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Many-body localization enables iterative quantum optimization. Nat Commun 2022; 13:5503. [PMID: 36127344 PMCID: PMC9489738 DOI: 10.1038/s41467-022-33179-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2021] [Accepted: 09/07/2022] [Indexed: 11/08/2022] Open
Abstract
Many discrete optimization problems are exponentially hard due to the underlying glassy landscape. This means that the optimization cost exhibits multiple local minima separated by an extensive number of switched discrete variables. Quantum computation was coined to overcome this predicament, but so far had only a limited progress. Here we suggest a quantum approximate optimization algorithm which is based on a repetitive cycling around the tricritical point of the many-body localization (MBL) transition. Each cycle includes quantum melting of the glassy state through a first order transition with a subsequent reentrance through the second order MBL transition. Keeping the reentrance path sufficiently close to the tricritical point separating the first and second order transitions, allows one to systematically improve optimization outcomes. The running time of this algorithm scales algebraically with the system size and the required precision. The corresponding exponents are related to critical indexes of the continuous MBL transition. There are several proposals for quantum algorithms solving optimisation problems, but so far none of them has provided a clear speedup. Here, the authors propose an iterative protocol featuring periodic cycling around the tricritical point of a many-body localization transition.
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Leschke H, Manai C, Ruder R, Warzel S. Existence of Replica-Symmetry Breaking in Quantum Glasses. PHYSICAL REVIEW LETTERS 2021; 127:207204. [PMID: 34860058 DOI: 10.1103/physrevlett.127.207204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2021] [Revised: 08/29/2021] [Accepted: 10/11/2021] [Indexed: 06/13/2023]
Abstract
By controlling quantum fluctuations via the Falk-Bruch inequality we give the first rigorous argument for the existence of a spin-glass phase in the quantum Sherrington-Kirkpatrick model with a "transverse" magnetic field if the temperature and the field are sufficiently low. The argument also applies to the generalization of the model with multispin interactions, sometimes dubbed as the transverse p-spin model.
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Affiliation(s)
- Hajo Leschke
- Institut für Theoretische Physik, Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - Chokri Manai
- Department of Mathematics and Munich Center for Quantum Science and Technology, TU München, 85747 Garching, Germany
| | - Rainer Ruder
- Institut für Theoretische Physik, Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - Simone Warzel
- Departments of Mathematics and Physics, Munich Center for Quantum Science and Technology, TU München, 85747 Garching, Germany
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Martínez-Peña R, Giorgi GL, Nokkala J, Soriano MC, Zambrini R. Dynamical Phase Transitions in Quantum Reservoir Computing. PHYSICAL REVIEW LETTERS 2021; 127:100502. [PMID: 34533342 DOI: 10.1103/physrevlett.127.100502] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2021] [Revised: 06/11/2021] [Accepted: 07/19/2021] [Indexed: 05/26/2023]
Abstract
Closed quantum systems exhibit different dynamical regimes, like many-body localization or thermalization, which determine the mechanisms of spread and processing of information. Here we address the impact of these dynamical phases in quantum reservoir computing, an unconventional computing paradigm recently extended into the quantum regime that exploits dynamical systems to solve nonlinear and temporal tasks. We establish that the thermal phase is naturally adapted to the requirements of quantum reservoir computing and report an increased performance at the thermalization transition for the studied tasks. Uncovering the underlying physical mechanisms behind optimal information processing capabilities of spin networks is essential for future experimental implementations and provides a new perspective on dynamical phases.
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Affiliation(s)
- Rodrigo Martínez-Peña
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Gian Luca Giorgi
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Johannes Nokkala
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Miguel C Soriano
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Roberta Zambrini
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
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Rademaker L, Abanin DA. Slow Nonthermalizing Dynamics in a Quantum Spin Glass. PHYSICAL REVIEW LETTERS 2020; 125:260405. [PMID: 33449733 DOI: 10.1103/physrevlett.125.260405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2019] [Accepted: 12/04/2020] [Indexed: 06/12/2023]
Abstract
Spin glasses and many-body localization (MBL) are prime examples of ergodicity breaking, yet their physical origin is quite different: the former phase arises due to rugged classical energy landscape, while the latter is a quantum-interference effect. Here, we study quantum dynamics of an isolated 1D spin glass under application of a transverse field. At high energy densities, the system is ergodic, relaxing via a resonance avalanche mechanism, that is also responsible for the destruction of MBL in nonglassy systems with power-law interactions. At low energy densities, the interaction-induced fields obtain a power-law soft gap, making the resonance avalanche mechanism inefficient. This leads to the persistence of the spin-glass order, as demonstrated by resonance analysis and by numerical studies. A small fraction of resonant spins forms a thermalizing system with long-range entanglement, making this regime distinct from the conventional MBL. The model considered can be realized in systems of trapped ions, opening the door to investigating slow quantum dynamics induced by glassiness.
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Affiliation(s)
- Louk Rademaker
- Department of Theoretical Physics, University of Geneva, 1211 Geneva, Switzerland
| | - Dmitry A Abanin
- Department of Theoretical Physics, University of Geneva, 1211 Geneva, Switzerland
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Thomson SJ, Urbani P, Schiró M. Quantum Quenches in Isolated Quantum Glasses out of Equilibrium. PHYSICAL REVIEW LETTERS 2020; 125:120602. [PMID: 33016769 DOI: 10.1103/physrevlett.125.120602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2019] [Revised: 07/23/2020] [Accepted: 08/19/2020] [Indexed: 06/11/2023]
Abstract
In this work, we address the question of how a closed quantum system thermalizes in the presence of a random external potential. By investigating the quench dynamics of the isolated quantum spherical p-spin model, a paradigmatic model of a mean-field glass, we aim to shed new light on this complex problem. Employing a closed-time Schwinger-Keldysh path integral formalism, we first initialize the system in a random, infinite-temperature configuration and allow it to equilibrate in contact with a thermal bath before switching off the bath and performing a quench. We find evidence that increasing the strength of either the interactions or the quantum fluctuations can act to lower the effective temperature of the isolated system and stabilize glassy behavior.
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Affiliation(s)
- S J Thomson
- Centre de Physique Théorique, CNRS, Institut Polytechnique de Paris, Route de Saclay, F-91128 Palaiseau, France
- Université Paris-Saclay, CNRS, CEA, Institut de physique théorique, 91191, Gif-sur-Yvette, France
| | - P Urbani
- Université Paris-Saclay, CNRS, CEA, Institut de physique théorique, 91191, Gif-sur-Yvette, France
| | - M Schiró
- JEIP, USR 3573 CNRS, Collège de France, PSL University, 11, place Marcelin Berthelot, 75231 Paris Cedex 05, France
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Mossi G, Scardicchio A. Ergodic and localized regions in quantum spin glasses on the Bethe lattice. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:20160424. [PMID: 29084889 PMCID: PMC5665780 DOI: 10.1098/rsta.2016.0424] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 06/19/2017] [Indexed: 06/07/2023]
Abstract
By considering the quantum dynamics of a transverse-field Ising spin glass on the Bethe lattice, we find the existence of a many-body localized (MBL) region at small transverse field and low temperature. The region is located within the thermodynamic spin glass phase. Accordingly, we conjecture that quantum dynamics inside the glassy region is split into a small MBL region and a large delocalized (but not necessarily ergodic) region. This has implications for the analysis of the performance of quantum adiabatic algorithms.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.
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Affiliation(s)
- G Mossi
- SISSA, Via Bonomea 265, 34136 Trieste, Italy
- INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy
| | - A Scardicchio
- INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy
- Abdus Salam ICTP Trieste, Strada Costiera 11, 34151 Trieste, Italy
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Ponte P, Laumann CR, Huse DA, Chandran A. Thermal inclusions: how one spin can destroy a many-body localized phase. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:20160428. [PMID: 29084891 PMCID: PMC5665782 DOI: 10.1098/rsta.2016.0428] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 09/11/2017] [Indexed: 06/07/2023]
Abstract
Many-body localized (MBL) systems lie outside the framework of statistical mechanics, as they fail to equilibrate under their own quantum dynamics. Even basic features of MBL systems, such as their stability to thermal inclusions and the nature of the dynamical transition to thermalizing behaviour, remain poorly understood. We study a simple central spin model to address these questions: a two-level system interacting with strength J with N≫1 localized bits subject to random fields. On increasing J, the system transitions from an MBL to a delocalized phase on the vanishing scale Jc(N)∼1/N, up to logarithmic corrections. In the transition region, the single-site eigenstate entanglement entropies exhibit bimodal distributions, so that localized bits are either 'on' (strongly entangled) or 'off' (weakly entangled) in eigenstates. The clusters of 'on' bits vary significantly between eigenstates of the same sample, which provides evidence for a heterogeneous discontinuous transition out of the localized phase in single-site observables. We obtain these results by perturbative mapping to bond percolation on the hypercube at small J and by numerical exact diagonalization of the full many-body system. Our results support the arguments that the MBL phase is unstable in systems with short-range interactions and quenched randomness in dimensions d that are high but finite.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.
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Affiliation(s)
- Pedro Ponte
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5
- Department of Physics and Astronomy, University of Waterloo, Ontario, Canada N2L 3G1
| | - C R Laumann
- Department of Physics, Boston University, Boston, MA 02215, USA
| | - David A Huse
- Department of Physics, Princeton University, Princeton, NJ 08544, USA
| | - A Chandran
- Department of Physics, Boston University, Boston, MA 02215, USA
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