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Cited by 78Quantum many-body systemsCold Atom Physics and Bose-Einstein CondensatesQuantum Computing Algorithms and Architecture

Speeding up critical system dynamics through optimized evolution

Open access
Caneva, Tommaso, Calarco, Tommaso, Fazio, Rosario, Santoro, Giuseppe E., Montangero, Simone·2011·Physical Review A
DOI 10.1103/physreva.84.012312
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Abstract

The number of defects which are generated upon crossing a quantum phase transition can be minimized by choosing properly designed time-dependent pulses. In this work we determine what are the ultimate limits of this optimization. We discuss under which conditions the production of defects across the phase transition is vanishing small. Furthermore we show that the minimum time required to enter this regime is $T\ensuremath{\sim}\ensuremath{\pi}/\ensuremath{\Delta}$, where $\ensuremath{\Delta}$ is the minimum spectral gap, unveiling an intimate connection between an optimized unitary dynamics and the intrinsic measure of the Hilbert space for pure states. Surprisingly, the dynamics is nonadiabatic; this result can be understood by assuming a simple two-level dynamics for the many-body system. Finally we classify the possible dynamical regimes in terms of the action $s=T\ensuremath{\Delta}$.

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Crossref · 10.1103/physreva.84.012312

Cites

45 of 45 references verified0 citation errors · 0 not checkable

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  • For action greater than pi, corresponding to durations longer than the quantum speed limit time, the Krotov algorithm always converges and adiabatic dynamics can be effectively achieved.

    “For s π, which corresponds to durations τ τ QSL , the Krotov algorithm always converges and this is defined as a region in which adiabatic dynamics can be effectively achieved.”

    From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [115]

  • Defining the action as the driving time times the minimum gap, the quantum speed limit defines different dynamical regimes when driving through a critical point.

    “Defining the action, s = τ ∆, where Δ is the minimum gap between the ground and first excited state, it is possible to show that the quantum speed limit defines different dynamical regimes when driving through the critical point.”

    From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [115]

  • Using the minimal time approach with the Krotov algorithm, the time to drive between ground states of different phases is bounded by the quantum speed limit time.

    “Once again employing the minimal time approach, through the Krotov algorithm, this time was shown to be bounded by the quantum speed limit time [115].”

    From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [115]

  • For linear driving, the action diverges as the system size increases.

    “if the driving is done linearly this action is shown to diverge as the system size is increased.”

    From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [115]

  • With optimized pulses of duration equal to the quantum speed limit time, the action is about pi, confirmed in the Landau-Zener, Grover search, and Lipkin-Meshkov-Glick models, and likely general.

    “Conversely, using the optimised pulses with duration τ = τ QSL we find s ∼ π, and confirmed to occur in three distinct models, the Landau-Zener, Grover's search algorithm, and the Lipkin-Meshkov-Glick (LMG) model, and therefore likely to hold in general.”

    From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [115]

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Cites

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Research works printed but not linked: 6

  1. [14]P. Doria, T. Calarco, and S. Montangero (2010), arXiv:1003.3750. · arXiv
  2. [15]A. Rahmani and C. Chamon (2010), arXiv:1011.3061. · arXiv
  3. [21]A. Smerzi (2010), arXiv:1002.2760. · arXiv
  4. [32]A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore (2010), arXiv:1007.5331. · arXiv
  5. [40]C. Zener, Proc. Royal Soc. A 137 , 696 (1932).
  6. [44]B. Altshuler, H. Krovi, and J. Roland (2009), arXiv:0912.0746. · arXiv

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Related

Authors
Caneva, T., Calarco, T., Fazio, R., Santoro, G. E., & Montangero, S.
Affiliations
  • Scuola Internazionale Superiore di Studi Avanzati (IT)
  • Universität Ulm (DE)
  • The Abdus Salam International Centre for Theoretical Physics (ICTP) (IT)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2011-07-12
Volume
84
Issue
1
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.84.012312
OpenAlex
W2087039395
Cited by
78
References
45
Citations by year
2026: 1 · 2025: 6 · 2023: 2 · 2022: 7 · 2021: 4 · 2020: 5 · 2019: 5 · 2018: 4 · 2017: 6 · 2016: 9 · 2015: 10 · 2014: 10 · 2013: 5 · 2012: 3
FWCI
3.30
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • SDL (submittedVersion)
  • Archivio istituzionale della ricerca (Alma Mater Studiorum Università di Bologna) (submittedVersion)
  • Scuola Normale Superiore di Pisa (submittedVersion)
  • Padua Research Archive (University of Padova) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
Keywords
quantum phase transitions, critical dynamics, defect formation, nonadiabatic dynamics, spectral gap, minimum time, two-level model, many-body systems, unitary dynamics, Hilbert spaces

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