by F. Binder, L. A. Correa, C. Gogolin, J. An- ders, and G. Adesso (Springer International Publishing, Cham, 2018) pp. 127–148

    work page 2018

  53. [56]

    Kiely, S

    A. Kiely, S. Campbell, and G. T. Landi, Classical dissipa- tive cost of quantum control, Phys. Rev. A106, 012202 (2022)

    work page 2022

  54. [57]

    Carolan, A

    E. Carolan, A. Kiely, and S. Campbell, Counterdiabatic control in the impulse regime, Phys. Rev. A105, 012605 (2022)

    work page 2022

  55. [58]

    Auff` eves, Quantum Technologies Need a Quantum En- ergy Initiative, PRX Quantum3, 020101 (2022)

    A. Auff` eves, Quantum Technologies Need a Quantum En- ergy Initiative, PRX Quantum3, 020101 (2022)

    work page 2022

  56. [59]

    Fellous-Asiani, J

    M. Fellous-Asiani, J. H. Chai, Y. Thonnart, H. K. Ng, R. S. Whitney, and A. Auff` eves, Optimizing Resource Efficiencies for Scalable Full-Stack Quantum Computers, PRX Quantum4, 040319 (2023)

    work page 2023

  57. [60]

    Dridi, K

    G. Dridi, K. Liu, and S. Gu´ erin, Optimal Robust Quan- tum Control by Inverse Geometric Optimization, Phys. Rev. Lett.125, 250403 (2020)

    work page 2020

  58. [61]

    Harutyunyan, F

    M. Harutyunyan, F. Holweck, D. Sugny, and S. Gu´ erin, Digital optimal robust control, Phys. Rev. Lett.131, 200801 (2023)

    work page 2023

  59. [62]

    Van Damme, Q

    L. Van Damme, Q. Ansel, S. J. Glaser, and D. Sugny, Robust optimal control of two-level quantum systems, Phys. Rev. A95, 063403 (2017)

    work page 2017

  60. [63]

    Carolan, B

    E. Carolan, B. C ¸ akmak, and S. Campbell, Robustness of controlled Hamiltonian approaches to unitary quantum gates, Phys. Rev. A108, 022423 (2023)

    work page 2023

  61. [64]

    M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Ari- mondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Man- nella, , and O. Morsch, High-fidelity quantum driving, Nature Physics8, 147 (2012)

    work page 2012

  62. [65]

    G. C. Hegerfeldt, Driving at the quantum speed limit: Optimal control of a two-level system, Phys. Rev. Lett. 111, 260501 (2013)

    work page 2013

  63. [66]

    Zenesini, H

    A. Zenesini, H. Lignier, G. Tayebirad, J. Radogostowicz, D. Ciampini, R. Mannella, S. Wimberger, O. Morsch, and E. Arimondo, Time-resolved measurement of landau- 7 zener tunneling in periodic potentials, Phys. Rev. Lett. 103, 090403 (2009)

    work page 2009

  64. [67]

    Tayebirad, A

    G. Tayebirad, A. Zenesini, D. Ciampini, R. Mannella, O. Morsch, E. Arimondo, N. L¨ orch, and S. Wimberger, Time-resolved measurement of landau-zener tunneling in different bases, Phys. Rev. A82, 013633 (2010)

    work page 2010

  65. [68]

    Kobzar, T

    K. Kobzar, T. E. Skinner, N. Khaneja, S. J. Glaser, and B. Luy, Exploring the limits of broadband excitation and inversion pulses, Journal of Magnetic Resonance170, 236 (2004)

    work page 2004

  66. [69]

    Kobzar, S

    K. Kobzar, S. Ehni, T. E. Skinner, S. J. Glaser, and B. Luy, Exploring the limits of broadband 90 and 180 universal rotation pulses, Journal of Magnetic Resonance 225, 142 (2012)

    work page 2012

  67. [70]

    Khaneja, T

    N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbr¨ uggen, and S. J. Glaser, Optimal control of coupled spin dynam- ics: design of NMR pulse sequences by gradient ascent algorithms, J. Magn. Res.172, 296 (2005)

    work page 2005

  68. [71]

    J.-j. Zhu, X. Laforgue, X. Chen, and S. Gu´ erin, Robust quantum control by smooth quasi-square pulses, J. Phys. B: At. Mol. Opt. Phys.55, 194001 (2022)

    work page 2022

  69. [72]

    B. d. L. Bernardo, Time-rescaled quantum dynamics as a shortcut to adiabaticity, Phys. Rev. Res.2, 013133 (2020)

    work page 2020

  70. [73]

    J. L. M. Ferreira, ˆA. F. d. S. Fran¸ ca, A. Rosas, and B. d. L. Bernardo, Shortcuts to adiabaticity designed via time-rescaling follow the same transitionless route, arXiv 10.48550/arXiv.2406.07433 (2024), 2406.07433

    work page doi:10.48550/arxiv.2406.07433 2024

  71. [74]

    del Campo, Probing Quantum Speed Limits with Ul- tracold Gases, Phys

    A. del Campo, Probing Quantum Speed Limits with Ul- tracold Gases, Phys. Rev. Lett.126, 180603 (2021)

    work page 2021

  72. [75]

    Alipour, A

    S. Alipour, A. Chenu, A. T. Rezakhani, and A. del Campo, Shortcuts to Adiabaticity in Driven Open Quantum Systems: Balanced Gain and Loss and Non-Markovian Evolution, Quantum4, 336 (2020), 1907.07460v2

    work page arXiv 2020