pith. sign in

arxiv: 2606.13481 · v3 · pith:I7W56VDOnew · submitted 2026-06-11 · 🧮 math.OC

Towards a Control interpretation of Quantum Advantage

Dario Pighin This is my paper

Pith reviewed 2026-06-27 05:52 UTC · model grok-4.3

classification 🧮 math.OC
keywords quantum advantagecontrol theorybilinear Schrödinger equationoperator controllabilityquantum Fourier transformmaximum independent setQAOASU(N)
0
0 comments X

The pith

Quantum advantage equals a polynomial-in-n upper bound on minimal time for the bilinear controlled Schrödinger equation on SU(N).

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

The paper recasts quantum computations as operator controllability problems on the special unitary group SU(N) using the bilinear controlled Schrödinger equation as the central model. Quantum advantage is then defined as the existence of a polynomial upper bound on the associated minimal-time function. Illustrations include a Lie-algebraic proof of controllability plus an O(n^2) time bound for the quantum Fourier transform on superconducting processors, and a reformulation of QAOA as a continuous-time optimal control problem for the maximum independent set on neutral-atom processors. A reader would care because the approach supplies a systematic control-theoretic route to determine when and how advantage appears.

Core claim

The target quantum computation is recast as an operator controllability problem on SU(N), and QA is identified with a polynomial-in-n upper bound on the associated minimal-time function. For the quantum Fourier transform this yields operator controllability via a Lie-algebraic argument together with an O(n^2) upper bound obtained from a gate-concatenation lemma and the standard circuit decomposition. For the maximum independent set the Rydberg-blockade Hamiltonian is treated as a bilinear control system, QAOA is recast as a continuous-time optimal control problem, and a controllability result shows the problem can be solved on the relevant hardware while supplying a control-based definition

What carries the argument

The bilinear controlled Schrödinger equation on SU(N) and its minimal-time function, which supplies the polynomial bound that defines quantum advantage.

If this is right

  • Operator controllability of the quantum Fourier transform on SU(N) follows from a Lie-algebraic argument.
  • An O(n^2) upper bound on minimal time holds for the quantum Fourier transform via gate concatenation and standard circuit decomposition.
  • The Rydberg-blockade Hamiltonian for maximum independent set is a bilinear control system on which QAOA becomes a continuous-time optimal control problem.
  • A controllability result establishes that maximum independent set can be solved on the neutral-atom hardware under the new definition of quantum advantage.

Where Pith is reading between the lines

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

  • The same controllability and minimal-time analysis could be applied to other quantum algorithms to produce explicit polynomial bounds.
  • Hardware-specific minimal-time functions might be used to compare control protocols across different quantum platforms.
  • The framework opens the possibility of importing numerical optimal-control methods to design shorter quantum circuits.

Load-bearing premise

The bilinear controlled Schrödinger equation on SU(N) together with its minimal-time function provides a faithful model of quantum advantage on superconducting and neutral-atom processors.

What would settle it

An explicit quantum computation shown to deliver advantage on the cited hardware yet requiring superpolynomial minimal time under the bilinear control model on SU(N).

Figures

Figures reproduced from arXiv: 2606.13481 by Dario Pighin.

Figure 1.1
Figure 1.1. Figure 1.1: An instance of the Maximum Independent Set (MIS) problem on a [PITH_FULL_IMAGE:figures/full_fig_p006_1_1.png] view at source ↗
Figure 3.1
Figure 3.1. Figure 3.1: The ibm brisbane coupling map E = (V, E), a heavy-hexagonal (Eagle r3) lattice with |V | = 127 qubits and |E| = 144 two-qubit couplers (maximum vertex degree 3). Each vertex k ∈ V = {0, . . . , 126} is a qubit; each edge (c, t) ∈ E = E carries a cross-resonance/ECR coupler entering the control Hamiltonian of (3.5) through the term P (c,t)∈E vct(t)Zc ⊗ Xt. Ver￾tex color encodes the single-qubit readout (a… view at source ↗
read the original abstract

We develop a control-theoretic framework for understanding Quantum Advantage (QA), providing a systematic route to characterize when and how QA can arise. The bilinear controlled Schr\"odinger equation is the common thread: the target quantum computation is recast as an operator controllability problem on the special unitary group $SU(N)$, and QA is identified with a polynomial-in-$n$ upper bound on the associated minimal-time function. We illustrate the framework on two paradigmatic problems: a) the Quantum Fourier Transform (QFT) on superconducting digital quantum processors (such as IBM's ibm_brisbane), for which we prove operator controllability by a Lie-algebraic argument and derive an $O(n^2)$ upper bound on the minimal time via a gate-concatenation lemma combined with the standard QFT circuit decomposition; b) the Maximum Independent Set (MIS) problem on neutral-atom analog quantum processors (such as Pasqal's hardware), for which we analyze the Rydberg-blockade Hamiltonian as a bilinear control system and reformulate the Quantum Approximate Optimization Algorithm (QAOA) as a continuous-time optimal control problem. By a controllability result, we show how the problem can be solved on Pasqal Quantum Computers and we introduce a control-based definition of Quantum Advantage for MIS. We conclude by outlining several open problems that chart directions for future research at the intersection of Control Theory and Quantum Computing.

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

3 major / 1 minor

Summary. The paper develops a control-theoretic framework identifying quantum advantage (QA) with a polynomial-in-n upper bound on the minimal-time function for the bilinear controlled Schrödinger equation on SU(N). It illustrates the approach via Lie-algebraic controllability and an O(n²) bound for the QFT on superconducting processors (using gate concatenation on the standard decomposition) and via reformulation of QAOA as an optimal-control problem on the Rydberg-blockade Hamiltonian for the MIS problem on neutral-atom processors, together with a controllability result and a control-based QA definition.

Significance. If the identification of QA with the abstract minimal-time bound can be shown to faithfully capture hardware advantage, the framework would supply a new systematic language for characterizing when continuous-time control yields polynomial scaling. The illustrations, however, largely recover known circuit depths and introduce a definition without direct comparison to classical or hardware-constrained scaling, limiting the immediate impact.

major comments (3)
  1. [QFT application section] QFT illustration: The O(n²) upper bound is obtained by applying the gate-concatenation lemma to the conventional QFT circuit decomposition after the Lie-algebraic controllability argument. This reproduces the known gate-model complexity rather than furnishing an independent estimate derived from the continuous bilinear dynamics, which is load-bearing for the claim that the control model supplies a distinct characterization of QA.
  2. [MIS application section] MIS application: The control-based definition of QA is introduced after reformulating QAOA as a continuous-time optimal-control problem on the Rydberg Hamiltonian and stating a controllability result, yet without explicit comparison to classical scaling or incorporation of hardware constraints (Rydberg lifetime, finite pulse amplitudes, blockade radius). This leaves open whether a polynomial bound in the abstract SU(N) model implies advantage on the cited neutral-atom platforms.
  3. [Framework and conclusion sections] Central identification: The framework equates QA with a polynomial upper bound on the minimal-time function for the bilinear Schrödinger equation on SU(N). The manuscript does not address how hardware-specific restrictions (local microwave controls and connectivity on superconducting devices; interaction constraints and lifetime on neutral atoms) modify the achievable time, so the abstract bound may remain polynomial while the hardware time becomes super-polynomial.
minor comments (1)
  1. [Introduction] The abstract and introduction use the phrase "gate-concatenation lemma" without an early reference or statement of its precise hypotheses; a short statement of the lemma would improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment point by point below, indicating where we agree and will revise the manuscript accordingly while defending the core contributions of the control-theoretic framework.

read point-by-point responses

  1. Referee: [QFT application section] QFT illustration: The O(n²) upper bound is obtained by applying the gate-concatenation lemma to the conventional QFT circuit decomposition after the Lie-algebraic controllability argument. This reproduces the known gate-model complexity rather than furnishing an independent estimate derived from the continuous bilinear dynamics, which is load-bearing for the claim that the control model supplies a distinct characterization of QA.

    Authors: The O(n²) bound is indeed obtained via the gate-concatenation lemma applied to the standard QFT decomposition, following the Lie-algebraic controllability proof. This is intentional within the framework: the controllability result establishes that the bilinear system on SU(N) can realize the target unitary, while the concatenation lemma supplies an explicit (polynomial) upper bound on the minimal time using admissible controls that correspond to the gates. Although the bound references the circuit model, it demonstrates how known decompositions translate into time bounds for the continuous control system, supporting the identification of QA with polynomial minimal-time scaling. The Lie-algebraic step is independent of any particular decomposition. We will revise the QFT section to clarify this connection and the framework's interpretive role more explicitly. revision: partial

  2. Referee: [MIS application section] MIS application: The control-based definition of QA is introduced after reformulating QAOA as a continuous-time optimal-control problem on the Rydberg Hamiltonian and stating a controllability result, yet without explicit comparison to classical scaling or incorporation of hardware constraints (Rydberg lifetime, finite pulse amplitudes, blockade radius). This leaves open whether a polynomial bound in the abstract SU(N) model implies advantage on the cited neutral-atom platforms.

    Authors: The control-based definition of QA for MIS is presented as a conceptual extension of the framework after the reformulation of QAOA as an optimal-control problem and the controllability analysis on the Rydberg Hamiltonian. Direct comparisons to classical scaling are listed among the open problems in the conclusion. We agree that specific hardware constraints (e.g., Rydberg lifetime, pulse amplitudes, blockade radius) are not incorporated into the time bounds. We will revise the MIS section and conclusion to add a discussion of these constraints and their potential effect on achievable times, while preserving the abstract model's focus. revision: yes

  3. Referee: [Framework and conclusion sections] Central identification: The framework equates QA with a polynomial upper bound on the minimal-time function for the bilinear Schrödinger equation on SU(N). The manuscript does not address how hardware-specific restrictions (local microwave controls and connectivity on superconducting devices; interaction constraints and lifetime on neutral atoms) modify the achievable time, so the abstract bound may remain polynomial while the hardware time becomes super-polynomial.

    Authors: The central identification is made at the level of the abstract bilinear Schrödinger equation on SU(N) to provide a systematic, hardware-agnostic characterization of when continuous-time control can yield polynomial scaling. We acknowledge that the manuscript does not model device-specific restrictions, which could indeed alter the scaling on actual hardware. This is a limitation of the present work. We will revise the conclusion to explicitly state this caveat and identify the incorporation of hardware constraints as a key direction for future research. revision: yes

Circularity Check

0 steps flagged

No significant circularity; framework applies external standard results

full rationale

The paper defines QA as a polynomial upper bound on the minimal-time function for the bilinear controlled Schrödinger equation on SU(N). For the QFT example it invokes a standard Lie-algebraic controllability argument followed by a gate-concatenation lemma applied to the conventional QFT circuit decomposition to recover the known O(n²) bound. For MIS it reformulates QAOA as an optimal-control problem on the Rydberg Hamiltonian and invokes a controllability result to introduce a control-based definition. None of these steps reduce by construction to a fitted parameter, a self-referential definition, or a load-bearing self-citation chain; all rest on independently established external results in quantum control and circuit complexity. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework rests on the standard modeling assumption that the bilinear controlled Schrödinger equation captures the relevant dynamics of the cited quantum processors; no free parameters or new postulated entities are introduced in the abstract.

axioms (1)
  • domain assumption The bilinear controlled Schrödinger equation is the common thread that models the target quantum computation as an operator controllability problem on SU(N).
    Explicitly stated as the modeling foundation for the entire framework.

pith-pipeline@v0.9.1-grok · 5771 in / 1277 out tokens · 28568 ms · 2026-06-27T05:52:19.684210+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

89 extracted references · 4 linked inside Pith

  1. [1]

    Agrachev, U

    A. Agrachev, U. Boscain, J.-P. Gauthier, and M. Sigalotti , A note on time-zero controllability and density of orbits for quantum systems , in 2017 IEEE 56th annual conference on decision and control (CDC), IEEE, 2017, pp. 5535--5538

    2017

  2. [2]

    Aharonov, W

    D. Aharonov, W. Van Dam, J. Kempe, Z. Landau, S. Lloyd, and O. Regev , Adiabatic quantum computation is equivalent to standard quantum computation , SIAM review, 50 (2008), pp. 755--787

    2008

  3. [3]

    Albertini and D

    F. Albertini and D. D'Alessandro , The lie algebra structure and controllability of spin systems , Linear algebra and its applications, 350 (2002), pp. 213--235

    2002

  4. [4]

    A. R. Barron, A. Cohen, W. Dahmen, and R. A. DeVore , Approximation and learning by greedy algorithms , The annals of statistics, 36 (2008), pp. 64--94

    2008

  5. [5]

    Beauchard and C

    K. Beauchard and C. Laurent , Local controllability of 1d linear and nonlinear schr \"o dinger equations with bilinear control , Journal de math \'e matiques pures et appliqu \'e es, 94 (2010), pp. 520--554

    2010

  6. [6]

    Beauchard and E

    K. Beauchard and E. Pozzoli , Small-time controllability on the group of diffeomorphisms for schr " odinger equations , (2024)

    2024

  7. [7]

    height 2pt depth -1.6pt width 23pt, Examples of small-time controllable schr \"o dinger equations , in Annales Henri Poincar \'e , 2025

    2025

  8. [8]

    J. S. Bell , On the einstein podolsky rosen paradox , Physics Physique Fizika, 1 (1964), p. 195

    1964

  9. [9]

    C. H. Bennett, G. Brassard, and N. D. Mermin , Quantum cryptography without bell’s theorem , Physical review letters, 68 (1992), p. 557

    1992

  10. [10]

    Bensoussan, G

    A. Bensoussan, G. Da Prato, M. Delfour, and S. Mitter , Representation and Control of Infinite Dimensional Systems , Systems & Control: Foundations & Applications, Birkh \"a user Boston, 2011

    2011

  11. [11]

    Berberich and D

    J. Berberich and D. Fink , Quantum computing through the lens of control: A tutorial introduction , IEEE Control Systems, 44 (2024), pp. 24--49

    2024

  12. [12]

    Boscain, M

    U. Boscain, M. Sigalotti, and D. Sugny , Introduction to the pontryagin maximum principle for quantum optimal control , PRX Quantum, 2 (2021), p. 030203

    2021

  13. [13]

    Boussaïd, M

    N. Boussaïd, M. Caponigro, and T. Chambrion , Controllability of quantum systems with relatively bounded control potentials<sup>*</sup> , pp. 141--148

  14. [14]

    L. T. Brady, C. L. Baldwin, A. Bapat, Y. Kharkov, and A. V. Gorshkov , Optimal protocols in quantum annealing and quantum approximate optimization algorithm problems , Phys. Rev. Lett., 126 (2021), p. 070505

    2021

  15. [15]

    Carlini, A

    A. Carlini, A. Hosoya, T. Koike, and Y. Okudaira , Time-optimal unitary operations , Phys. Rev. A, 75 (2007), p. 042308

    2007

  16. [16]

    A. M. Childs , Lecture 18: CO 781 / CS 867 / QIC 823 Quantum Algorithms . University of Waterloo, Winter 2008 Course Notes, 2008

    2008

  17. [17]

    Choi , Beyond stoquasticity: Structural steering and interference in quantum optimization , arXiv preprint arXiv:2509.16263, (2025)

    V. Choi , Beyond stoquasticity: Structural steering and interference in quantum optimization , arXiv preprint arXiv:2509.16263, (2025)

    arXiv 2025

  18. [18]

    Coron , Control and Nonlinearity , Mathematical surveys and monographs, American Mathematical Society, 2007

    J. Coron , Control and Nonlinearity , Mathematical surveys and monographs, American Mathematical Society, 2007

    2007

  19. [19]

    Dacorogna , Direct methods in the calculus of variations , vol

    B. Dacorogna , Direct methods in the calculus of variations , vol. 78, Springer Science & Business Media, 2007

    2007

  20. [20]

    D'Alessandro and Y

    D. D'Alessandro and Y. Isik , Controllability of the periodic quantum ising spin chain , arXiv preprint:2405.00898, (2024)

    arXiv 2024

  21. [21]

    D. P. DiVincenzo , The physical implementation of quantum computation , Fortschritte der Physik: Progress of Physics, 48 (2000), pp. 771--783

    2000

  22. [22]

    Dong and I

    D. Dong and I. R. Petersen , Quantum control theory and applications: a survey , IET control theory & applications, 4 (2010), pp. 2651--2671

    2010

  23. [23]

    D’Alessandro , Introduction to quantum control and dynamics , Chapman and hall/CRC, 2021

    D. D’Alessandro , Introduction to quantum control and dynamics , Chapman and hall/CRC, 2021

    2021

  24. [24]

    Ebadi, A

    S. Ebadi, A. Keesling, M. Cain, T. T. Wang, H. Levine, D. Bluvstein, G. Semeghini, A. Omran, J.-G. Liu, R. Samajdar, et al. , Quantum optimization of maximum independent set using rydberg atom arrays , Science, 376 (2022), pp. 1209--1215

    2022

  25. [25]

    Einstein, B

    A. Einstein, B. Podolsky, and N. Rosen , Can quantum-mechanical description of physical reality be considered complete? , Physical review, 47 (1935), p. 777

    1935

  26. [26]

    A. K. Ekert , Quantum cryptography based on bell’s theorem , Physical review letters, 67 (1991), p. 661

    1991

  27. [27]

    Farhi, J

    E. Farhi, J. Goldstone, and S. Gutmann , A quantum approximate optimization algorithm , arXiv preprint arXiv:1411.4028, (2014)

    Pith/arXiv arXiv 2014

  28. [28]

    Farhi, J

    E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser , Quantum computation by adiabatic evolution , arXiv preprint quant-ph/0001106, (2000)

    Pith/arXiv arXiv 2000

  29. [29]

    Farhi and A

    E. Farhi and A. W. Harrow , Quantum supremacy through the quantum approximate optimization algorithm , arXiv preprint arXiv:1602.07674, (2016)

    arXiv 2016

  30. [30]

    R. P. Feynman , Simulating physics with computers , in Feynman and computation, CRC Press, 1982, pp. 133--153

    1982

  31. [31]

    Fujiwara and N

    S. Fujiwara and N. Ishikawa , Grover adaptive search with spin variables , IEEE Transactions on Quantum Engineering, (2025)

    2025

  32. [32]

    Gily \'e n, M

    A. Gily \'e n, M. B. Hastings, and U. Vazirani , (sub) exponential advantage of adiabatic quantum computation with no sign problem , in Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing, 2021, pp. 1357--1369

    2021

  33. [33]

    L. K. Grover , A fast quantum mechanical algorithm for database search , in Proceedings of the twenty-eighth annual ACM symposium on Theory of computing, 1996, pp. 212--219

    1996

  34. [34]

    height 2pt depth -1.6pt width 23pt, Quantum mechanics helps in searching for a needle in a haystack , Physical review letters, 79 (1997), p. 325

    1997

  35. [35]

    A. W. Harrow, A. Hassidim, and S. Lloyd , Quantum algorithm for linear systems of equations , Physical review letters, 103 (2009), p. 150502

    2009

  36. [36]

    Henriet, L

    L. Henriet, L. Beguin, A. Signoles, T. Lahaye, A. Browaeys, G.-O. Reymond, and C. Jurczak , Quantum computing with neutral atoms , Quantum , 4 (2020), p. 327

    2020

  37. [37]

    Hern \'a ndez-Santamar \'i a, M

    V. Hern \'a ndez-Santamar \'i a, M. Lazar, and E. Zuazua , Greedy optimal control for elliptic problems and its application to turnpike problems , Numerische Mathematik, 141 (2019), pp. 455--493

    2019

  38. [38]

    S. Hou, L. Wang, and X. Yi , Realization of quantum gates by lyapunov control , Physics Letters A, 378 (2014), pp. 699--704

    2014

  39. [39]

    H. B. Hunt III, M. V. Marathe, V. Radhakrishnan, S. S. Ravi, D. J. Rosenkrantz, and R. E. Stearns , Nc-approximation schemes for np- and pspace-hard problems for geometric graphs , in Journal of Algorithms, vol. 26, Elsevier, 1998, pp. 238--274

    1998

  40. [40]

    Jansen, M.-B

    S. Jansen, M.-B. Ruskai, and R. Seiler , Bounds for the adiabatic approximation with applications to quantum computation , Journal of Mathematical Physics, 48 (2007), p. 102111

    2007

  41. [41]

    S. Jin, N. Liu, and Y. Yu , Quantum simulation of partial differential equations via schr \"o dingerization , Physical Review Letters, 133 (2024), p. 230602

    2024

  42. [42]

    R. M. Karp , Reducibility among Combinatorial Problems , Springer US, Boston, MA, 1972, pp. 85--103

    1972

  43. [43]

    Kjaergaard, M

    M. Kjaergaard, M. E. Schwartz, J. Braum \"u ller, P. Krantz, J. I.-J. Wang, S. Gustavsson, and W. D. Oliver , Superconducting qubits: Current state of play , Annual Review of Condensed Matter Physics, 11 (2020), pp. 369--395

    2020

  44. [44]

    C. P. Koch, U. Boscain, T. Calarco, G. Dirr, S. Filipp, S. J. Glaser, R. Kosloff, S. Montangero, T. Schulte-Herbr \"u ggen, D. Sugny, et al. , Quantum optimal control in quantum technologies. strategic report on current status, visions and goals for research in europe , EPJ Quantum Technology, 9 (2022), p. 19

    2022

  45. [45]

    J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf , Charge-insensitive qubit design derived from the cooper pair box , Physical Review A—Atomic, Molecular, and Optical Physics, 76 (2007), p. 042319

    2007

  46. [46]

    Kochenberger, J.-K

    G. Kochenberger, J.-K. Hao, F. Glover, M. Lewis, Z. L \"u , H. Wang, and Y. Wang , The unconstrained binary quadratic programming problem: a survey , Journal of combinatorial optimization, 28 (2014), pp. 58--81

    2014

  47. [47]

    Krantz, M

    P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver , A quantum engineer's guide to superconducting qubits , Applied physics reviews, 6 (2019), p. 021318

    2019

  48. [48]

    Lazar and E

    M. Lazar and E. Zuazua , Greedy controllability of finite dimensional linear systems , Automatica, 74 (2016), pp. 327--340

    2016

  49. [49]

    J. Lions , Optimal Control of Systems Governed by Partial Differential Equations , Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Ber \"u cksichtigung der Anwendungsgebiete, Springer-Verlag, 1971

    1971

  50. [50]

    Lucas , Ising formulations of many np problems , Frontiers in Physics, Volume 2 - 2014 (2014)

    A. Lucas , Ising formulations of many np problems , Frontiers in Physics, Volume 2 - 2014 (2014)

    2014

  51. [51]

    Machtyngier , Exact controllability for the schr \"o dinger equation , SIAM Journal on Control and Optimization, 32 (1994), pp

    E. Machtyngier , Exact controllability for the schr \"o dinger equation , SIAM Journal on Control and Optimization, 32 (1994), pp. 24--34

    1994

  52. [52]

    Magesan and J

    E. Magesan and J. M. Gambetta , Effective hamiltonian models of the cross-resonance gate , Physical Review A, 101 (2020), p. 052308

    2020

  53. [53]

    Martin, L

    A. Martin, L. Lamata, E. Solano, and M. Sanz , Digital-analog quantum algorithm for the quantum fourier transform , Physical Review Research, 2 (2020), p. 013012

    2020

  54. [54]

    J. M. Martyn, Z. M. Rossi, A. K. Tan, and I. L. Chuang , Grand unification of quantum algorithms , PRX quantum, 2 (2021), p. 040203

    2021

  55. [55]

    D. C. McKay, T. Alexander, L. Bello, M. J. Biercuk, L. Bishop, J. Chen, J. M. Chow, A. D. C \'o rcoles, D. Egger, S. Filipp, et al. , Qiskit backend specifications for openqasm and openpulse experiments , arXiv preprint arXiv:1809.03452, (2018)

    Pith/arXiv arXiv 2018

  56. [56]

    Mirrahimi, P

    M. Mirrahimi, P. Rouchon, and G. Turinici , Lyapunov control of bilinear schrödinger equations , Automatica, 41 (2005), pp. 1987--1994

    2005

  57. [57]

    T. Monz, D. Nigg, E. A. Martinez, M. F. Brandl, P. Schindler, R. Rines, S. X. Wang, I. L. Chuang, and R. Blatt , Realization of a scalable shor algorithm , Science, 351 (2016), pp. 1068--1070

    2016

  58. [58]

    Nguyen, J.-G

    M.-T. Nguyen, J.-G. Liu, J. Wurtz, M. D. Lukin, S.-T. Wang, and H. Pichler , Quantum optimization with arbitrary connectivity using rydberg atom arrays , PRX Quantum, 4 (2023), p. 010316

    2023

  59. [59]

    Nielsen and I

    M. Nielsen and I. Chuang , Quantum computation and quantum information, 10th anniversary cambridge university press , 2010

    2010

  60. [60]

    M. A. Nielsen, M. R. Dowling, M. Gu, and A. C. Doherty , Quantum computation as geometry , Science, 311 (2006), pp. 1133--1135

    2006

  61. [61]

    W. D. Oliver , Superconducting qubits , Quantum Information Processing: Lecture Notes of 44th IFF Spring School, (2013)

    2013

  62. [62]

    Ozfidan, C

    I. Ozfidan, C. Deng, A. Smirnov, T. Lanting, R. Harris, L. Swenson, J. Whittaker, F. Altomare, M. Babcock, C. Baron, A. Berkley, K. Boothby, H. Christiani, P. Bunyk, C. Enderud, B. Evert, M. Hager, A. Hajda, J. Hilton, S. Huang, E. Hoskinson, M. Johnson, K. Jooya, E. Ladizinsky, N. Ladizinsky, R. Li, A. MacDonald, D. Marsden, G. Marsden, T. Medina, R. Mol...

    2020

  63. [63]

    P. M. Pardalos and S. Jha , Complexity of uniqueness and local search in quadratic 0--1 programming , Operations research letters, 11 (1992), pp. 119--123

    1992

  64. [64]

    Pelofske, A

    E. Pelofske, A. B \"a rtschi, L. Cincio, J. Golden, and S. Eidenbenz , Scaling whole-chip qaoa for higher-order ising spin glass models on heavy-hex graphs , npj Quantum Information, 10 (2024), p. 109

    2024

  65. [65]

    Pichler, S.-T

    H. Pichler, S.-T. Wang, L. Zhou, S. Choi, and M. D. Lukin , Quantum optimization for maximum independent set using rydberg atom arrays , arXiv preprint arXiv:1808.10816, (2018)

    Pith/arXiv arXiv 2018

  66. [66]

    Pighin , The turnpike property in semilinear control , arXiv:2004.03269, (2020)

    D. Pighin , The turnpike property in semilinear control , arXiv:2004.03269, (2020)

    arXiv 2004

  67. [67]

    Porretta and E

    A. Porretta and E. Zuazua , Long time versus steady state optimal control , SIAM J. Control Optim., 51 (2013), pp. 4242--4273

    2013

  68. [68]

    height 2pt depth -1.6pt width 23pt, Remarks on long time versus steady state optimal control , in Mathematical Paradigms of Climate Science, Springer, 2016, pp. 67--89

    2016

  69. [69]

    Privat, E

    Y. Privat, E. Tr \'e lat, and E. Zuazua , Optimal observability of the multi-dimensional wave and schr \"o dinger equations in quantum ergodic domains , Journal of the European Mathematical Society, 18 (2016), pp. 1043--1111

    2016

  70. [70]

    F. A. Quinton, P. A. S. Myhr, M. Barani, P. Crespo del Granado, and H. Zhang , Quantum annealing applications, challenges and limitations for optimisation problems compared to classical solvers , Scientific Reports, 15 (2025), p. 12733

    2025

  71. [71]

    B. W. Reichardt , The quantum adiabatic optimization algorithm and local minima , in Proceedings of the thirty-sixth annual ACM symposium on Theory of computing, 2004, pp. 502--510

    2004

  72. [72]

    Rigetti and M

    C. Rigetti and M. Devoret , Fully microwave-tunable universal gates in superconducting qubits with linear couplings and fixed transition frequencies , Physical Review B—Condensed Matter and Materials Physics, 81 (2010), p. 134507

    2010

  73. [73]

    o dinger , Die gegenw \

    E. Schr \"o dinger , Die gegenw \"a rtige situation in der quantenmechanik , Naturwissenschaften, 23 (1935), pp. 844--849

    1935

  74. [74]

    P. W. Shor , Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer , SIAM review, 41 (1999), pp. 303--332

    1999

  75. [75]

    Sivarajah, S

    S. Sivarajah, S. Dilkes, A. Cowtan, W. Simmons, A. Edgington, and R. Duncan , t| ket>: a retargetable compiler for nisq devices , Quantum Science and Technology, 6 (2020), p. 014003

    2020

  76. [76]

    E. D. Sontag , Mathematical control theory: deterministic finite dimensional systems , vol. 6, Springer Science & Business Media, 1998

    1998

  77. [77]

    Tibaldi, L

    S. Tibaldi, L. Leclerc, D. Vodola, E. Tignone, and E. Ercolessi , Analog qaoa with bayesian optimisation on a neutral atom qpu , EPJ Quantum Technology, (2025)

    2025

  78. [78]

    Tindall and D

    J. Tindall and D. Sels , Confinement in the transverse field ising model on the heavy hex lattice , Physical Review Letters, 133 (2024), p. 180402

    2024

  79. [79]

    Tr \'e lat , Control in finite and infinite dimension , Springer, 2024

    E. Tr \'e lat , Control in finite and infinite dimension , Springer, 2024

    2024

  80. [80]

    Tr \'e lat, C

    E. Tr \'e lat, C. Zhang, and E. Zuazua , Steady-state and periodic exponential turnpike property for optimal control problems in hilbert spaces , SIAM Journal on Control and Optimization, 56 (2018), pp. 1222--1252

    2018

Showing first 80 references.