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Bond LJ, Safavi-Naini A, Minář J. Fast Quantum State Preparation and Bath Dynamics Using Non-Gaussian Variational Ansatz and Quantum Optimal Control. PHYSICAL REVIEW LETTERS 2024; 132:170401. [PMID: 38728702 DOI: 10.1103/physrevlett.132.170401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2023] [Revised: 01/15/2024] [Accepted: 03/25/2024] [Indexed: 05/12/2024]
Abstract
Fast preparation of quantum many-body states is essential for myriad quantum algorithms and metrological applications. Here, we develop a new pathway for fast, nonadiabatic preparation of quantum many-body states that combines quantum optimal control with a variational Ansatz based on non-Gaussian states. We demonstrate our approach on the spin-boson model, a single spin interacting with the bath. We use a multipolaron Ansatz to prepare near-critical ground states. For one mode, we achieve a reduction in infidelity of up to ≈60 (≈10) times compared to linear (optimized local adiabatic) ramps; for many modes, we achieve a reduction in infidelity of up to ≈5 times compared to nonadiabatic linear ramps. Further, we show that the typical control quantity, the leakage from the variational manifold, provides only a loose bound on the state's fidelity. Instead, in analogy to the bond dimension of matrix product states, we suggest a controlled convergence criterion based on the number of polarons. Finally, motivated by the possibility of realizations in trapped ions, we study the dynamics of a system with bath properties going beyond the paradigm of (sub- and/or super-) Ohmic couplings.
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Affiliation(s)
- Liam J Bond
- Institute for Theoretical Physics, Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
- QuSoft, Science Park 123, 1098 XG Amsterdam, The Netherlands
| | - Arghavan Safavi-Naini
- Institute for Theoretical Physics, Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
- QuSoft, Science Park 123, 1098 XG Amsterdam, The Netherlands
| | - Jiří Minář
- Institute for Theoretical Physics, Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
- QuSoft, Science Park 123, 1098 XG Amsterdam, The Netherlands
- CWI, Science Park 904, 1098 XH Amsterdam, The Netherlands
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2
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Frías-Pérez M, Tagliacozzo L, Bañuls MC. Converting Long-Range Entanglement into Mixture: Tensor-Network Approach to Local Equilibration. PHYSICAL REVIEW LETTERS 2024; 132:100402. [PMID: 38518338 DOI: 10.1103/physrevlett.132.100402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Accepted: 01/30/2024] [Indexed: 03/24/2024]
Abstract
In the out-of-equilibrium evolution induced by a quench, fast degrees of freedom generate long-range entanglement that is hard to encode with standard tensor networks. However, local observables only sense such long-range correlations through their contribution to the reduced local state as a mixture. We present a tensor network method that identifies such long-range entanglement and efficiently transforms it into mixture, much easier to represent. In this way, we obtain an effective description of the time-evolved state as a density matrix that captures the long-time behavior of local operators with finite computational resources.
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Affiliation(s)
- Miguel Frías-Pérez
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Luca Tagliacozzo
- Institute of Fundamental Physics IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain
| | - Mari Carmen Bañuls
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
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Hallam A, Desaules JY, Papić Z. Embedding Semiclassical Periodic Orbits into Chaotic Many-Body Hamiltonians. PHYSICAL REVIEW LETTERS 2023; 131:110401. [PMID: 37774274 DOI: 10.1103/physrevlett.131.110401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2023] [Accepted: 08/21/2023] [Indexed: 10/01/2023]
Abstract
Protecting coherent quantum dynamics from chaotic environment is key to realizations of fragile many-body phenomena and their applications in quantum technology. We present a general construction that embeds a desired periodic orbit into a family of nonintegrable many-body Hamiltonians, whose dynamics is otherwise chaotic. Our construction is based on time-dependent variational principle that projects quantum dynamics onto a manifold of low-entangled states, and it complements earlier approaches for embedding nonthermal eigenstates, known as quantum many-body scars, into thermalizing spectra. By designing terms that suppress "leakage" of the dynamics outside the variational manifold, we engineer families of Floquet models that host exact scarred dynamics, as we illustrate using a driven Affleck-Kennedy-Lieb-Tasaki model and a recent experimental realization of scars in a dimerized superconducting qubit chain.
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Affiliation(s)
- Andrew Hallam
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Jean-Yves Desaules
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Zlatko Papić
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
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Azad F, Hallam A, Morley J, Green AG. Phase transitions in the classical simulability of open quantum systems. Sci Rep 2023; 13:8866. [PMID: 37258551 DOI: 10.1038/s41598-023-35336-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2023] [Accepted: 05/16/2023] [Indexed: 06/02/2023] Open
Abstract
We introduce a Langevin unravelling of the density matrix evolution of an open quantum system over matrix product states, which we term the time-dependent variational principle-Langevin equation. This allows the study of entanglement dynamics as a function of both temperature and coupling to the environment. As the strength of coupling to and temperature of the environment is increased, we find a transition where the entanglement of the individual trajectories saturates, permitting a classical simulation of the system for all times. This is the Hamiltonian open system counterpart of the saturation in entanglement found in random circuits with projective or weak measurements. If a system is open, there is a limit to the advantage in simulating its behaviour on a quantum computer, even when that evolution harbours important quantum effects. Moreover, if a quantum simulator is in this phase, it cannot simulate with quantum advantage.
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Affiliation(s)
- F Azad
- London Centre for Nanotechnology, University College London, Gordon St., London, WC1H 0AH, UK
| | - A Hallam
- School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, UK
| | - J Morley
- London Centre for Nanotechnology, University College London, Gordon St., London, WC1H 0AH, UK
| | - A G Green
- London Centre for Nanotechnology, University College London, Gordon St., London, WC1H 0AH, UK.
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Dborin J, Wimalaweera V, Barratt F, Ostby E, O'Brien TE, Green AG. Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer. Nat Commun 2022; 13:5977. [PMID: 36216839 PMCID: PMC9550817 DOI: 10.1038/s41467-022-33737-4] [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: 05/18/2022] [Accepted: 09/30/2022] [Indexed: 11/15/2022] Open
Abstract
The phenomena of quantum criticality underlie many novel collective phenomena found in condensed matter systems. They present a challenge for classical and quantum simulation, in part because of diverging correlation lengths and consequently strong finite-size effects. Tensor network techniques that work directly in the thermodynamic limit can negotiate some of these difficulties. Here, we optimise a translationally invariant, sequential quantum circuit on a superconducting quantum device to simulate the groundstate of the quantum Ising model through its quantum critical point. We further demonstrate how the dynamical quantum critical point found in quenches of this model across its quantum critical point can be simulated. Our approach avoids finite-size scaling effects by using sequential quantum circuits inspired by infinite matrix product states. We provide efficient circuits and a variety of error mitigation strategies to implement, optimise and time-evolve these states. Strongly correlated condensed matter systems are among those for which quantum simulation should be able to give an advantage. Here, the authors use a translationally invariant tensor network technique to simulate a quantum critical system on a superconducting quantum processor.
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Affiliation(s)
- James Dborin
- London Centre for Nanotechnology, University College London, Gordon St., London, WC1H 0AH, UK
| | - Vinul Wimalaweera
- London Centre for Nanotechnology, University College London, Gordon St., London, WC1H 0AH, UK
| | - F Barratt
- Department of Physics, University of Massachusetts, Amherst, MA, 01003, USA
| | - Eric Ostby
- Google Quantum AI, 80636, Munich, Germany
| | | | - A G Green
- London Centre for Nanotechnology, University College London, Gordon St., London, WC1H 0AH, UK.
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Asadpour V, Fazel-Rezai R, Vatankhah M, Akbarzadeh-Totonchi MR. Pain Identification in Electroencephalography Signal Using Fuzzy Inference System. ARTIF INTELL 2022. [DOI: 10.5772/intechopen.103753] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Diagnosing pain mechanisms is one of main approaches to improve clinical treatments. Especially, detection of existence and/or level of pain could be vital when oral information is not present for instant for neonates, disabled persons, anesthetized patients and animals. Various researches have been performed to originate and classify the pain; however, consistent results are surprising. The aim of this study is to show a strict relation between electroencephalography (EEG) features and perceptual pain levels and to clarify the relation of classified signal to pain origin. Cortical regions on scalp are assigned based on an evolutional method for optimized alignment of electrodes that improve the clinical monitoring results. The EEG signals are recorded during relax condition and variety of pain conditions. Evolutionary optimization method is used to reduce the features space dimension and computational costs. A hybrid adaptive network fuzzy inference system (ANFIS) and support vector machine (SVM) scheme is used for classification of pain levels. ANFIS optimizer is used to fine tune the non-linear alignment of kernels of SVM. The results show that pain levels could be differentiated with high accuracy and robustness even for few recording electrodes. The proposed classification method provides up to 95% accuracy.
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Liao Y, Vikram A, Galitski V. Many-Body Level Statistics of Single-Particle Quantum Chaos. PHYSICAL REVIEW LETTERS 2020; 125:250601. [PMID: 33416379 DOI: 10.1103/physrevlett.125.250601] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2020] [Accepted: 10/26/2020] [Indexed: 06/12/2023]
Abstract
We consider a noninteracting many-fermion system populating levels of a unitary random matrix ensemble (equivalent to the q=2 complex Sachdev-Ye-Kitaev model)-a generic model of single-particle quantum chaos. We study the corresponding many-particle level statistics by calculating the spectral form factor analytically using algebraic methods of random matrix theory, and match it with an exact numerical simulation. Despite the integrability of the theory, the many-body spectral rigidity is found to have a surprisingly rich landscape. In particular, we find a residual repulsion of distant many-body levels stemming from single-particle chaos, together with islands of level attraction. These results are encoded in an exponential ramp in the spectral form factor, which we show to be a universal feature of nonergodic many-fermion systems embedded in a chaotic medium.
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Affiliation(s)
- Yunxiang Liao
- Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Amit Vikram
- Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Victor Galitski
- Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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Wouters M. Quantum trajectories for the variational description of closed systems: A case study with Gaussian states. Phys Rev E 2020; 102:043314. [PMID: 33212612 DOI: 10.1103/physreve.102.043314] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2020] [Accepted: 09/15/2020] [Indexed: 11/07/2022]
Abstract
In this paper, it is proposed to improve the quality of a variational description of a closed quantum system by adding fictitious dissipation that reduces the entanglement. The proposal is implemented for a small Bose-Hubbard chain in the mean field regime, which shows chaotic behavior and associated fast growth of quantum fluctuations. For appropriately chosen dissipation, good agreement with the truncated Wigner approximation is found. This shows that, when chaos leads to the breakdown of a variational method, adding fictitious dissipation can be a cure.
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Affiliation(s)
- Michiel Wouters
- TQC, Universiteit Antwerpen, Universiteitsplein 1, B-2610 Antwerpen, Belgium
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Berera A, Clark D. Information production in homogeneous isotropic turbulence. Phys Rev E 2019; 100:041101. [PMID: 31771016 DOI: 10.1103/physreve.100.041101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2019] [Indexed: 11/07/2022]
Abstract
We study the Reynolds number scaling of the Kolmogorov-Sinai entropy and attractor dimension for three-dimensional homogeneous isotropic turbulence through the use of direct numerical simulation. To do so, we obtain Lyapunov spectra for a range of different Reynolds numbers by following the divergence of a large number of orthogonal fluid trajectories. We find that the attractor dimension grows with the Reynolds number as Re^{2.35} with this exponent being larger than predicted by either dimensional arguments or intermittency models. The distribution of Lyapunov exponents is found to be finite around λ≈0 contrary to a possible divergence suggested by Ruelle. The relevance of the Kolmogorov-Sinai entropy and Lyapunov spectra in comparing complex physical systems is discussed.
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Affiliation(s)
- Arjun Berera
- School of Physics and Astronomy, University of Edinburgh, JCMB, King's Buildings, Peter Guthrie Tait Road EH9 3FD, Edinburgh, United Kingdom
| | - Daniel Clark
- School of Physics and Astronomy, University of Edinburgh, JCMB, King's Buildings, Peter Guthrie Tait Road EH9 3FD, Edinburgh, United Kingdom
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