1
|
Perfetto G, Carollo F, Garrahan JP, Lesanovsky I. Quantum reaction-limited reaction-diffusion dynamics of annihilation processes. Phys Rev E 2023; 108:064104. [PMID: 38243424 DOI: 10.1103/physreve.108.064104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Accepted: 10/23/2023] [Indexed: 01/21/2024]
Abstract
We investigate the quantum reaction-diffusion dynamics of fermionic particles which coherently hop in a one-dimensional lattice and undergo annihilation reactions. The latter are modelled as dissipative processes which involve losses of pairs 2A→∅, triplets 3A→∅, and quadruplets 4A→∅ of neighboring particles. When considering classical particles, the corresponding decay of their density in time follows an asymptotic power-law behavior. The associated exponent in one dimension is different from the mean-field prediction whenever diffusive mixing is not too strong and spatial correlations are relevant. This specifically applies to 2A→∅, while the mean-field power-law prediction just acquires a logarithmic correction for 3A→∅ and is exact for 4A→∅. A mean-field approach is also valid, for all the three processes, when the diffusive mixing is strong, i.e., in the so-called reaction-limited regime. Here we show that the picture is different for quantum systems. We consider the quantum reaction-limited regime and we show that for all the three processes power-law behavior beyond mean field is present as a consequence of quantum coherences, which are not related to space dimensionality. The decay in 3A→∅ is further, highly intricate, since the power-law behavior therein only appears within an intermediate time window, while at long times the density decay is not power law. Our results show that emergent critical behavior in quantum dynamics has a markedly different origin, based on quantum coherences, to that applying to classical critical phenomena, which is, instead, solely determined by the relevance of spatial correlations.
Collapse
Affiliation(s)
- Gabriele Perfetto
- Institut für Theoretische Physik, Universität Tübingen, 72076 Tübingen, Germany
| | - Federico Carollo
- Institut für Theoretische Physik, Universität Tübingen, 72076 Tübingen, Germany
| | - Juan P Garrahan
- School of Physics, Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics, Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Igor Lesanovsky
- Institut für Theoretische Physik, Universität Tübingen, 72076 Tübingen, Germany
- School of Physics, Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics, Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| |
Collapse
|
2
|
Shen R, Chen T, Aliyu MM, Qin F, Zhong Y, Loh H, Lee CH. Proposal for Observing Yang-Lee Criticality in Rydberg Atomic Arrays. PHYSICAL REVIEW LETTERS 2023; 131:080403. [PMID: 37683169 DOI: 10.1103/physrevlett.131.080403] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2023] [Revised: 06/27/2023] [Accepted: 07/25/2023] [Indexed: 09/10/2023]
Abstract
Yang-Lee edge singularities (YLES) are the edges of the partition function zeros of an interacting spin model in the space of complex control parameters. They play an important role in understanding non-Hermitian phase transitions in many-body physics, as well as characterizing the corresponding nonunitary criticality. Even though such partition function zeroes have been measured in dynamical experiments where time acts as the imaginary control field, experimentally demonstrating such YLES criticality with a physical imaginary field has remained elusive due to the difficulty of physically realizing non-Hermitian many-body models. We provide a protocol for observing the YLES by detecting kinked dynamical magnetization responses due to broken PT symmetry, thus enabling the physical probing of nonunitary phase transitions in nonequilibrium settings. In particular, scaling analyses based on our nonunitary time evolution circuit with matrix product states accurately recover the exponents uniquely associated with the corresponding nonunitary CFT. We provide an explicit proposal for observing YLES criticality in Floquet quenched Rydberg atomic arrays with laser-induced loss, which paves the way towards a universal platform for simulating non-Hermitian many-body dynamical phenomena.
Collapse
Affiliation(s)
- Ruizhe Shen
- Department of Physics, National University of Singapore, Singapore 117551, Singapore
| | - Tianqi Chen
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 639798, Singapore
| | - Mohammad Mujahid Aliyu
- Centre for Quantum Technologies, National University of Singapore, 117543 Singapore, Singapore
| | - Fang Qin
- Department of Physics, National University of Singapore, Singapore 117551, Singapore
| | - Yin Zhong
- School of Physical Science and Technology and Key Laboratory for Magnetism and Magnetic Materials of the MoE, Lanzhou University, Lanzhou 730000, China
- Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou 730000, China
| | - Huanqian Loh
- Department of Physics, National University of Singapore, Singapore 117551, Singapore
- Centre for Quantum Technologies, National University of Singapore, 117543 Singapore, Singapore
| | - Ching Hua Lee
- Department of Physics, National University of Singapore, Singapore 117551, Singapore
- Joint School of National University of Singapore and Tianjin University, International Campus of Tianjin University, Binhai New City, Fuzhou 350207, China
| |
Collapse
|
3
|
Perfetto G, Carollo F, Garrahan JP, Lesanovsky I. Reaction-Limited Quantum Reaction-Diffusion Dynamics. PHYSICAL REVIEW LETTERS 2023; 130:210402. [PMID: 37295117 DOI: 10.1103/physrevlett.130.210402] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2022] [Revised: 02/03/2023] [Accepted: 04/10/2023] [Indexed: 06/12/2023]
Abstract
We consider the quantum nonequilibrium dynamics of systems where fermionic particles coherently hop on a one-dimensional lattice and are subject to dissipative processes analogous to those of classical reaction-diffusion models. Particles can either annihilate in pairs, A+A→0, or coagulate upon contact, A+A→A, and possibly also branch, A→A+A. In classical settings, the interplay between these processes and particle diffusion leads to critical dynamics as well as to absorbing-state phase transitions. Here, we analyze the impact of coherent hopping and of quantum superposition, focusing on the so-called reaction-limited regime. Here, spatial density fluctuations are quickly smoothed out due to fast hopping, which for classical systems is described by a mean-field approach. By exploiting the time-dependent generalized Gibbs ensemble method, we demonstrate that quantum coherence and destructive interference play a crucial role in these systems and are responsible for the emergence of locally protected dark states and collective behavior beyond mean field. This can manifest both at stationarity and during the relaxation dynamics. Our analytical results highlight fundamental differences between classical nonequilibrium dynamics and their quantum counterpart and show that quantum effects indeed change collective universal behavior.
Collapse
Affiliation(s)
- Gabriele Perfetto
- Institut für Theoretische Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Federico Carollo
- Institut für Theoretische Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Juan P Garrahan
- School of Physics, Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics, Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Igor Lesanovsky
- Institut für Theoretische Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
- School of Physics, Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics, Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| |
Collapse
|
4
|
Gillman E, Carollo F, Lesanovsky I. Using (1+1)D quantum cellular automata for exploring collective effects in large-scale quantum neural networks. Phys Rev E 2023; 107:L022102. [PMID: 36932502 DOI: 10.1103/physreve.107.l022102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2022] [Accepted: 01/13/2023] [Indexed: 06/18/2023]
Abstract
Central to the field of quantum machine learning is the design of quantum perceptrons and neural network architectures. A key question in this regard is the impact of quantum effects on the way such models process information. Here, we establish a connection between (1+1)D quantum cellular automata, which implement a discrete nonequilibrium quantum many-body dynamics through successive applications of local quantum gates, and quantum neural networks (QNNs), which process information by feeding it through perceptrons interconnecting adjacent layers. Exploiting this link, we construct a class of QNNs that are highly structured-aiding both interpretability and helping to avoid trainability issues in machine learning tasks-yet can be connected rigorously to continuous-time Lindblad dynamics. We further analyze the universal properties of an example case, identifying a change of critical behavior when quantum effects are varied, showing their potential impact on the collective dynamical behavior underlying information processing in large-scale QNNs.
Collapse
Affiliation(s)
- Edward Gillman
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Federico Carollo
- Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Igor Lesanovsky
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| |
Collapse
|
5
|
Tang S, Yang C, Li D, Shao X. Implementation of Quantum Algorithms via Fast Three-Rydberg-Atom CCZ Gates. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1371. [PMID: 37420391 DOI: 10.3390/e24101371] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2022] [Revised: 09/20/2022] [Accepted: 09/21/2022] [Indexed: 07/09/2023]
Abstract
Multiqubit CCZ gates form one of the building blocks of quantum algorithms and have been involved in achieving many theoretical and experimental triumphs. Designing a simple and efficient multiqubit gate for quantum algorithms is still by no means trivial as the number of qubits increases. Here, by virtue of the Rydberg blockade effect, we propose a scheme to rapidly implement a three-Rydberg-atom CCZ gate via a single Rydberg pulse, and successfully apply the gate to realize the three-qubit refined Deutsch-Jozsa algorithm and three-qubit Grover search. The logical states of the three-qubit gate are encoded to the same ground states to avoid an adverse effect of the atomic spontaneous emission. Furthermore, there is no requirement for individual addressing of atoms in our protocol.
Collapse
Affiliation(s)
- Shiqing Tang
- College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang 421002, China
| | - Chong Yang
- College of Physics Science and Technology, Shenyang Normal University, Shenyang 110034, China
| | - Dongxiao Li
- College of Physics Science and Technology, Shenyang Normal University, Shenyang 110034, China
| | - Xiaoqiang Shao
- Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China
- Center for Advanced Optoelectronic Functional Materials Research, and Key Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China
| |
Collapse
|
6
|
Carollo F, Lesanovsky I. Nonequilibrium Dark Space Phase Transition. PHYSICAL REVIEW LETTERS 2022; 128:040603. [PMID: 35148125 DOI: 10.1103/physrevlett.128.040603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2021] [Revised: 09/22/2021] [Accepted: 01/06/2022] [Indexed: 06/14/2023]
Abstract
We introduce the concept of dark space phase transition, which may occur in open many-body quantum systems where irreversible decay, interactions, and quantum interference compete. Our study is based on a quantum many-body model that is inspired by classical nonequilibrium processes which feature phase transitions into an absorbing state, such as epidemic spreading. The possibility for different dynamical paths to interfere quantum mechanically results in collective dynamical behavior without classical counterpart. We identify two competing dark states, a trivial one corresponding to a classical absorbing state and an emergent one which is quantum coherent. We establish a nonequilibrium phase transition within this dark space that features a phenomenology which cannot be encountered in classical systems. Such emergent two-dimensional dark space may find technological applications, e.g., for the collective encoding of a quantum information.
Collapse
Affiliation(s)
- Federico Carollo
- Institut für Theoretische Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Igor Lesanovsky
- Institut für Theoretische Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
- School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, The University of Nottingham, Nottingham NG7 2RD, United Kingdom
| |
Collapse
|
7
|
|
8
|
Sampuli EM, Wang Y, Xia Y, Song J. Effects of dissipation induced blockade on the dynamics of two qubits without direct interaction. OPTICS EXPRESS 2021; 29:584-596. [PMID: 33726291 DOI: 10.1364/oe.410208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2020] [Accepted: 12/14/2020] [Indexed: 06/12/2023]
Abstract
We study the effects of dissipation induced blockade on the dynamics of an open quantum system having two qubits in nonequilibrium independent baths. The qubits are driven by a classical field with a temporally modulated detuning. The introduction of blockade induced via two effective baths together with the effect of the driving field enable us to observe maximal entanglement oscillation of about unity that decays with a quasi-steady entanglement state oscillating about the 1/2 limit with adjustable decay rate. When the temperature difference between two baths is not large, maximal entanglement oscillation can still be observed in the model. In addition, the adjustment of the nonequilibrium thermal baths by modulating the dissipation and the application of time-dependent detuning give rise to rich entanglement dynamics. We further demonstrate numerically the practical implementation of the proposed scheme with a universal cavity QED setting.
Collapse
|
9
|
Causer L, Lesanovsky I, Bañuls MC, Garrahan JP. Dynamics and large deviation transitions of the XOR-Fredrickson-Andersen kinetically constrained model. Phys Rev E 2020; 102:052132. [PMID: 33327088 DOI: 10.1103/physreve.102.052132] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2020] [Accepted: 11/09/2020] [Indexed: 11/07/2022]
Abstract
We study a one-dimensional classical stochastic kinetically constrained model (KCM) inspired by Rydberg atoms in their "facilitated" regime, where sites can flip only if a single of their nearest neighbors is excited. We call this model "XOR-FA" to distinguish it from the standard Fredrickson-Andersen (FA) model. We describe the dynamics of the XOR-FA model, including its relation to simple exclusion processes in its domain wall representation. The interesting relaxation dynamics of the XOR-FA is related to the prominence of large dynamical fluctuations that lead to phase transitions between active and inactive dynamical phases as in other KCMs. By means of numerical tensor network methods we study in detail such transitions in the dynamical large deviation regime.
Collapse
Affiliation(s)
- Luke Causer
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom.,Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Igor Lesanovsky
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom.,Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom.,Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Mari Carmen Bañuls
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany.,Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 München, Germany
| | - Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom.,Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| |
Collapse
|
10
|
Gillman E, Carollo F, Lesanovsky I. Nonequilibrium Phase Transitions in (1+1)-Dimensional Quantum Cellular Automata with Controllable Quantum Correlations. PHYSICAL REVIEW LETTERS 2020; 125:100403. [PMID: 32955309 DOI: 10.1103/physrevlett.125.100403] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2020] [Accepted: 08/05/2020] [Indexed: 06/11/2023]
Abstract
Motivated by recent progress in the experimental development of quantum simulators based on Rydberg atoms, we introduce and investigate the dynamics of a class of (1+1)-dimensional quantum cellular automata. These nonequilibrium many-body models, which are quantum generalizations of the Domany-Kinzel cellular automaton, possess two key features: they display stationary behavior and nonequilibrium phase transitions despite being isolated systems. Moreover, they permit the controlled introduction of local quantum correlations, which allows for the impact of quantumness on the dynamics and phase transition to be assessed. We show that projected entangled pair state tensor networks permit a natural and efficient representation of the cellular automaton. Here, the degree of quantumness and complexity of the dynamics is reflected in the difficulty of contracting the tensor network.
Collapse
Affiliation(s)
- Edward Gillman
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
| | - Federico Carollo
- Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Igor Lesanovsky
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
- Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| |
Collapse
|