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Cited by 475Advanced Thermodynamics and Statistical MechanicsQuantum Information and CryptographyAdvanced Thermodynamic Systems and Engines

Quantacell: powerful charging of quantum batteries

Open access
Binder, Felix C, Vinjanampathy, Sai, Modi, Kavan, Goold, John·2015·New Journal of Physics
DOI 10.1088/1367-2630/17/7/075015
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Abstract

We study the problem of charging a quantum battery in finite time. We demonstrate an analytical optimal protocol for the case of a single qubit. Extending this analysis to an array of N qubits, we demonstrate that an N-fold advantage in power per qubit can be achieved when global operations are permitted. The exemplary analytic argument for this quantum advantage in the charging power is backed up by numerical analysis using optimal control techniques. It is demonstrated that the quantum advantage for power holds when, with cyclic operation in mind, initial and final states are required to be separable.

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Written from the paper’s full text.

TL;DR

The paper derives an analytical optimal protocol for charging a single-qubit quantum battery in finite time and extends it to arrays of N qubits. It shows that global entangling operations can yield an N-fold advantage in power per qubit over local parallel charging, even when initial and final states are separable.

Key findings

  • For a single qubit, the power-optimal driving is along a geodesic at constant angular speed \(E_{\max}\), with no driving along the reference Hamiltonian direction.
  • For an array of N qubits, global driving with the same maximum energy gap \(E_{\max}^{(N)}=N E_{\max}\) achieves an N-fold increase in power per qubit compared with parallel local driving.
  • The quantum advantage persists under cyclic operation with separable initial and final states; entanglement appears only during the protocol.
  • Numerical optimal control for full charging shows the minimum charging time scales as \(1/N\), and for a four-qubit solution entanglement across the 12–34 bipartition vanishes at the start and end.

Methods

  • Analytical derivation for a single qubit using the von Neumann equation, Bloch-sphere parametrization, and optimization of a family of objective functions interpolating power and ergotropy under a trace-norm bound on the driving Hamiltonian.
  • Extension to N-qubit arrays comparing parallel local driving with global entangling driving, with average work per qubit set to unity in the examples.
  • Numerical optimal control for full charging of N qubits and for entanglement dynamics in a four-qubit numerical solution.

Limitations

  • Stated: a full optimization over all possible unitary transformations is not analytically feasible, so the N-qubit advantage is demonstrated with a specific evolution.
  • Stated: future work is needed to allow for degradation/purifying stages and to generalize the approach to open systems with noise and decoherence.
  • Evident: the analysis assumes ideal cyclic unitary dynamics and purity preservation; no experimental implementation or realistic noise model is provided.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1088/1367-2630/17/7/075015

Cites

18 of 18 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 4 cited sources checked · 0 supported · 0 flagged

  • Findingown data

    For an array of N qubits, an N-fold advantage in power per qubit can be achieved when global operations are permitted.

    “Extending this analysis to an array of N qubits, we demonstrate that an N-fold advantage in power per qubit can be achieved when global operations are permitted.”
    • Also stated in: § Additional information · plain
      “Permitting for the same constraint as in the parallel case, that is E NE N max ( ) max = , an N-fold increase in power per qubit is achieved.”
    Quote in the paperSubstantial claim
  • Findingnone given

    Entangling processes can achieve higher power than local operations even when correlations only appear during the process but not in the input and output states.

    “That is, entangling processes, which allow for the creation of quantum correlations, can achieve a higher power than local operations.This is the case even when correlations are only allowed to appear during the process but not in the input and output states.”
    Quote in the paperSubstantial claim
  • Findingown data

    An analytical optimal protocol for charging a single qubit in finite time is derived.

    “We demonstrate an analytical optimal protocol for the case of a single qubit.”
    • Also stated in: § 5. Conclusion · boosted
      “In this article we have given a full derivation of a qubit protocol that achieves maximum power when charging a quantum battery-a work qubit-under constrained driving.”
    Quote in the paperSubstantial claim
  • Findingnone given

    For α<1 and θ<π the optimum is always reached for finite T.

    “This can be regarded as pathological and it is worth pointing out that for 1 α < and θ π < the optimum is always reached for finite T.”
    Quote in the paperNot a substantial claim
  • Findingown data

    The quantum advantage for power holds when initial and final states are required to be separable.

    “It is demonstrated that the quantum advantage for power holds when, with cyclic operation in mind, initial and final states are required to be separable.”
    • Also stated in: § Additional information · hedged
      “Interestingly, the advantage from correlations appears even though initial and final states are separable.”
    Quote in the paperSubstantial claim
  • May combine two claims. 3
  • Classified as probably not a substantial claim. 1

  • May combine two claims.

    Findingreasoning

    For parallel driving, the work done is W=N, the average work per qubit is unity, and the driving time is T_par=π/E_max.

    “The work done is trivially W N 〈 〉 = -that is, the average work per qubit is unity and the driving time is T E par max π = .”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingnone given

    For parallel driving, the driving Hamiltonian possesses N+1 equidistant eigenvalues with the gap between the largest and the lowest eigenvalue given by NE_max.

    “It possesses N 1 + equidistant eigenvalues with the gap between the largest and the lowest eigenvalue given by NE max .”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data

    In the four-qubit numerical solution, the qubits are disentangled at the beginning and at the end of the dynamics, indicated by vanishing entropies.

    “We note that at the beginning and at the end of the dynamics, the qubits are disentangled, indicated by vanishing entropies.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation

    Quantum speed limits bound the evolution time by the inverse mean energy or its variance and apply to time-dependent unitary evolution between any two quantum states.

    “Such infinitely powerful driving, however, would be in conflict with so-called quantum speed limits which bound the evolution time by the inverse mean energy (Margolus and Levitin 1998), or, alternatively, its variance (Mandelstam and Tamm 1945) and apply to time-dependent unitary evolution between any two quantum states (Deffner and Lutz 2013).”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites Margolus and Levitin 1998

      Not checked in the free run.

    • cites Mandelstam and Tamm 1945

      Not checked in the free run.

    • cites Deffner and Lutz 2013 source

      Not checked in the free run.

4 of 4

  • The paper relies on this without support.

    All thermal states are passive.

    “Note that all thermal states are passive.”
1 of 1

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Similar techniques have been used to optimally charge a quantum battery.

    “In addition, similar techniques have been employed to optimally charge a quantum battery [110,111].”

    From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [110]

  • Γ_C1 = √k and Γ_C2 = k are achievable if the total number of batteries N can be divided by k, i.e., if N/k = s ∈ N.

    “For comparison, it has been shown elsewhere that Γ C1 = √ k and Γ C2 = k are achievable if the total number of batteries N can be divided by k , i.e. , if N/k = s ∈ N [15, 36].”

    From Enhancing the Charging Power of Quantum Batteries (2017) · cites this paper as [15]

  • The Hamiltonian used in the example above, and in Ref. [15], to saturate the bound for quantum advantage involves N-body interactions.

    “The Hamiltonian used in the example above, and in Ref. [15], to saturate the bound for quantum advantage involves N -body interactions.”

    From Enhancing the Charging Power of Quantum Batteries (2017) · cites this paper as [15]

  • The quantum advantage is tight for orthogonal initial and final states, due to the example given in Ref. [15].

    “The quantum advantage is tight for orthogonal initial and final states, due to the example given in Ref. [15].”

    From Enhancing the Charging Power of Quantum Batteries (2017) · cites this paper as [15]

  • In the case where N/k = s ∈ N, a speed-up can be obtained for pure states using the time-independent Hamiltonian H = √s ∑_{μ=1}^s h_μ, with h_μ = |1⟩^{⊗k}⟨d|^{⊗k} + h.c., assuming each h_μ acts on a completely different set of k batteries.

    “In this particular case, such a speed-up can be obtained for pure states using the time-independent Hamiltonian H = √ s ∑ s µ =1 h µ , with h µ = | 1 〉 ⊗ k 〈 d | ⊗ k + h.c. , assuming that each h µ acts on a completely different set of k batteries, i.e. , [ h µ , h µ ′ ] = 0 ∀ µ, µ ′ .”

    From Enhancing the Charging Power of Quantum Batteries (2017) · cites this paper as [15]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Final-state purity requirement is stated in opposite ways

    Minor

    The protocol's no-degradation condition requires no reduction in marginal purity at the end. The numerical-results discussion instead describes individual availability at the final time as occurring "with loss of purity."

1 of 1

Cites

Flagged first, then by citations

Research works printed but not linked: 3

  1. 10.1103/physreve.91.032118 · DOI
  2. Mandelstam L, 1945, J. Phys. (USSR), 9, 249
  3. 10.1103/physrevlett.111.260501 · DOI · Paper page

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Related

Authors
Binder, F. C., Vinjanampathy, S., Modi, K., & Goold, J.
Affiliations
  • University of Oxford (GB)
  • Centre for Quantum Technologies (SG)
  • Monash University (AU)
  • The Abdus Salam International Centre for Theoretical Physics (ICTP) (IT)
ORCID
Venue
New Journal of Physics
Publisher
IOP Publishing
Published
2015-07-22
Volume
17
Issue
7
Pages
075015
ISSN
1367-2630 (ISSN-L)
DOI
10.1088/1367-2630/17/7/075015
OpenAlex
W1526062388
Cited by
475
References
17
Citations by year
2026: 100 · 2025: 83 · 2024: 69 · 2023: 41 · 2022: 50 · 2021: 33 · 2020: 36 · 2019: 25 · 2018: 21 · 2017: 6 · 2016: 9 · 2015: 2
FWCI
7.97
Type
journal article
Language
en
Open access
Licence
Locations
  • New Journal of Physics (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • Monash University Research Portal (Monash University) (submittedVersion, cc-by)
  • National University of Singapore (submittedVersion, cc-by)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • National Research Foundation
  • National Research Foundation Singapore
  • Centre for Quantum Technologies
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Engineering › Mechanical Engineering › Advanced Thermodynamic Systems and Engines
Keywords
quantum batteries, battery charging, optimal control, qubit arrays, global operations, charging power, separable states, cyclic operation, quantum advantage

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