1
|
Parajuli P, Govindarajan A, Tian L. State preparation in a Jaynes-Cummings lattice with quantum optimal control. Sci Rep 2023; 13:19924. [PMID: 37963930 PMCID: PMC10645998 DOI: 10.1038/s41598-023-47002-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2023] [Accepted: 11/07/2023] [Indexed: 11/16/2023] Open
Abstract
High-fidelity preparation of quantum states in an interacting many-body system is often hindered by the lack of knowledge of such states and by limited decoherence times. Here, we study a quantum optimal control (QOC) approach for fast generation of quantum ground states in a finite-sized Jaynes-Cummings lattice with unit filling. Our result shows that the QOC approach can generate quantum many-body states with high fidelity when the evolution time is above a threshold time, and it can significantly outperform the adiabatic approach. We study the dependence of the threshold time on the parameter constraints and the connection of the threshold time with the quantum speed limit. We also show that the QOC approach can be robust against control errors. Our result can lead to advances in the application of the QOC to many-body state preparation.
Collapse
Affiliation(s)
- Prabin Parajuli
- School of Natural Sciences, University of California, Merced, California, 95343, USA
| | - Anuvetha Govindarajan
- School of Natural Sciences, University of California, Merced, California, 95343, USA
| | - Lin Tian
- School of Natural Sciences, University of California, Merced, California, 95343, USA.
| |
Collapse
|
2
|
Vallejo-Fabila I, Torres-Herrera EJ. Late-time universal distribution functions of observables in one-dimensional many-body quantum systems. Phys Rev E 2023; 108:044102. [PMID: 37978615 DOI: 10.1103/physreve.108.044102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Accepted: 09/12/2023] [Indexed: 11/19/2023]
Abstract
We study the probability distribution function of the long-time values of observables being time-evolved by Hamiltonians modeling clean and disordered one-dimensional chains of many spin-1/2 particles. In particular, we analyze the return probability and its version for a completely extended initial state, the so-called spectral form factor. We complement our analysis with the spin autocorrelation and connected spin-spin correlation functions, both of interest in experiments with quantum simulators. We show that the distribution function has a universal shape provided the central limit theorem holds. Explicitly, the shape is exponential for the return probability and spectral form factor, meanwhile it is Gaussian for the few-body observables. We also discuss implications over the so-called many-body localization. Remarkably, our approach requires only a single sample of the dynamics and small system sizes, which could be quite advantageous when dealing specially with disordered systems.
Collapse
Affiliation(s)
- I Vallejo-Fabila
- Instituto de Física, Benemérita Universidad Autónoma de Puebla, Puebla, 72570, México
| | | |
Collapse
|
3
|
Cao Z, Bao R, Zheng J, Hou Z. Fast Functionalization with High Performance in the Autonomous Information Engine. J Phys Chem Lett 2023; 14:66-72. [PMID: 36566388 DOI: 10.1021/acs.jpclett.2c03335] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Mandal and Jarzynski have proposed a fully autonomous information heat engine, consisting of a demon, a mass, and a memory register interacting with a thermal reservoir. This device converts thermal energy into mechanical work by writing information to a memory register or, conversely, erasing information by consuming mechanical work. Here, we derive a speed limit inequality between the relaxation time of state transformation and the distance between the initial and final distributions, where the combination of the dynamical activity and entropy production plays an important role. Such inequality provides a hint that a speed-performance trade-off relation exists between the relaxation time to a functional state and the average production. To obtain fast functionalization while maintaining the performance, we show that the relaxation dynamics of the information heat engine can be accelerated significantly by devising an optimal initial state of the demon. Our design principle is inspired by the so-called Mpemba effect, where water freezes faster when initially heated.
Collapse
Affiliation(s)
- Zhiyu Cao
- Department of Chemical Physics and Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui230026, China
| | - Ruicheng Bao
- Department of Chemical Physics and Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui230026, China
| | - Jiming Zheng
- Department of Chemical Physics and Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui230026, China
| | - Zhonghuai Hou
- Department of Chemical Physics and Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui230026, China
| |
Collapse
|
4
|
Garcia L, Bofill JM, Moreira IDPR, Albareda G. Highly Adiabatic Time-Optimal Quantum Driving at Low Energy Cost. PHYSICAL REVIEW LETTERS 2022; 129:180402. [PMID: 36374669 DOI: 10.1103/physrevlett.129.180402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2022] [Revised: 05/25/2022] [Accepted: 09/13/2022] [Indexed: 06/16/2023]
Abstract
Time-efficient control schemes for manipulating quantum systems are of great importance in quantum technologies, where environmental forces rapidly degrade the quality of pure states over time. In this Letter, we formulate an approach to time-optimal control that circumvents the boundary-value problem that plagues the quantum brachistochrone equation at the expense of relaxing the form of the control Hamiltonian. In this setting, a coupled system of equations, one for the control Hamiltonian and another one for the duration of the protocol, realizes an ansatz-free approach to quantum control theory. We show how driven systems, in the form of a Landau-Zener type Hamiltonian, can be efficiently maneuvered to speed up a given state transformation in a highly adiabatic manner and with a low energy cost.
Collapse
Affiliation(s)
- Lluc Garcia
- Departament de Química Inorgànica i Orgànica, Secció de Química Orgànica, University of Barcelona, Martí i Franquès 1-11, 08028 Barcelona, Spain
- Institute of Theoretical and Computational Chemistry, University of Barcelona, Martí i Franquès 1-11, 08028 Barcelona, Spain
| | - Josep Maria Bofill
- Departament de Química Inorgànica i Orgànica, Secció de Química Orgànica, University of Barcelona, Martí i Franquès 1-11, 08028 Barcelona, Spain
- Institute of Theoretical and Computational Chemistry, University of Barcelona, Martí i Franquès 1-11, 08028 Barcelona, Spain
| | - Ibério de P R Moreira
- Institute of Theoretical and Computational Chemistry, University of Barcelona, Martí i Franquès 1-11, 08028 Barcelona, Spain
- Departament de Ciència de Materials i Química Física, University of Barcelona, Martí i Franquès 1-11, 08028 Barcelona, Spain
| | - Guillermo Albareda
- Institute of Theoretical and Computational Chemistry, University of Barcelona, Martí i Franquès 1-11, 08028 Barcelona, Spain
- Ideaded, Carrer de la Tecnologia, 35, 08840 Viladecans, Barcelona, Spain
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
| |
Collapse
|
5
|
Zheltikov AM. State-vector geometry and guided-wave physics behind optical super-resolution. OPTICS LETTERS 2022; 47:1586-1589. [PMID: 35363684 DOI: 10.1364/ol.441643] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2021] [Accepted: 12/17/2021] [Indexed: 06/14/2023]
Abstract
We examine the state-vector geometry and guided-wave physics underpinning spatial super-resolution, which can be attained in far-field linear microscopy via a combination of statistical analysis, quantum optics, and spatial mode demultiplexing. A suitably tailored guided-wave signal pickup is shown to provide an information channel that can distill the super-resolving spatial modes, thus enabling an estimation of sub-Rayleigh space intervals ξ. We derive closed-form analytical expressions describing the distribution of the ξ-estimation Fisher information over waveguide modes, showing that this information remains nonvanishing as ξ → 0, thus preventing the variance of ξ estimation from diverging at ξ → 0. We demonstrate that the transverse refractive index profile nQ(r) tailored to support the optimal wave function ψQ(r) for super-resolving ξ estimation encodes the same information about ξ as the entire manifold of waveguide modes needed to represent ψQ(r). Unlike ψQ(r), nQ(r) does not need a representation in a lengthy manifold of eigenmodes and can be found instead via adaptive feedback-controlled learning.
Collapse
|
6
|
Becker S, Datta N, Lami L, Rouzé C. Energy-Constrained Discrimination of Unitaries, Quantum Speed Limits, and a Gaussian Solovay-Kitaev Theorem. PHYSICAL REVIEW LETTERS 2021; 126:190504. [PMID: 34047578 DOI: 10.1103/physrevlett.126.190504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2020] [Accepted: 03/31/2021] [Indexed: 06/12/2023]
Abstract
We investigate the energy-constrained (EC) diamond norm distance between unitary channels acting on possibly infinite-dimensional quantum systems, and establish a number of results. First, we prove that optimal EC discrimination between two unitary channels does not require the use of any entanglement. Extending a result by Acín, we also show that a finite number of parallel queries suffices to achieve zero error discrimination even in this EC setting. Second, we employ EC diamond norms to study a novel type of quantum speed limits, which apply to pairs of quantum dynamical semigroups. We expect these results to be relevant for benchmarking internal dynamics of quantum devices. Third, we establish a version of the Solovay-Kitaev theorem that applies to the group of Gaussian unitaries over a finite number of modes, with the approximation error being measured with respect to the EC diamond norm relative to the photon number Hamiltonian.
Collapse
Affiliation(s)
- Simon Becker
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Nilanjana Datta
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Ludovico Lami
- Institut für Theoretische Physik und IQST, Universität Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany
| | - Cambyse Rouzé
- Zentrum Mathematik, Technische Universität München, 85748 Garching, Germany
| |
Collapse
|
7
|
Del Campo A. Probing Quantum Speed Limits with Ultracold Gases. PHYSICAL REVIEW LETTERS 2021; 126:180603. [PMID: 34018797 DOI: 10.1103/physrevlett.126.180603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2020] [Accepted: 03/31/2021] [Indexed: 06/12/2023]
Abstract
Quantum speed limits (QSLs) rule the minimum time for a quantum state to evolve into a distinguishable state in an arbitrary physical process. These fundamental results constrain a notion of distance traveled by the quantum state, known as the Bures angle, in terms of the speed of evolution set by nonadiabatic energy fluctuations. I theoretically propose how to measure QSLs in an ultracold quantum gas confined in a time-dependent harmonic trap. In this highly-dimensional system of continuous variables, quantum tomography is prohibited. Yet, QSLs can be probed whenever the dynamics is self-similar by measuring as a function of time the cloud size of the ultracold gas. This makes it possible to determine the Bures angle and energy fluctuations, as I discuss for various ultracold atomic systems.
Collapse
Affiliation(s)
- Adolfo Del Campo
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg; Donostia International Physics Center, E-20018 San Sebastián, Spain; IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spain; Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA and Theory Division, Los Alamos National Laboratory, MS-B213, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
8
|
Zheltikov AM. Keldysh time bounds of laser-driven ionization dynamics. OPTICS LETTERS 2021; 46:989-992. [PMID: 33649644 DOI: 10.1364/ol.414407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Accepted: 12/17/2020] [Indexed: 06/12/2023]
Abstract
We revisit the energy-time uncertainty underpinning of the pointwise bounds of laser-driven ionization dynamics. When resolved within the driver pulse and its field cycle, these bounds are shown to manifest the key signature tendencies of photoionization current dynamics-a smooth growth within the pulse in the regime of multiphoton ionization and an abrupt, almost stepwise photocurrent buildup within a fraction of the field cycle in the limit of tunneling ionization. In both regimes, the Keldysh time, defined as the ratio of the Keldysh parameter to the driver frequency, serves as a benchmark for the minimum time of photoionization, setting an upper bound for the photoelectron current buildup rate.
Collapse
|
9
|
Lee J, Tsutsui I. Uncertainty Relation for Errors Focusing on General POVM Measurements with an Example of Two-State Quantum Systems. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E1222. [PMID: 33286990 PMCID: PMC7712972 DOI: 10.3390/e22111222] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/04/2020] [Revised: 10/04/2020] [Accepted: 10/19/2020] [Indexed: 11/17/2022]
Abstract
A novel uncertainty relation for errors of general quantum measurement is presented. The new relation, which is presented in geometric terms for maps representing measurement, is completely operational and can be related directly to tangible measurement outcomes. The relation violates the naïve bound ℏ/2 for the position-momentum measurement, whilst nevertheless respecting Heisenberg's philosophy of the uncertainty principle. The standard Kennard-Robertson uncertainty relation for state preparations expressed by standard deviations arises as a corollary to its special non-informative case. For the measurement on two-state quantum systems, the relation is found to offer virtually the tightest bound possible; the equality of the relation holds for the measurement performed over every pure state. The Ozawa relation for errors of quantum measurements will also be examined in this regard. In this paper, the Kolmogorovian measure-theoretic formalism of probability-which allows for the representation of quantum measurements by positive-operator valued measures (POVMs)-is given special attention, in regard to which some of the measure-theory specific facts are remarked along the exposition as appropriate.
Collapse
Affiliation(s)
- Jaeha Lee
- Institute of Industrial Science, The University of Tokyo, Chiba 277-8574, Japan
| | - Izumi Tsutsui
- Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), Ibaraki 305-0801, Japan;
| |
Collapse
|
10
|
Fogarty T, Deffner S, Busch T, Campbell S. Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit. PHYSICAL REVIEW LETTERS 2020; 124:110601. [PMID: 32242725 DOI: 10.1103/physrevlett.124.110601] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2019] [Accepted: 02/18/2020] [Indexed: 06/11/2023]
Abstract
A remarkable feature of quantum many-body systems is the orthogonality catastrophe that describes their extensively growing sensitivity to local perturbations and plays an important role in condensed matter physics. Here we show that the dynamics of the orthogonality catastrophe can be fully characterized by the quantum speed limit and, more specifically, that any quenched quantum many-body system, whose variance in ground state energy scales with the system size, exhibits the orthogonality catastrophe. Our rigorous findings are demonstrated by two paradigmatic classes of many-body systems-the trapped Fermi gas and the long-range interacting Lipkin-Meshkov-Glick spin model.
Collapse
Affiliation(s)
- Thomás Fogarty
- Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
| | - Sebastian Deffner
- Department of Physics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA
| | - Thomas Busch
- Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
| | - Steve Campbell
- School of Physics, University College Dublin, Belfield Dublin 4, Ireland
| |
Collapse
|
11
|
Time-Energy and Time-Entropy Uncertainty Relations in Nonequilibrium Quantum Thermodynamics under Steepest-Entropy-Ascent Nonlinear Master Equations. ENTROPY 2019; 21:e21070679. [PMID: 33267393 PMCID: PMC7515176 DOI: 10.3390/e21070679] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/13/2019] [Revised: 07/07/2019] [Accepted: 07/08/2019] [Indexed: 11/29/2022]
Abstract
In the domain of nondissipative unitary Hamiltonian dynamics, the well-known Mandelstam–Tamm–Messiah time–energy uncertainty relation τFΔH≥ℏ/2 provides a general lower bound to the characteristic time τF=ΔF/|d〈F〉/dt| with which the mean value of a generic quantum observable F can change with respect to the width ΔF of its uncertainty distribution (square root of F fluctuations). A useful practical consequence is that in unitary dynamics the states with longer lifetimes are those with smaller energy uncertainty ΔH (square root of energy fluctuations). Here we show that when unitary evolution is complemented with a steepest-entropy-ascent model of dissipation, the resulting nonlinear master equation entails that these lower bounds get modified and depend also on the entropy uncertainty ΔS (square root of entropy fluctuations). For example, we obtain the time–energy-and–time–entropy uncertainty relation (2τFΔH/ℏ)2+(τFΔS/kBτ)2≥1 where τ is a characteristic dissipation time functional that for each given state defines the strength of the nonunitary, steepest-entropy-ascent part of the assumed master equation. For purely dissipative dynamics this reduces to the time–entropy uncertainty relation τFΔS≥kBτ, meaning that the nonequilibrium dissipative states with longer lifetime are those with smaller entropy uncertainty ΔS.
Collapse
|
12
|
Shiraishi N, Funo K, Saito K. Speed Limit for Classical Stochastic Processes. PHYSICAL REVIEW LETTERS 2018; 121:070601. [PMID: 30169075 DOI: 10.1103/physrevlett.121.070601] [Citation(s) in RCA: 63] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2018] [Indexed: 05/10/2023]
Abstract
We consider the speed limit for classical stochastic Markov processes with and without the local detailed balance condition. We find that, for both cases, a trade-off inequality exists between the speed of the state transformation and the entropy production. The dynamical activity is related to a time scale and plays a crucial role in the inequality. For the dynamics without the local detailed balance condition, we use the Hatano-Sasa entropy production instead of the standard entropy production. Our inequalities consist of the quantities that are commonly used in stochastic thermodynamics and explicitly show underlying physical mechanisms.
Collapse
Affiliation(s)
- Naoto Shiraishi
- Department of Physics, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 2288521, Japan
| | - Ken Funo
- School of Physics, Peking University, Beijing 100871, China
| | - Keiji Saito
- Department of Physics, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 2288521, Japan
| |
Collapse
|
13
|
Abstract
The quantum speed limit (QSL), or the energy-time uncertainty relation, describes the fundamental maximum rate for quantum time evolution and has been regarded as being unique in quantum mechanics. In this study, we obtain a classical speed limit corresponding to the QSL using Hilbert space for the classical Liouville equation. Thus, classical mechanics has a fundamental speed limit, and the QSL is not a purely quantum phenomenon but a universal dynamical property of Hilbert space. Furthermore, we obtain similar speed limits for the imaginary-time Schrödinger equations such as the classical master equation.
Collapse
Affiliation(s)
- Manaka Okuyama
- Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan
| | - Masayuki Ohzeki
- Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
| |
Collapse
|
14
|
Lychkovskiy O, Gamayun O, Cheianov V. Time Scale for Adiabaticity Breakdown in Driven Many-Body Systems and Orthogonality Catastrophe. PHYSICAL REVIEW LETTERS 2017; 119:200401. [PMID: 29219349 DOI: 10.1103/physrevlett.119.200401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2016] [Indexed: 06/07/2023]
Abstract
The adiabatic theorem is a fundamental result in quantum mechanics, which states that a system can be kept arbitrarily close to the instantaneous ground state of its Hamiltonian if the latter varies in time slowly enough. The theorem has an impressive record of applications ranging from foundations of quantum field theory to computational molecular dynamics. In light of this success it is remarkable that a practicable quantitative understanding of what "slowly enough" means is limited to a modest set of systems mostly having a small Hilbert space. Here we show how this gap can be bridged for a broad natural class of physical systems, namely, many-body systems where a small move in the parameter space induces an orthogonality catastrophe. In this class, the conditions for adiabaticity are derived from the scaling properties of the parameter-dependent ground state without a reference to the excitation spectrum. This finding constitutes a major simplification of a complex problem, which otherwise requires solving nonautonomous time evolution in a large Hilbert space.
Collapse
Affiliation(s)
- Oleg Lychkovskiy
- Skolkovo Institute of Science and Technology, Skolkovo Innovation Center 3, Moscow 143026, Russia
- Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina str. 8, Moscow 119991, Russia
- Russian Quantum Center, Novaya St. 100A, Skolkovo, Moscow Region 143025, Russia
| | - Oleksandr Gamayun
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
- Bogolyubov Institute for Theoretical Physics, 14-b Metrolohichna str., Kyiv 03680, Ukraine
| | - Vadim Cheianov
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
| |
Collapse
|
15
|
Campbell S, Deffner S. Trade-Off Between Speed and Cost in Shortcuts to Adiabaticity. PHYSICAL REVIEW LETTERS 2017; 118:100601. [PMID: 28339279 DOI: 10.1103/physrevlett.118.100601] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2016] [Indexed: 05/25/2023]
Abstract
Achieving effectively adiabatic dynamics is a ubiquitous goal in almost all areas of quantum physics. Here, we study the speed with which a quantum system can be driven when employing transitionless quantum driving. As a main result, we establish a rigorous link between this speed, the quantum speed limit, and the (energetic) cost of implementing such a shortcut to adiabaticity. Interestingly, this link elucidates a trade-off between speed and cost, namely, that instantaneous manipulation is impossible as it requires an infinite cost. These findings are illustrated for two experimentally relevant systems-the parametric oscillator and the Landau-Zener model-which reveal that the spectral gap governs the quantum speed limit as well as the cost for realizing the shortcut.
Collapse
Affiliation(s)
- Steve Campbell
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
- Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, 20133 Milan, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria 16, 20133 Milan, Italy
| | - Sebastian Deffner
- Department of Physics, University of Maryland Baltimore County, Baltimore, Maryland 21250, USA
| |
Collapse
|
16
|
Song YJ, Tan QS, Kuang LM. Control quantum evolution speed of a single dephasing qubit for arbitrary initial states via periodic dynamical decoupling pulses. Sci Rep 2017; 7:43654. [PMID: 28272546 PMCID: PMC5341562 DOI: 10.1038/srep43654] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2016] [Accepted: 01/26/2017] [Indexed: 01/03/2023] Open
Abstract
We investigate the possibility to control quantum evolution speed of a single dephasing qubit for arbitrary initial states by the use of periodic dynamical decoupling (PDD) pulses. It is indicated that the quantum speed limit time (QSLT) is determined by initial and final quantum coherence of the qubit, as well as the non-Markovianity of the system under consideration during the evolution when the qubit is subjected to a zero-temperature Ohmic-like dephasing reservoir. It is shown that final quantum coherence of the qubit and the non-Markovianity of the system can be modulated by PDD pulses. Our results show that for arbitrary initial states of the dephasing qubit with non-vanishing quantum coherence, PDD pulses can be used to induce potential acceleration of the quantum evolution in the short-time regime, while PDD pulses can lead to potential speedup and slow down in the long-time regime. We demonstrate that the effect of PDD on the QSLT for the Ohmic or sub-Ohmic spectrum (Markovian reservoir) is much different from that for the super-Ohmic spectrum (non-Markovian reservoir).
Collapse
Affiliation(s)
- Ya-Ju Song
- Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China
| | - Qing-Shou Tan
- College of Physics and Electronic Engineering, Hainan Normal University, Haikou 571158, China
| | - Le-Man Kuang
- Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China
| |
Collapse
|
17
|
Jing J, Wu LA, Del Campo A. Fundamental Speed Limits to the Generation of Quantumness. Sci Rep 2016; 6:38149. [PMID: 27901118 PMCID: PMC5128863 DOI: 10.1038/srep38149] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2016] [Accepted: 11/04/2016] [Indexed: 01/30/2023] Open
Abstract
Quantum physics dictates fundamental speed limits during time evolution. We present a quantum speed limit governing the generation of nonclassicality and the mutual incompatibility of two states connected by time evolution. This result is used to characterize the timescale required to generate a given amount of quantumness under an arbitrary physical process. The bound is found to be tight under pure dephasing dynamics. More generally, our analysis reveals the dependence on the initial and final states and non-Markovian effects.
Collapse
Affiliation(s)
- Jun Jing
- Institute of Atomic and Molecular Physics and Jilin Provincial Key Laboratory of Applied Atomic and Molecular Spectroscopy, Jilin University, Changchun 130012, Jilin, China.,Department of Theoretical Physics and History of Science, The University of the Basque Country (EHU/UPV), PO Box 644, 48080 Bilbao, Spain
| | - Lian-Ao Wu
- Department of Theoretical Physics and History of Science, The University of the Basque Country (EHU/UPV), PO Box 644, 48080 Bilbao, Spain.,Ikerbasque, Basque Foundation for Science, 48011 Bilbao, Spain
| | - Adolfo Del Campo
- Department of Physics, University of Massachusetts, Boston, MA 02125, USA
| |
Collapse
|
18
|
Speedup of quantum evolution of multiqubit entanglement states. Sci Rep 2016; 6:27349. [PMID: 27283757 PMCID: PMC4901278 DOI: 10.1038/srep27349] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2016] [Accepted: 05/17/2016] [Indexed: 11/19/2022] Open
Abstract
As is well known, quantum speed limit time (QSLT) can be used to characterize the maximal speed of evolution of quantum systems. We mainly investigate the QSLT of generalized N-qubit GHZ-type states and W-type states in the amplitude-damping channels. It is shown that, in the case N qubits coupled with independent noise channels, the QSLT of the entangled GHZ-type state is closely related to the number of qubits in the small-scale system. And the larger entanglement of GHZ-type states can lead to the shorter QSLT of the evolution process. However, the QSLT of the W-type states are independent of the number of qubits and the initial entanglement. Furthermore, by considering only M qubits among the N-qubit system respectively interacting with their own noise channels, QSLTs for these two types states are shorter than in the case N qubits coupled with independent noise channels. We therefore reach the interesting result that the potential speedup of quantum evolution of a given N-qubit GHZ-type state or W-type state can be realized in the case the number of the applied noise channels satisfying M < N.
Collapse
|
19
|
Marvian I, Lidar DA. Quantum Speed Limits for Leakage and Decoherence. PHYSICAL REVIEW LETTERS 2015; 115:210402. [PMID: 26636833 DOI: 10.1103/physrevlett.115.210402] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2015] [Indexed: 06/05/2023]
Abstract
We introduce state-independent, nonperturbative Hamiltonian quantum speed limits for population leakage and fidelity loss, for a gapped open system interacting with a reservoir. These results hold in the presence of initial correlations between the system and the reservoir, under the sole assumption that their interaction and its commutator with the reservoir Hamiltonian are norm bounded. The reservoir need not be thermal and can be time dependent. We study the significance of energy mismatch between the system and the local degrees of freedom of the reservoir that directly interact with the system. We demonstrate that, in general, by increasing the system gap we may reduce this energy mismatch, and, consequently, drive the system and the reservoir into resonance; this can accelerate fidelity loss, irrespective of the thermal properties or state of the reservoir. This implies that quantum error suppression strategies based on increasing the gap are not uniformly beneficial. Our speed limits also yield an elementary lower bound on the relaxation time of spin systems.
Collapse
Affiliation(s)
- Iman Marvian
- Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089, USA
- Department of Physics, University of Southern California, Los Angeles, California 90089, USA
| | - Daniel A Lidar
- Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089, USA
- Department of Physics, University of Southern California, Los Angeles, California 90089, USA
- Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| |
Collapse
|
20
|
Zhang YJ, Han W, Xia YJ, Yu YM, Fan H. Role of initial system-bath correlation on coherence trapping. Sci Rep 2015; 5:13359. [PMID: 26303160 PMCID: PMC4548186 DOI: 10.1038/srep13359] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2015] [Accepted: 07/23/2015] [Indexed: 12/24/2022] Open
Abstract
We study the coherence trapping of a qubit correlated initially with a non-Markovian bath in a pure dephasing channel. By considering the initial qubit-bath correlation and the bath spectral density, we find that the initial qubit-bath correlation can lead to a more efficient coherence trapping than that of the initially separable qubit-bath state. The stationary coherence in the long time limit can be maximized by optimizing the parameters of the initially correlated qubit-bath state and the bath spectral density. In addition, the effects of this initial correlation on the maximal evolution speed for the qubit trapped to its stationary coherence state are also explored.
Collapse
Affiliation(s)
- Ying-Jie Zhang
- Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Department of Physics, Qufu Normal University, Qufu 273165, China.,Beijing National Laboratory of Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Wei Han
- Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Department of Physics, Qufu Normal University, Qufu 273165, China
| | - Yun-Jie Xia
- Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Department of Physics, Qufu Normal University, Qufu 273165, China
| | - Yan-Mei Yu
- Beijing National Laboratory of Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Heng Fan
- Beijing National Laboratory of Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.,Innovative Center of Quantum Matter, Beijing 100190, China
| |
Collapse
|
21
|
Coden DSA, Romero RH, Räsänen E. Controlled high-fidelity navigation in the charge stability diagram of a double quantum dot. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:115303. [PMID: 25738833 DOI: 10.1088/0953-8984/27/11/115303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We propose an efficient control protocol for charge transfer in a double quantum dot. We consider numerically a two-dimensional model system, where the quantum dots are subjected to time-dependent electric fields corresponding to experimental gate voltages. Our protocol enables navigation in the charge stability diagram from a state to another through controllable variation of the fields. We show that the well-known adiabatic Landau-Zener transition-when supplemented with a time-dependent field tailored with optimal control theory-can remarkably improve the transition speed. The results also lead to a simple control scheme obtained from the experimental charge stability diagram that requires only a single parameter. Eventually, we can achieve the ultrafast performance of the composite pulse protocol that allows the system to be driven at the quantum speed limit.
Collapse
Affiliation(s)
- Diego S Acosta Coden
- Instituto de Modelado e Innovación Tecnológica (CONICET-UNNE) and Facultad de Ciencias Exactas y Naturales y Agrimensura, Avenida Libertad 5400, W3404AAS Corrientes, Argentina
| | | | | |
Collapse
|
22
|
Quantum speed limits in open systems: non-Markovian dynamics without rotating-wave approximation. Sci Rep 2015; 5:8444. [PMID: 25676589 PMCID: PMC4649631 DOI: 10.1038/srep08444] [Citation(s) in RCA: 67] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2014] [Accepted: 01/20/2015] [Indexed: 12/20/2022] Open
Abstract
We derive an easily computable quantum speed limit (QSL) time bound for open systems whose initial states can be chosen as either pure or mixed states. Moreover, this QSL time is applicable to either Markovian or non-Markovian dynamics. By using of a hierarchy equation method, we numerically study the QSL time bound in a qubit system interacting with a single broadened cavity mode without rotating-wave, Born and Markovian approximation. By comparing with rotating-wave approximation (RWA) results, we show that the counter-rotating terms are helpful to increase evolution speed. The problem of non-Markovianity is also considered. We find that for non-RWA cases, increasing system-bath coupling can not always enhance the non-Markovianity, which is qualitatively different from the results with RWA. When considering the relation between QSL and non-Markovianity, we find that for small broadening widths of the cavity mode, non-Markovianity can increase the evolution speed in either RWA or non-RWA cases, while, for larger broadening widths, it is not true for non-RWA cases.
Collapse
|
23
|
Abstract
The minimal time a system needs to evolve from an initial state to its one orthogonal state is defined as the quantum speed limit time, which can be used to characterize the maximal speed of evolution of a quantum system. This is a fundamental question of quantum physics. We investigate the generic bound on the minimal evolution time of the open dynamical quantum system. This quantum speed limit time is applicable to both mixed and pure initial states. We then apply this result to the damped Jaynes-Cummings model and the Ohimc-like dephasing model starting from a general time-evolution state. The bound of this time-dependent state at any point in time can be found. For the damped Jaynes-Cummings model, when the system starts from the excited state, the corresponding bound first decreases and then increases in the Markovian dynamics. While in the non-Markovian regime, the speed limit time shows an interesting periodic oscillatory behavior. For the case of Ohimc-like dephasing model, this bound would be gradually trapped to a fixed value. In addition, the roles of the relativistic effects on the speed limit time for the observer in non-inertial frames are discussed.
Collapse
|
24
|
Deffner S, Lutz E. Quantum speed limit for non-Markovian dynamics. PHYSICAL REVIEW LETTERS 2013; 111:010402. [PMID: 23862985 DOI: 10.1103/physrevlett.111.010402] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2013] [Indexed: 06/02/2023]
Abstract
We derive a Margolus-Levitin-type bound on the minimal evolution time of an arbitrarily driven open quantum system. We express this quantum speed limit time in terms of the operator norm of the nonunitary generator of the dynamics. We apply these results to the damped Jaynes-Cummings model and demonstrate that the corresponding bound is tight. We further show that non-Markovian effects can speed up quantum evolution and therefore lead to a smaller quantum speed limit time.
Collapse
Affiliation(s)
- Sebastian Deffner
- Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | | |
Collapse
|
25
|
Taddei MM, Escher BM, Davidovich L, de Matos Filho RL. Quantum speed limit for physical processes. PHYSICAL REVIEW LETTERS 2013; 110:050402. [PMID: 23414007 DOI: 10.1103/physrevlett.110.050402] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2012] [Indexed: 06/01/2023]
Abstract
The evaluation of the minimal evolution time between two distinguishable states of a system is important for assessing the maximal speed of quantum computers and communication channels. Lower bounds for this minimal time have been proposed for unitary dynamics. Here we show that it is possible to extend this concept to nonunitary processes, using an attainable lower bound that is connected to the quantum Fisher information for time estimation. This result is used to delimit the minimal evolution time for typical noisy channels.
Collapse
Affiliation(s)
- M M Taddei
- Instituto de Física, Universidade Federal do Rio de Janeiro, 21.941-972 Rio de Janeiro (RJ), Brazil.
| | | | | | | |
Collapse
|
26
|
Caneva T, Murphy M, Calarco T, Fazio R, Montangero S, Giovannetti V, Santoro GE. Optimal control at the quantum speed limit. PHYSICAL REVIEW LETTERS 2009; 103:240501. [PMID: 20366188 DOI: 10.1103/physrevlett.103.240501] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2009] [Indexed: 05/29/2023]
Abstract
Optimal control theory is a promising candidate for a drastic improvement of the performance of quantum information tasks. We explore its ultimate limit in paradigmatic cases, and demonstrate that it coincides with the maximum speed limit allowed by quantum evolution.
Collapse
Affiliation(s)
- T Caneva
- International School for Advanced Studies (SISSA), Via Beirut 2-4, I-34014 Trieste, Italy
| | | | | | | | | | | | | |
Collapse
|
27
|
Levitin LB, Toffoli T. Fundamental limit on the rate of quantum dynamics: the unified bound is tight. PHYSICAL REVIEW LETTERS 2009; 103:160502. [PMID: 19905679 DOI: 10.1103/physrevlett.103.160502] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2009] [Indexed: 05/28/2023]
Abstract
How fast a quantum state can evolve has attracted considerable attention in connection with quantum measurement and information processing. A lower bound on the orthogonalization time, based on the energy spread DeltaE, was found by Mandelstam and Tamm. Another bound, based on the average energy E, was established by Margolus and Levitin. The bounds coincide and can be attained by certain initial states if DeltaE=E. Yet, the problem remained open when DeltaE not equal E. We consider the unified bound that involves both DeltaE and E. We prove that there exist no initial states that saturate the bound if DeltaE not equal E. However, the bound remains tight: for any values of DeltaE and E, there exists a one-parameter family of initial states that can approach the bound arbitrarily close when the parameter approaches its limit. These results establish the fundamental limit of the operation rate of any information processing system.
Collapse
Affiliation(s)
- Lev B Levitin
- Electrical and Computer Engineering, Boston University, Boston, Massachusetts 02215, USA.
| | | |
Collapse
|
28
|
Li Y, Ullrich CA. Time-dependent V-representability on lattice systems. J Chem Phys 2008; 129:044105. [DOI: 10.1063/1.2955733] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
29
|
Luo S. Wigner-Yanase skew information and uncertainty relations. PHYSICAL REVIEW LETTERS 2003; 91:180403. [PMID: 14611271 DOI: 10.1103/physrevlett.91.180403] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2003] [Indexed: 05/24/2023]
Abstract
The Wigner-Araki-Yanase theorem puts a limitation on the measurement of observables in the presence of a conserved quantity, and the notion of Wigner-Yanase skew information quantifies the amount of information on the values of observables not commuting with the conserved quantity. We demonstrate that the statistical idea underlying the skew information is the Fisher information in the theory of statistical estimation. A quantum Cramér-Rao inequality and a new uncertainty relation in terms of the skew information are established, which shed considerable new light on the relationships between quantum measurement and statistical inference. The result is applied to estimating the evolution speed of quantum states.
Collapse
Affiliation(s)
- Shunlong Luo
- Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100080 Beijing, People's Republic of China.
| |
Collapse
|
30
|
Gea-Banacloche J. Minimum energy requirements for quantum computation. PHYSICAL REVIEW LETTERS 2002; 89:217901. [PMID: 12443450 DOI: 10.1103/physrevlett.89.217901] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2002] [Indexed: 05/24/2023]
Abstract
A lower bound on the amount of energy needed to carry out an elementary logical operation on a quantum computer, with a given accuracy and in a given time, is derived. The bound arises from the requirement that the controls used to manipulate the qubits, which ultimately are themselves quan-tum mechanical systems, must nonetheless be classical to a sufficiently good approximation; it is expected to hold under a wide variety of conditions, and independently of the nature of the physical systems used to encode the qubits. This could have important consequences for very large-scale quantum computations.
Collapse
Affiliation(s)
- Julio Gea-Banacloche
- Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA
| |
Collapse
|
31
|
Fring A, Kostrykin V, Schrader R. Ionization probabilities through ultra-intense fields in the extreme limit. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/30/24/020] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
32
|
Kaluza M, Muckerman JT. Short-pulse population inversion and transmittance. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 51:1694-1697. [PMID: 9911764 DOI: 10.1103/physreva.51.1694] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
33
|
Plata J. Analytical solutions for a resonantly driven two-doublet system. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1994; 49:2759-2765. [PMID: 9910556 DOI: 10.1103/physreva.49.2759] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
34
|
Pfeifer P. Scalar Aharonov-Bohm experiment with unpolarized neutrons. PHYSICAL REVIEW LETTERS 1994; 72:305. [PMID: 10056111 DOI: 10.1103/physrevlett.72.305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|