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Kang YH, Shi ZC, Song J, Xia Y. Effective non-adiabatic holonomic quantum computation of cavity modes via invariant-based reverse engineering. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210279. [PMID: 36335947 DOI: 10.1098/rsta.2021.0279] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2021] [Accepted: 02/22/2022] [Indexed: 06/16/2023]
Abstract
In this paper, we propose a protocol to realize non-adiabatic holonomic quantum computation (NHQC) of cavity modes via invariant-based reverse engineering. Coupling cavity modes with an auxiliary atom trapped in a cavity, we derive effective Hamiltonians with the help of laser pulses. Based on the derived Hamiltonians, invariant-based reverse engineering is used to find proper evolution paths for NHQC. Moreover, the systematic-error-sensitivity nullified optimal control method is considered in the parameter selections, making the protocol insensitive to the influence of systematic errors of pulses. We also estimate the imperfections induced by random noise and decoherence. Numerical results show that the protocol holds robustness against these imperfections. Therefore, the protocol may provide useful perspectives to quantum computation with optical qubits in cavity quantum electrodynamics systems. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.
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Affiliation(s)
- Yi-Hao Kang
- Department of Physics, Harbin Institute of Technology, Harbin 150001, People's Republic of China
- Fujian Key Laboratory of Quantum Information and Quantum Optics (Fuzhou University), Fuzhou 350116, People's Republic of China
| | - Zhi-Cheng Shi
- Fujian Key Laboratory of Quantum Information and Quantum Optics (Fuzhou University), Fuzhou 350116, People's Republic of China
- Department of Physics, Fuzhou University, Fuzhou 350116, People's Republic of China
| | - Jie Song
- Department of Physics, Harbin Institute of Technology, Harbin 150001, People's Republic of China
| | - Yan Xia
- Fujian Key Laboratory of Quantum Information and Quantum Optics (Fuzhou University), Fuzhou 350116, People's Republic of China
- Department of Physics, Fuzhou University, Fuzhou 350116, People's Republic of China
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Zhang C, Guo Z, Cao H. Symmetry-Like Relation of Relative Entropy Measure of Quantum Coherence. ENTROPY 2020; 22:e22030297. [PMID: 33286071 PMCID: PMC7516754 DOI: 10.3390/e22030297] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 01/18/2020] [Revised: 02/18/2020] [Accepted: 02/25/2020] [Indexed: 11/17/2022]
Abstract
Quantum coherence is an important physical resource in quantum information science, and also as one of the most fundamental and striking features in quantum physics. To quantify coherence, two proper measures were introduced in the literature, the one is the relative entropy of coherence Cr(ρ)=S(ρdiag)−S(ρ) and the other is the ℓ1-norm of coherence Cℓ1(ρ)=∑i≠j|ρij|. In this paper, we obtain a symmetry-like relation of relative entropy measure Cr(ρA1A2⋯An) of coherence for an n-partite quantum states ρA1A2⋯An, which gives lower and upper bounds for Cr(ρ). As application of our inequalities, we conclude that when each reduced states ρAi is pure, ρA1⋯An is incoherent if and only if the reduced states ρAi and trAiρA1⋯An(i=1,2,…,n) are all incoherent. Meanwhile, we discuss the conjecture that Cr(ρ)≤Cℓ1(ρ) for any state ρ, which was proved to be valid for any mixed qubit state and any pure state, and open for a general state. We observe that every mixture η of a state ρ satisfying the conjecture with any incoherent state σ also satisfies the conjecture. We also observe that when the von Neumann entropy is defined by the natural logarithm ln instead of log2, the reduced relative entropy measure of coherence C¯r(ρ)=−ρdiaglnρdiag+ρlnρ satisfies the inequality C¯r(ρ)≤Cℓ1(ρ) for any state ρ.
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Smith A, Knolle J, Moessner R, Kovrizhin DL. Absence of Ergodicity without Quenched Disorder: From Quantum Disentangled Liquids to Many-Body Localization. PHYSICAL REVIEW LETTERS 2017; 119:176601. [PMID: 29219477 DOI: 10.1103/physrevlett.119.176601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2017] [Indexed: 06/07/2023]
Abstract
We study the time evolution after a quantum quench in a family of models whose degrees of freedom are fermions coupled to spins, where quenched disorder appears neither in the Hamiltonian parameters nor in the initial state. Focusing on the behavior of entanglement, both spatial and between subsystems, we show that the model supports a state exhibiting combined area and volume-law entanglement, being characteristic of the quantum disentangled liquid. This behavior appears for one set of variables, which is related via a duality mapping to another set, where this structure is absent. Upon adding density interactions between the fermions, we identify an exact mapping to an XXZ spin chain in a random binary magnetic field, thereby establishing the existence of many-body localization with its logarithmic entanglement growth in a fully disorder-free system.
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Affiliation(s)
- A Smith
- T.C.M. group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - J Knolle
- T.C.M. group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - R Moessner
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - D L Kovrizhin
- Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, United Kingdom
- NRC Kurchatov Institute, 1 Kurchatov Square, 123182 Moscow, Russia
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Smith A, Knolle J, Kovrizhin DL, Moessner R. Disorder-Free Localization. PHYSICAL REVIEW LETTERS 2017; 118:266601. [PMID: 28707931 DOI: 10.1103/physrevlett.118.266601] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2017] [Indexed: 06/07/2023]
Abstract
The venerable phenomena of Anderson localization, along with the much more recent many-body localization, both depend crucially on the presence of disorder. The latter enters either in the form of quenched disorder in the parameters of the Hamiltonian, or through a special choice of a disordered initial state. Here, we present a model with localization arising in a very simple, completely translationally invariant quantum model, with only local interactions between spins and fermions. By identifying an extensive set of conserved quantities, we show that the system generates purely dynamically its own disorder, which gives rise to localization of fermionic degrees of freedom. Our work gives an answer to a decades old question whether quenched disorder is a necessary condition for localization. It also offers new insights into the physics of many-body localization, lattice gauge theories, and quantum disentangled liquids.
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Affiliation(s)
- A Smith
- T.C.M. Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - J Knolle
- T.C.M. Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - D L Kovrizhin
- Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, United Kingdom
- NRC Kurchatov Institute, 1 Kurchatov Square, 123182 Moscow, Russia
| | - R Moessner
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
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Reichsöllner L, Schindewolf A, Takekoshi T, Grimm R, Nägerl HC. Quantum Engineering of a Low-Entropy Gas of Heteronuclear Bosonic Molecules in an Optical Lattice. PHYSICAL REVIEW LETTERS 2017; 118:073201. [PMID: 28256882 DOI: 10.1103/physrevlett.118.073201] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2016] [Indexed: 06/06/2023]
Abstract
We demonstrate a generally applicable technique for mixing two-species quantum degenerate bosonic samples in the presence of an optical lattice, and we employ it to produce low-entropy samples of ultracold ^{87}Rb^{133}Cs Feshbach molecules with a lattice filling fraction exceeding 30%. Starting from two spatially separated Bose-Einstein condensates of Rb and Cs atoms, Rb-Cs atom pairs are efficiently produced by using the superfluid-to-Mott insulator quantum phase transition twice, first for the Cs sample, then for the Rb sample, after nulling the Rb-Cs interaction at a Feshbach resonance's zero crossing. We form molecules out of atom pairs and characterize the mixing process in terms of sample overlap and mixing speed. The dense and ultracold sample of more than 5000 RbCs molecules is an ideal starting point for experiments in the context of quantum many-body physics with long-range dipolar interactions.
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Affiliation(s)
- Lukas Reichsöllner
- Institut für Experimentalphysik, Universität Innsbruck, 6020 Innsbruck, Austria
| | - Andreas Schindewolf
- Institut für Experimentalphysik, Universität Innsbruck, 6020 Innsbruck, Austria
| | - Tetsu Takekoshi
- Institut für Experimentalphysik, Universität Innsbruck, 6020 Innsbruck, Austria
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria
| | - Rudolf Grimm
- Institut für Experimentalphysik, Universität Innsbruck, 6020 Innsbruck, Austria
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria
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Andraschko F, Enss T, Sirker J. Purification and many-body localization in cold atomic gases. PHYSICAL REVIEW LETTERS 2014; 113:217201. [PMID: 25479517 DOI: 10.1103/physrevlett.113.217201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2014] [Indexed: 06/04/2023]
Abstract
We propose to observe many-body localization in cold atomic gases by realizing a Bose-Hubbard chain with binary disorder and studying its nonequilibrium dynamics. In particular, we show that measuring the difference in occupation between even and odd sites, starting from a prepared density-wave state, provides clear signatures of localization. Furthermore, we confirm as hallmarks of the many-body localized phase a logarithmic increase of the entanglement entropy in time and Poissonian level statistics. Our numerical density-matrix renormalization group calculations for infinite system size are based on a purification approach; this allows us to perform the disorder average exactly, thus producing data without any statistical noise and with maximal simulation times of up to a factor 10 longer than in the clean case.
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Affiliation(s)
- Felix Andraschko
- Department of Physics and Research Center OPTIMAS, Technical University Kaiserslautern, D-67663 Kaiserslautern, Germany and Department of Physics and Astronomy, University of Manitoba, Winnipeg R3T 2N2, Canada
| | - Tilman Enss
- Institut für Theoretische Physik, Universität Heidelberg, D-69120 Heidelberg, Germany
| | - Jesko Sirker
- Department of Physics and Research Center OPTIMAS, Technical University Kaiserslautern, D-67663 Kaiserslautern, Germany and Department of Physics and Astronomy, University of Manitoba, Winnipeg R3T 2N2, Canada
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Gadway B, Pertot D, Reeves J, Vogt M, Schneble D. Glassy behavior in a binary atomic mixture. PHYSICAL REVIEW LETTERS 2011; 107:145306. [PMID: 22107210 DOI: 10.1103/physrevlett.107.145306] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2011] [Revised: 08/14/2011] [Indexed: 05/31/2023]
Abstract
We experimentally study one-dimensional, lattice-modulated Bose gases in the presence of an uncorrelated disorder potential formed by localized impurity atoms, and compare to the case of correlated quasidisorder formed by an incommensurate lattice. While the effects of the two disorder realizations are comparable deeply in the strongly interacting regime, both showing signatures of Bose-glass formation, we find a dramatic difference near the superfluid-to-insulator transition. In this transition region, we observe that random, uncorrelated disorder leads to a shift of the critical lattice depth for the breakdown of transport as opposed to the case of correlated quasidisorder, where no such shift is seen. Our findings, which are consistent with recent predictions for interacting bosons in one dimension, illustrate the important role of correlations in disordered atomic systems.
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Affiliation(s)
- Bryce Gadway
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA.
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Horstmann B, Dürr S, Roscilde T. Localization of cold atoms in state-dependent optical lattices via a Rabi Pulse. PHYSICAL REVIEW LETTERS 2010; 105:160402. [PMID: 21230951 DOI: 10.1103/physrevlett.105.160402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2010] [Revised: 08/10/2010] [Indexed: 05/30/2023]
Abstract
We propose a novel realization of Anderson localization in nonequilibrium states of ultracold atoms in an optical lattice. A Rabi pulse transfers part of the population to a different internal state with infinite effective mass. These frozen atoms create a quantum superposition of different disorder potentials, localizing the mobile atoms. For weakly interacting mobile atoms, Anderson localization is obtained. The localization length increases with increasing disorder and decreasing interaction strength, contrary to the expectation for equilibrium localization.
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Affiliation(s)
- Birger Horstmann
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany
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Hastings MB. Inference from matrix products: a heuristic spin-glass algorithm. PHYSICAL REVIEW LETTERS 2008; 101:167206. [PMID: 18999711 DOI: 10.1103/physrevlett.101.167206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2008] [Indexed: 05/27/2023]
Abstract
We present an algorithm for finding ground states of two-dimensional spin-glass systems based on ideas from matrix product states in quantum information theory. The algorithm works directly at zero temperature and defines an approximation to the energy whose accuracy depends on a parameter k. We test the algorithm against exact methods on random field and random bond Ising models, and we find that accurate results require a k which scales roughly polynomially with the system size. The algorithm also performs well when tested on small systems with arbitrary interactions, where no fast, exact algorithms exist. The time required is significantly less than Monte Carlo schemes.
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Affiliation(s)
- M B Hastings
- Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
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Alvarez GA, Danieli EP, Levstein PR, Pastawski HM. Quantum parallelism as a tool for ensemble spin dynamics calculations. PHYSICAL REVIEW LETTERS 2008; 101:120503. [PMID: 18851351 DOI: 10.1103/physrevlett.101.120503] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2007] [Indexed: 05/26/2023]
Abstract
Efficient simulations of quantum evolutions of spin-1/2 systems are relevant for ensemble quantum computation as well as in typical NMR experiments. We propose an efficient method to calculate the dynamics of an observable provided that the initial excitation is "local." It resorts to a single entangled pure initial state built as a superposition, with random phases, of the pure elements that compose the mixture. This ensures self-averaging of any observable, drastically reducing the calculation time. The procedure is tested for two representative systems: a spin star (cluster with random long range interactions) and a spin ladder.
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Affiliation(s)
- Gonzalo A Alvarez
- Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Córdoba, Argentina.
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Vidal G. Class of quantum many-body states that can be efficiently simulated. PHYSICAL REVIEW LETTERS 2008; 101:110501. [PMID: 18851269 DOI: 10.1103/physrevlett.101.110501] [Citation(s) in RCA: 100] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2006] [Indexed: 05/26/2023]
Abstract
We introduce the multiscale entanglement renormalization ansatz, a class of quantum many-body states on a D-dimensional lattice that can be efficiently simulated with a classical computer, in that the expectation value of local observables can be computed exactly and efficiently. The multiscale entanglement renormalization ansatz is equivalent to a quantum circuit of logarithmic depth that has a very characteristic causal structure. It is also the ansatz underlying entanglement renormalization, a novel coarse-graining scheme for many-body quantum systems on a lattice.
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Affiliation(s)
- G Vidal
- School of Physical Sciences, The University of Queensland, QLD 4072, Australia
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12
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Roscilde T, Cirac JI. Quantum emulsion: a glassy phase of bosonic mixtures in optical lattices. PHYSICAL REVIEW LETTERS 2007; 98:190402. [PMID: 17677607 DOI: 10.1103/physrevlett.98.190402] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2006] [Indexed: 05/16/2023]
Abstract
We numerically investigate mixtures of two interacting bosonic species with unequal parameters in one-dimensional optical lattices. In large parameter regions full phase segregation is seen to minimize the energy of the system, but the true ground state is masked by an exponentially large number of metastable states characterized by microscopic phase separation. The ensemble of these quantum emulsion states, reminiscent of emulsions of immiscible fluids, has macroscopic properties analogous to those of a Bose glass, namely, a finite compressibility in absence of superfluidity. Their metastability is probed by extensive quantum Monte Carlo simulations generating rich correlated stochastic dynamics. The tuning of the repulsion of one of the two species via a Feshbach resonance drives the system through a quantum phase transition to the superfluid state.
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Affiliation(s)
- Tommaso Roscilde
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany
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