1
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Rasola M, Möttönen M. Autonomous quantum heat engine based on non-Markovian dynamics of an optomechanical Hamiltonian. Sci Rep 2024; 14:9448. [PMID: 38658607 PMCID: PMC11043434 DOI: 10.1038/s41598-024-59881-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2024] [Accepted: 04/16/2024] [Indexed: 04/26/2024] Open
Abstract
We propose a recipe for demonstrating an autonomous quantum heat engine where the working fluid consists of a harmonic oscillator, the frequency of which is tuned by a driving mode. The working fluid is coupled two heat reservoirs each exhibiting a peaked power spectrum, a hot reservoir peaked at a higher frequency than the cold reservoir. Provided that the driving mode is initialized in a coherent state with a high enough amplitude and the parameters of the utilized optomechanical Hamiltonian and the reservoirs are appropriate, the driving mode induces an approximate Otto cycle for the working fluid and consequently its oscillation amplitude begins to increase in time. We build both an analytical and a non-Markovian quasiclassical model for this quantum heat engine and show that reasonably powerful coherent fields can be generated as the output of the quantum heat engine. This general theoretical proposal heralds the in-depth studies of quantum heat engines in the non-Markovian regime. Further, it paves the way for specific physical realizations, such as those in optomechanical systems, and for the subsequent experimental realization of an autonomous quantum heat engine.
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Affiliation(s)
- Miika Rasola
- QCD Labs, QTF Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 13500, 00076, Aalto, Finland.
| | - Mikko Möttönen
- QCD Labs, QTF Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 13500, 00076, Aalto, Finland
- QTF Centre of Excellence, VTT Technical Research Centre of Finland Ltd., P.O. Box 1000, 02044 VTT, Espoo, Finland
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2
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Del Rio L, Renner R. Publisher Correction: Reply to: Quantum mechanical rules for observed observers and the consistency of quantum theory. Nat Commun 2024; 15:3388. [PMID: 38649686 PMCID: PMC11035585 DOI: 10.1038/s41467-024-47826-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2024] Open
Affiliation(s)
- Lídia Del Rio
- Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland.
| | - Renato Renner
- Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland.
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3
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Del Rio L, Renner R. Reply to: Quantum mechanical rules for observed observers and the consistency of quantum theory. Nat Commun 2024; 15:3024. [PMID: 38594243 PMCID: PMC11004133 DOI: 10.1038/s41467-024-47172-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2022] [Accepted: 03/22/2024] [Indexed: 04/11/2024] Open
Affiliation(s)
- Lídia Del Rio
- Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland.
| | - Renato Renner
- Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland.
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4
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Yordanov V. Derivation of Dirac equation from the stochastic optimal control principles of quantum mechanics. Sci Rep 2024; 14:6507. [PMID: 38499582 PMCID: PMC10948848 DOI: 10.1038/s41598-024-56582-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2023] [Accepted: 03/08/2024] [Indexed: 03/20/2024] Open
Abstract
In this paper, we present a stochastic approach to relativistic quantum mechanics. We formulate the three fundamental principles of this theory and derive the Dirac equations based on them. This approach enables us to bring more insight into the nature of Dirac's spinors. Furthermore, we provide a physical interpretation of the stochastic optimal control theory of quantum mechanics.
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Affiliation(s)
- Vasil Yordanov
- Faculty of Physics, Sofia University, 5 James Bourchier Blvd., 1164, Sofia, Bulgaria.
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5
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Bravyi S, Cross AW, Gambetta JM, Maslov D, Rall P, Yoder TJ. High-threshold and low-overhead fault-tolerant quantum memory. Nature 2024; 627:778-782. [PMID: 38538939 PMCID: PMC10972743 DOI: 10.1038/s41586-024-07107-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2023] [Accepted: 01/23/2024] [Indexed: 04/01/2024]
Abstract
The accumulation of physical errors1-3 prevents the execution of large-scale algorithms in current quantum computers. Quantum error correction4 promises a solution by encoding k logical qubits onto a larger number n of physical qubits, such that the physical errors are suppressed enough to allow running a desired computation with tolerable fidelity. Quantum error correction becomes practically realizable once the physical error rate is below a threshold value that depends on the choice of quantum code, syndrome measurement circuit and decoding algorithm5. We present an end-to-end quantum error correction protocol that implements fault-tolerant memory on the basis of a family of low-density parity-check codes6. Our approach achieves an error threshold of 0.7% for the standard circuit-based noise model, on par with the surface code7-10 that for 20 years was the leading code in terms of error threshold. The syndrome measurement cycle for a length-n code in our family requires n ancillary qubits and a depth-8 circuit with CNOT gates, qubit initializations and measurements. The required qubit connectivity is a degree-6 graph composed of two edge-disjoint planar subgraphs. In particular, we show that 12 logical qubits can be preserved for nearly 1 million syndrome cycles using 288 physical qubits in total, assuming the physical error rate of 0.1%, whereas the surface code would require nearly 3,000 physical qubits to achieve said performance. Our findings bring demonstrations of a low-overhead fault-tolerant quantum memory within the reach of near-term quantum processors.
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Affiliation(s)
- Sergey Bravyi
- IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY, USA
| | - Andrew W Cross
- IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY, USA
| | - Jay M Gambetta
- IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY, USA
| | - Dmitri Maslov
- IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY, USA.
| | - Patrick Rall
- IBM Quantum, MIT-IBM Watson AI Laboratory, Cambridge, MA, USA
| | - Theodore J Yoder
- IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY, USA
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6
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Goldstein S, Tumulka R, Zanghì N. On the spin dependence of detection times and the nonmeasurability of arrival times. Sci Rep 2024; 14:3775. [PMID: 38355849 PMCID: PMC10866986 DOI: 10.1038/s41598-024-53777-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2023] [Accepted: 02/05/2024] [Indexed: 02/16/2024] Open
Abstract
According to a well-known principle of quantum physics, the statistics of the outcomes of any quantum experiment are governed by a Positive-Operator-Valued Measure (POVM). In particular, for experiments designed to measure a specific physical quantity, like the time of a particle's first arrival at a surface, this principle establishes that if the probability distribution of that quantity does not arise from a POVM, no such experiment exists. Such is the case with the arrival time distributions proposed by Das and Dürr, due to the nature of their spin dependence.
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Affiliation(s)
- Sheldon Goldstein
- Departments of Mathematics and Physics, Rutgers University, Hill Center, 110 Frelinghuysen Road, Piscataway, NJ, 08854-8019, USA
| | - Roderich Tumulka
- Fachbereich Mathematik, Eberhard-Karls-Universität Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany.
| | - Nino Zanghì
- Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146, Genoa, Italy
- Istituto Nazionale di Fisica Nucleare (Sezione di Genova), Genoa, Italy
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7
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Slager RJ, Bouhon A, Ünal FN. Non-Abelian Floquet braiding and anomalous Dirac string phase in periodically driven systems. Nat Commun 2024; 15:1144. [PMID: 38326295 PMCID: PMC10850167 DOI: 10.1038/s41467-024-45302-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2022] [Accepted: 01/18/2024] [Indexed: 02/09/2024] Open
Abstract
While a significant fraction of topological materials has been characterized using symmetry requirements1-4, the past two years have witnessed the rise of novel multi-gap dependent topological states5-9, the properties of which go beyond these approaches and are yet to be fully explored. Although already of active interest at equilibrium10-15, we show that the combination of out-of-equilibrium processes and multi-gap topological insights galvanize a new direction within topological phases of matter. We show that periodic driving can induce anomalous multi-gap topological properties that have no static counterpart. In particular, we identify Floquet-induced non-Abelian braiding, which in turn leads to a phase characterized by an anomalous Euler class, being the prime example of a multi-gap topological invariant. Most strikingly, we also retrieve the first example of an 'anomalous Dirac string phase'. This gapped out-of-equilibrium phase features an unconventional Dirac string configuration that physically manifests itself via anomalous edge states on the boundary. Our results not only provide a stepping stone for the exploration of intrinsically dynamical and experimentally viable multi-gap topological phases, but also demonstrate periodic driving as a powerful way to observe these non-Abelian braiding processes notably in quantum simulators.
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Affiliation(s)
- Robert-Jan Slager
- TCM Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE, United Kingdom.
| | - Adrien Bouhon
- TCM Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE, United Kingdom
| | - F Nur Ünal
- TCM Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE, United Kingdom.
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8
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Sen I. Physical interpretation of non-normalizable harmonic oscillator states and relaxation to pilot-wave equilibrium. Sci Rep 2024; 14:669. [PMID: 38218953 PMCID: PMC10787783 DOI: 10.1038/s41598-023-50814-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2023] [Accepted: 12/26/2023] [Indexed: 01/15/2024] Open
Abstract
Non-normalizable states are difficult to interpret in the orthodox quantum formalism but often occur as solutions to physical constraints in quantum gravity. We argue that pilot-wave theory gives a straightforward physical interpretation of non-normalizable quantum states, as the theory requires only a normalized density of configurations to generate statistical predictions. In order to better understand such states, we conduct the first study of non-normalizable solutions of the harmonic oscillator from a pilot-wave perspective. We show that, contrary to intuitions from orthodox quantum mechanics, the non-normalizable eigenstates and their superpositions are bound states in the sense that the velocity field [Formula: see text] at large [Formula: see text]. We argue that defining a physically meaningful equilibrium density for such states requires a new notion of equilibrium, named pilot-wave equilibrium, which is a generalisation of the notion of quantum equilibrium. We define a new H-function [Formula: see text], and prove that a density in pilot-wave equilibrium minimises [Formula: see text], is equivariant, and remains in equilibrium with time. We prove an H-theorem for the coarse-grained [Formula: see text], under assumptions similar to those for relaxation to quantum equilibrium. We give an explanation of the emergence of quantization in pilot-wave theory in terms of instability of non-normalizable states due to perturbations and environmental interactions. Lastly, we discuss applications in quantum field theory and quantum gravity, and implications for pilot-wave theory and quantum foundations in general.
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Affiliation(s)
- Indrajit Sen
- Institute for Quantum Studies, Chapman University, One University Drive, Orange, CA, 92866, USA.
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9
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Dabelow L, Reimann P. Stalled response near thermal equilibrium in periodically driven systems. Nat Commun 2024; 15:294. [PMID: 38177163 PMCID: PMC10766978 DOI: 10.1038/s41467-023-44487-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2023] [Accepted: 12/14/2023] [Indexed: 01/06/2024] Open
Abstract
The question of how systems respond to perturbations is ubiquitous in physics. Predicting this response for large classes of systems becomes particularly challenging if many degrees of freedom are involved and linear response theory cannot be applied. Here, we consider isolated many-body quantum systems which either start out far from equilibrium and then thermalize, or find themselves near thermal equilibrium from the outset. We show that time-periodic perturbations of moderate strength, in the sense that they do not heat up the system too quickly, give rise to the following phenomenon of stalled response: While the driving usually causes quite considerable reactions as long as the unperturbed system is far from equilibrium, the driving effects are strongly suppressed when the unperturbed system approaches thermal equilibrium. Likewise, for systems prepared near thermal equilibrium, the response to the driving is barely noticeable right from the beginning. Numerical results are complemented by a quantitatively accurate analytical description and by simple qualitative arguments.
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Affiliation(s)
- Lennart Dabelow
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama, 351-0198, Japan
- School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, UK
| | - Peter Reimann
- Faculty of Physics, Bielefeld University, 33615, Bielefeld, Germany.
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10
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Oppenheim J, Sparaciari C, Šoda B, Weller-Davies Z. Gravitationally induced decoherence vs space-time diffusion: testing the quantum nature of gravity. Nat Commun 2023; 14:7910. [PMID: 38049417 PMCID: PMC10696068 DOI: 10.1038/s41467-023-43348-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2023] [Accepted: 11/08/2023] [Indexed: 12/06/2023] Open
Abstract
We consider two interacting systems when one is treated classically while the other system remains quantum. Consistent dynamics of this coupling has been shown to exist, and explored in the context of treating space-time classically. Here, we prove that any such hybrid dynamics necessarily results in decoherence of the quantum system, and a breakdown in predictability in the classical phase space. We further prove that a trade-off between the rate of this decoherence and the degree of diffusion induced in the classical system is a general feature of all classical quantum dynamics; long coherence times require strong diffusion in phase-space relative to the strength of the coupling. Applying the trade-off relation to gravity, we find a relationship between the strength of gravitationally-induced decoherence versus diffusion of the metric and its conjugate momenta. This provides an experimental signature of theories in which gravity is fundamentally classical. Bounds on decoherence rates arising from current interferometry experiments, combined with precision measurements of mass, place significant restrictions on theories where Einstein's classical theory of gravity interacts with quantum matter. We find that part of the parameter space of such theories are already squeezed out, and provide figures of merit which can be used in future mass measurements and interference experiments.
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Affiliation(s)
- Jonathan Oppenheim
- Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, UK.
| | - Carlo Sparaciari
- Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, UK
| | - Barbara Šoda
- Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, UK
- Department of Physics, University of Waterloo, Waterloo, ON, Canada
- Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada
| | - Zachary Weller-Davies
- Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, UK
- Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada
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11
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Ye J, Huang Y, Liu K. U-net based vortex detection in Bose-Einstein condensates with automatic correction for manually mislabeled data. Sci Rep 2023; 13:21278. [PMID: 38042934 PMCID: PMC10693587 DOI: 10.1038/s41598-023-48719-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Accepted: 11/29/2023] [Indexed: 12/04/2023] Open
Abstract
Quantum vortices in Bose-Einstein condensates (BECs) are essential phenomena in condensed matter physics, and precisely locating their positions, especially the vortex core, is a precondition for studying their properties. With the rise of machine learning, there is a possibility to expedite the localization process and provide accurate predictions. However, traditional machine learning requires particular considerable amount of manual data annotation, leading to uncontrollable accuracy. In this paper, we utilize the U-Net method to detect vortex positions accurately at the pixel level and propose an Automatic Correction Labeling (ACL) approach to optimize the acquisition of data sets for vortex localization in BECs. This approach addresses inaccuracies in the labeled vortex positions and improves the accuracy of vortex localization, especially the vortex core positions, while enhancing the tolerance for human mislabeling. The main process involves Rough Labeling [Formula: see text] Machine Learning [Formula: see text] Probability Region Search [Formula: see text] Data Relabeling [Formula: see text] Machine Learning again. The objective of ACL is to secure more accurate labeled data for model retraining. Through vortex localization experiments conducted in a two-dimensional Bose-Einstein condensate, our results establish the following: 1. Even under conditions of biased and missing manual annotations, U-Net can still accurately locate vortex positions; 2. Vortices exhibit certain regularities, and training U-Net with a small number of samples yields excellent predictive consequences; 3. The machine learning vortex locator based on the ACL method effectively corrects errors in manually annotated data, significantly improving the model's performance metrics, thus enhancing the precision and metrics of vortex localization. This substantial advancement in the application of machine learning in vortex localization provides an effective way for vortex dynamics localization. Furthermore, this method of obtaining more accurate positions of approximate human labels through machine learning offers new insights for machine learning in other types of image recognition problems.
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Affiliation(s)
- Jing Ye
- Jiaxing Nanhu University, 572 Yuexiu South Road, Jiaxing, 314001, China
| | - Yue Huang
- Jiaxing Nanhu University, 572 Yuexiu South Road, Jiaxing, 314001, China
| | - Keyan Liu
- Jiaxing Nanhu University, 572 Yuexiu South Road, Jiaxing, 314001, China.
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12
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Abstract
Confinement of topological excitations into particle-like states - typically associated with theories of elementary particles - are known to occur in condensed matter systems, arising as domain-wall confinement in quantum spin chains. However, investigation of confinement in the condensed matter setting has rarely ventured beyond lattice spin systems. Here we analyze the confinement of sine-Gordon solitons into mesonic bound states in a perturbed quantum sine-Gordon model. The latter describes the scaling limit of a one-dimensional, quantum electronic circuit (QEC) array, constructed using experimentally-demonstrated QEC elements. The scaling limit is reached faster for the QEC array compared to spin chains, allowing investigation of the strong-coupling regime of this model. We compute the string tension of confinement of sine-Gordon solitons and the changes in the low-lying energy spectrum. These results, obtained using the density matrix renormalization group method, could be verified in a quench experiment using state-of-the-art QEC technologies.
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Affiliation(s)
- Ananda Roy
- Department of Physics and Astronomy, Rutgers University, Piscataway, NJ, 08854-8019, USA.
| | - Sergei L Lukyanov
- Department of Physics and Astronomy, Rutgers University, Piscataway, NJ, 08854-8019, USA.
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13
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Steinberg M, Feld S, Jahn A. Holographic codes from hyperinvariant tensor networks. Nat Commun 2023; 14:7314. [PMID: 37951990 PMCID: PMC10640591 DOI: 10.1038/s41467-023-42743-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2023] [Accepted: 10/20/2023] [Indexed: 11/14/2023] Open
Abstract
Holographic quantum-error correcting codes are models of bulk/boundary dualities such as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, where a higher-dimensional bulk geometry is associated with the code's logical degrees of freedom. Previous discrete holographic codes based on tensor networks have reproduced the general code properties expected from continuum AdS/CFT, such as complementary recovery. However, the boundary states of such tensor networks typically do not exhibit the expected correlation functions of CFT boundary states. In this work, we show that a new class of exact holographic codes, extending the previously proposed hyperinvariant tensor networks into quantum codes, produce the correct boundary correlation functions. This approach yields a dictionary between logical states in the bulk and the critical renormalization group flow of boundary states. Furthermore, these codes exhibit a state-dependent breakdown of complementary recovery as expected from AdS/CFT under small quantum gravity corrections.
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Affiliation(s)
- Matthew Steinberg
- QuTech, Delft University of Technology, 2628, CJ, Delft, The Netherlands
- Quantum and Computer Engineering Department, Delft University of Technology, 2628, CD, Delft, The Netherlands
| | - Sebastian Feld
- QuTech, Delft University of Technology, 2628, CJ, Delft, The Netherlands
- Quantum and Computer Engineering Department, Delft University of Technology, 2628, CD, Delft, The Netherlands
| | - Alexander Jahn
- Department of Physics, Freie Universität Berlin, 14195, Berlin, Germany.
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, 91125, USA.
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14
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Shor O, Benninger F, Khrennikov A. Quantization of events in the event-universe and the emergence of quantum mechanics. Sci Rep 2023; 13:17865. [PMID: 37857671 PMCID: PMC10587342 DOI: 10.1038/s41598-023-44550-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2023] [Accepted: 10/10/2023] [Indexed: 10/21/2023] Open
Abstract
Quantum mechanics (QM) is derived based on a universe composed solely of events, for example, outcomes of observables. Such an event universe is represented by a dendrogram (a finite tree) and in the limit of infinitely many events by the p-adic tree. The trees are endowed with an ultrametric expressing hierarchical relationships between events. All events are coupled through the tree structure. Such a holistic picture of event-processes was formalized within the Dendrographic Hologram Theory (DHT). The present paper is devoted to the emergence of QM from DHT. We used the generalization of the QM-emergence scheme developed by Smolin. Following this scheme, we did not quantize events but rather the differences between them and through analytic derivation arrived at Bohmian mechanics. We remark that, although Bohmian mechanics is not the main stream approach to quantum physics, it describes adequately all quantum experiments. Previously, we were able to embed the basic elements of general relativity (GR) into DHT, and now after Smolin-like quantization of DHT, we can take a step toward quantization of GR. Finally, we remark that DHT is nonlocal in the treelike geometry, but this nonlocality refers to relational nonlocality in the space of events and not Einstein's spatial nonlocality. By shifting from spatial nonlocality to relational we make Bohmian mechanics less exotic.
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Affiliation(s)
- Oded Shor
- Felsenstein Medical Research Centre, Petach Tikva, Israel
- Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel
| | - Felix Benninger
- Felsenstein Medical Research Centre, Petach Tikva, Israel
- Department of Neurology, Rabin Medical Centre, Petach Tikva, Israel
- Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel
| | - Andrei Khrennikov
- Department of Mathematics, Faculty of Technology, Linnaeus University, Vaxjö, Sweden.
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15
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Brown AR, Freedman MH, Lin HW, Susskind L. Universality in long-distance geometry and quantum complexity. Nature 2023; 622:58-62. [PMID: 37794268 PMCID: PMC10550822 DOI: 10.1038/s41586-023-06460-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Accepted: 07/20/2023] [Indexed: 10/06/2023]
Abstract
In physics, two systems that radically differ at short scales can exhibit strikingly similar macroscopic behaviour: they are part of the same long-distance universality class1. Here we apply this viewpoint to geometry and initiate a program of classifying homogeneous metrics on group manifolds2 by their long-distance properties. We show that many metrics on low-dimensional Lie groups have markedly different short-distance properties but nearly identical distance functions at long distances, and provide evidence that this phenomenon is even more robust in high dimensions. An application of these ideas of particular interest to physics and computer science is complexity geometry3-7-the study of quantum computational complexity using Riemannian geometry. We argue for the existence of a large universality class of definitions of quantum complexity, each linearly related to the other, a much finer-grained equivalence than typically considered. We conjecture that a new effective metric emerges at larger complexities that describes a broad class of complexity geometries, insensitive to various choices of microscopic penalty factors. We discuss the implications for recent conjectures in quantum gravity.
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Affiliation(s)
- Adam R Brown
- Google DeepMind, Mountain View, CA, USA.
- Department of Physics, Stanford University, Stanford, CA, USA.
| | - Michael H Freedman
- Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA, USA
| | - Henry W Lin
- Google DeepMind, Mountain View, CA, USA
- Department of Physics, Stanford University, Stanford, CA, USA
- Department of Physics, Princeton University, Princeton, NJ, USA
| | - Leonard Susskind
- Google DeepMind, Mountain View, CA, USA
- Department of Physics, Stanford University, Stanford, CA, USA
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16
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Kalka M, Spisak BJ, Woźniak D, Wołoszyn M, Kołaczek D. Dynamical entropic measure of nonclassicality of phase-dependent family of Schrödinger cat states. Sci Rep 2023; 13:16266. [PMID: 37758979 PMCID: PMC10533523 DOI: 10.1038/s41598-023-43421-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2023] [Accepted: 09/23/2023] [Indexed: 09/29/2023] Open
Abstract
The phase-space approach based on the Wigner distribution function is used to study the quantum dynamics of the three families of the Schrödinger cat states identified as the even, odd, and Yurke-Stoler states. The considered states are formed by the superposition of two Gaussian wave packets localized on opposite sides of a smooth barrier in a dispersive medium and moving towards each other. The process generated by this dynamics is analyzed regarding the influence of the barrier parameters on the nonclassical properties of these states in the phase space below and above the barrier regime. The performed analysis employs entropic measure resulting from the Wigner-Rényi entropy for the fixed Rényi index. The universal relation of this entropy for the Rényi index equal one half with the nonclassicality parameter understood as a measure of the negative part of the Wigner distribution function is proved. This relation is confirmed in the series of numerical simulations for the considered states. Furthermore, the obtained results allowed the determination of the lower bound of the Wigner-Rényi entropy for the Rényi index greater than or equal to one half.
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Affiliation(s)
- M Kalka
- Faculty of Physics and Applied Computer Science, AGH University of Krakow, al. Mickiewicza 30, 30-059, Krakow, Poland
| | - B J Spisak
- Faculty of Physics and Applied Computer Science, AGH University of Krakow, al. Mickiewicza 30, 30-059, Krakow, Poland.
| | - D Woźniak
- Faculty of Physics and Applied Computer Science, AGH University of Krakow, al. Mickiewicza 30, 30-059, Krakow, Poland
| | - M Wołoszyn
- Faculty of Physics and Applied Computer Science, AGH University of Krakow, al. Mickiewicza 30, 30-059, Krakow, Poland
| | - D Kołaczek
- Department of Applied Mathematics, University of Agriculture in Kraków, ul. Balicka 253c, 30-198, Kraków, Poland
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17
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van der Lugt T, Barrett J, Chiribella G. Device-independent certification of indefinite causal order in the quantum switch. Nat Commun 2023; 14:5811. [PMID: 37726274 PMCID: PMC10509257 DOI: 10.1038/s41467-023-40162-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2022] [Accepted: 07/14/2023] [Indexed: 09/21/2023] Open
Abstract
Quantum theory is compatible with scenarios in which the order of operations is indefinite. Experimental investigations of such scenarios, all of which have been based on a process known as the quantum switch, have provided demonstrations of indefinite causal order conditioned on assumptions on the devices used in the laboratory. But is a device-independent certification possible, similar to the certification of Bell nonlocality through the violation of Bell inequalities? Previous results have shown that the answer is negative if the switch is considered in isolation. Here, however, we present an inequality that can be used to device-independently certify indefinite causal order in the quantum switch in the presence of an additional spacelike-separated observer under an assumption asserting the impossibility of superluminal and retrocausal influences.
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Affiliation(s)
- Tein van der Lugt
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, United Kingdom.
| | - Jonathan Barrett
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, United Kingdom
- Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada
| | - Giulio Chiribella
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, United Kingdom.
- Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada.
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong, Hong Kong.
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18
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Zahia AA, Abd-Rabbou MY, Megahed AM, Obada ASF. Bidirectional field-steering and atomic steering induced by a magnon mode in a qubit-photon system. Sci Rep 2023; 13:14943. [PMID: 37696940 PMCID: PMC10495356 DOI: 10.1038/s41598-023-41907-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Accepted: 09/01/2023] [Indexed: 09/13/2023] Open
Abstract
This paper investigates the cavity-magnon steering and qubit-qubit steering of a hybrid quantum system consisting of a single-mode magnon, a two-qubit state, and a single-mode cavity field in the presence of their damping rates. The temporal wave vector of the system is obtained for the initial maximally entangled two-qubit state and initial vacuum state of the magnon and cavity modes. Additionally, the mathematical inequalities for obtaining the cavity-magnon steering and qubit-qubit steering are introduced. The findings reveal that steering between the magnon and cavity is asymmetric, while steering between the two qubits is symmetric in our system. Increasing the atom-field coupling improves steering from magnon to field, while reducing steering between the two qubits. Moreover, increasing magnon-field coupling enhances and elevates the lower bounds of qubit-qubit steering. Further, adding the damping rates causes deterioration of the cavity-magnon steering and qubit-qubit steering. However, the steering persistence is slightly greater when damping originates from the cavity field rather than the magnon modes based on the coupling parameters.
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Affiliation(s)
- Ahmed A Zahia
- Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
| | - M Y Abd-Rabbou
- Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo, 11884, Egypt.
| | - Ahmed M Megahed
- Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
| | - A-S F Obada
- Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo, 11884, Egypt
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19
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Das S, Caruso F. A hybrid-qudit representation of digital RGB images. Sci Rep 2023; 13:13671. [PMID: 37608205 PMCID: PMC10444894 DOI: 10.1038/s41598-023-39906-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2023] [Accepted: 08/01/2023] [Indexed: 08/24/2023] Open
Abstract
Quantum image processing is an emerging topic in the field of quantum information and technology. In this paper, we propose a new quantum image representation of RGB images with deterministic image retrieval, which is an improvement over all the similar existing representations in terms of using minimum resource. We use two entangled quantum registers constituting of total 7 qutrits to encode the color channels and their intensities. Additionally, we generalize the existing encoding methods by using both qubits and qutrits to encode the pixel positions of a rectangular image. This hybrid-qudit approach aligns well with the current progress of NISQ devices in incorporating higher dimensional quantum systems than qubits. We then describe the image encoding method using higher-order qubit-qutrit gates, and demonstrate the decomposition of these gates in terms of simpler elementary gates. We use the Google Cirq's quantum simulator to verify the image preparation in both the ideal noise-free scenario and in presence of realistic noise modelling. We show that the complexity of the image encoding process is linear in the number of pixels. Lastly, we discuss the image compression and some basic RGB image processing protocols using our representation.
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Affiliation(s)
- Sreetama Das
- Department of Physics and Astronomy, University of Florence, Via Sansone 1, Sesto Fiorentino, 50019, Italy.
- European Laboratory for Non-Linear Spectroscopy (LENS), University of Florence, Via Nello Carrara 1, Sesto Fiorentino, 50019, Italy.
| | - Filippo Caruso
- Department of Physics and Astronomy, University of Florence, Via Sansone 1, Sesto Fiorentino, 50019, Italy
- European Laboratory for Non-Linear Spectroscopy (LENS), University of Florence, Via Nello Carrara 1, Sesto Fiorentino, 50019, Italy
- QSTAR and CNR-INO, Largo Enrico Fermi 2, 50125, Firenze, Italy
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20
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Helsen J, Ioannou M, Kitzinger J, Onorati E, Werner AH, Eisert J, Roth I. Shadow estimation of gate-set properties from random sequences. Nat Commun 2023; 14:5039. [PMID: 37598209 PMCID: PMC10439944 DOI: 10.1038/s41467-023-39382-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2022] [Accepted: 06/12/2023] [Indexed: 08/21/2023] Open
Abstract
With quantum computing devices increasing in scale and complexity, there is a growing need for tools that obtain precise diagnostic information about quantum operations. However, current quantum devices are only capable of short unstructured gate sequences followed by native measurements. We accept this limitation and turn it into a new paradigm for characterizing quantum gate-sets. A single experiment-random sequence estimation-solves a wealth of estimation problems, with all complexity moved to classical post-processing. We derive robust channel variants of shadow estimation with close-to-optimal performance guarantees and use these as a primitive for partial, compressive and full process tomography as well as the learning of Pauli noise. We discuss applications to the quantum gate engineering cycle, and propose novel methods for the optimization of quantum gates and diagnosing cross-talk.
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Affiliation(s)
- J Helsen
- QuSoft, Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands.
- Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands.
| | - M Ioannou
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195, Berlin, Germany
| | - J Kitzinger
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195, Berlin, Germany
- Humboldt-Universität zu Berlin, Institut für Physik, 12489, Berlin, Germany
| | - E Onorati
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195, Berlin, Germany
- Department of Computer Science, University College London, London, UK
- Fakultät für Mathematik, Technische Universität München, München, Germany
| | - A H Werner
- Department of Mathematical Sciences, University of Copenhagen, 2100, København, Denmark
- NBIA, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100, København, Denmark
| | - J Eisert
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195, Berlin, Germany.
- Helmholtz-Zentrum Berlin für Materialien und Energie, 14109, Berlin, Germany.
- Fraunhofer Heinrich Hertz Institute, 10587, Berlin, Germany.
| | - I Roth
- Quantum Research Center, Technology Innovation Institute (TII), Abu Dhabi, UAE.
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21
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Sobral JA, Obernauer S, Turkel S, Pasupathy AN, Scheurer MS. Machine learning the microscopic form of nematic order in twisted double-bilayer graphene. Nat Commun 2023; 14:5012. [PMID: 37591848 PMCID: PMC10435506 DOI: 10.1038/s41467-023-40684-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Accepted: 08/01/2023] [Indexed: 08/19/2023] Open
Abstract
Modern scanning probe techniques, such as scanning tunneling microscopy, provide access to a large amount of data encoding the underlying physics of quantum matter. In this work, we show how convolutional neural networks can be used to learn effective theoretical models from scanning tunneling microscopy data on correlated moiré superlattices. Moiré systems are particularly well suited for this task as their increased lattice constant provides access to intra-unit-cell physics, while their tunability allows for the collection of high-dimensional data sets from a single sample. Using electronic nematic order in twisted double-bilayer graphene as an example, we show that incorporating correlations between the local density of states at different energies allows convolutional neural networks not only to learn the microscopic nematic order parameter, but also to distinguish it from heterostrain. These results demonstrate that neural networks are a powerful method for investigating the microscopic details of correlated phenomena in moiré systems and beyond.
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Affiliation(s)
- João Augusto Sobral
- Institute for Theoretical Physics III, University of Stuttgart, 70550, Stuttgart, Germany.
- Institute for Theoretical Physics, University of Innsbruck, A-6020, Innsbruck, Austria.
| | - Stefan Obernauer
- Institute for Theoretical Physics, University of Innsbruck, A-6020, Innsbruck, Austria
| | - Simon Turkel
- Department of Physics, Columbia University, 10027, New York, NY, USA
| | - Abhay N Pasupathy
- Department of Physics, Columbia University, 10027, New York, NY, USA
- Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, 11973, Upton, NY, USA
| | - Mathias S Scheurer
- Institute for Theoretical Physics III, University of Stuttgart, 70550, Stuttgart, Germany
- Institute for Theoretical Physics, University of Innsbruck, A-6020, Innsbruck, Austria
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22
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Akram J, Zheng C. Theoretical investigation of dynamics and concurrence of entangled [Formula: see text] and anti-[Formula: see text] symmetric polarized photons. Sci Rep 2023; 13:8542. [PMID: 37236997 PMCID: PMC10220064 DOI: 10.1038/s41598-023-34516-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Accepted: 05/03/2023] [Indexed: 05/28/2023] Open
Abstract
Non-Hermitian systems with parity-time [Formula: see text] symmetry and anti-parity-time [Formula: see text] symmetry have exceptional points (EPs) resulting from eigenvector co-coalescence with exceptional properties. In the quantum and classical domains, higher-order EPs for [Formula: see text] symmetry and [Formula: see text]-symmetry systems have been proposed and realized. Both two-qubits [Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text] symmetric systems have seen an increase in recent years, especially in the dynamics of quantum entanglement. However, to our knowledge, neither theoretical nor experimental investigations have been conducted for the dynamics of two-qubits entanglement in the [Formula: see text]-[Formula: see text] symmetric system. We investigate the [Formula: see text]-[Formula: see text] dynamics for the first time. Moreover, we examine the impact of different initial Bell-state conditions on entanglement dynamics in [Formula: see text]-[Formula: see text], [Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text] symmetric systems. Additionally, we conduct a comparative study of entanglement dynamics in the [Formula: see text]-[Formula: see text] symmetrical system, [Formula: see text]-[Formula: see text] symmetrical system, and [Formula: see text]-[Formula: see text] symmetrical systems in order to learn more about non-Hermitian quantum systems and their environments. Entangled qubits evolve in a [Formula: see text]-[Formula: see text] symmetric unbroken regime, the entanglement oscillates with two different oscillation frequencies, and the entanglement is well preserved for a long period of time for the case when non-Hermitian parts of both qubits are taken quite away from the exceptional points.
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Affiliation(s)
- Javed Akram
- eleQtron GmbH, Martinshardt 19, 57074 Siegen, Germany
- Department of Physics, COMSATS University Islamabad, Islamabad, 45550 Pakistan
| | - Chao Zheng
- Department of Physics, College of Science, North China University of Technology, Beijing, 100144 China
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23
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Gao HY, Wei LF. A microwave scattering spectral method to detect the nanomechanical vibrations embedded in a superconducting qubit. Sci Rep 2023; 13:4340. [PMID: 36928211 DOI: 10.1038/s41598-023-30914-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2022] [Accepted: 03/03/2023] [Indexed: 03/18/2023] Open
Abstract
Nanomechanical resonators (NMRs), as the quantum mechanical sensing probers, have played the important roles for various high-precision quantum measurements. Differing from the previous emission spectral probes (i.e., the NMR modified the atomic emission), in this paper we propose an alternative approach, i.e., by probing the scattering spectra of the quantum mechanical prober coupled to the driving microwaves, to characterize the physical features of the NMR embedded in a rf-SQUID based superconducting qubit. It is shown that, from the observed specifical frequency points in the spectra, i.e., either the dips or the peaks, the vibrational features (i.e., they are classical vibration or quantum mechanical one) and the physical parameters (typically such as the vibrational frequency and displacements) of the NMR can be determined effectively. The proposal is feasible with the current technique and should be useful to design the desired NMRs for various quantum metrological applications.
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24
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Wechs J, Branciard C, Oreshkov O. Existence of processes violating causal inequalities on time-delocalised subsystems. Nat Commun 2023; 14:1471. [PMID: 36928637 PMCID: PMC10020554 DOI: 10.1038/s41467-023-36893-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2022] [Accepted: 02/22/2023] [Indexed: 03/18/2023] Open
Abstract
It has been shown that it is theoretically possible for there to exist quantum and classical processes in which the operations performed by separate parties do not occur in a well-defined causal order. A central question is whether and how such processes can be realised in practice. In order to provide a rigorous framework for the notion that certain such processes have a realisation in standard quantum theory, the concept of time-delocalised quantum subsystem has been introduced. In this paper, we show that realisations on time-delocalised subsystems exist for all unitary extensions of tripartite processes. This class contains processes that violate causal inequalities, i.e., that can generate correlations that witness the incompatibility with definite causal order in a device-independent manner, and whose realisability has been a central open problem. We consider a known example of such a tripartite classical process that has a unitary extension, and study its realisation on time-delocalised subsystems. We then discuss this finding with regard to the assumptions that underlie causal inequalities, and argue that they are indeed a meaningful concept to show the absence of a definite causal order between the variables of interest.
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Affiliation(s)
- Julian Wechs
- QuIC, Ecole Polytechnique de Bruxelles, C.P. 165, Université Libre de Bruxelles, 1050, Brussels, Belgium. .,Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France.
| | - Cyril Branciard
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France.
| | - Ognyan Oreshkov
- QuIC, Ecole Polytechnique de Bruxelles, C.P. 165, Université Libre de Bruxelles, 1050, Brussels, Belgium.
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25
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Nikitchuk BY, Anikin EV, Maslova NS, Gippius NA. The symmetry in the model of two coupled Kerr oscillators leads to simultaneous multi-photon transitions. Sci Rep 2023; 13:2997. [PMID: 36810462 DOI: 10.1038/s41598-023-30197-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2022] [Accepted: 02/17/2023] [Indexed: 02/23/2023] Open
Abstract
We consider the model of two coupled oscillators with Kerr nonlinearities in the rotating-wave approximation. We demonstrate that for a certain set of parameters of the model, the multi-photon transitions occur between many pairs of the oscillator states simultaneously. Also, the position of the multi-photon resonances does not depend on the coupling strength between two oscillators. We prove rigorously that this is a consequence of a certain symmetry of the perturbation theory series for the model. In addition, we analyse the model in the quasi-classical limit by considering the dynamics of the pseudo-angular momentum. We identify the multi-photon transitions with the tunnelling transitions between the degenerate classical trajectories on the Bloch sphere.
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26
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Vesperini A, Bel-Hadj-Aissa G, Franzosi R. Entanglement and quantum correlation measures for quantum multipartite mixed states. Sci Rep 2023; 13:2852. [PMID: 36806198 PMCID: PMC9938213 DOI: 10.1038/s41598-023-29438-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2022] [Accepted: 02/03/2023] [Indexed: 02/19/2023] Open
Abstract
Entanglement, and quantum correlation, are precious resources for quantum technologies implementation based on quantum information science, such as quantum communication, quantum computing, and quantum interferometry. Nevertheless, to our best knowledge, a directly or numerically computable measure for the entanglement of multipartite mixed states is still lacking. In this work, (i) we derive a measure of the degree of quantum correlation for mixed multipartite states. The latter possesses a closed-form expression valid in the general case unlike, to our best knowledge, all other known measures of quantum correlation. (ii) We further propose an entanglement measure, derived from this quantum correlation measure using a novel regularization procedure for the density matrix. Therefore, a comparison of the proposed measures, of quantum correlation and entanglement, allows one to distinguish between quantum correlation detached from entanglement and the one induced by entanglement and, hence, to identify separable but non-classical states. We have tested our quantum correlation and entanglement measures, on states well-known in literature: a general Bell diagonal state and the Werner states, which are easily tractable with our regularization procedure, and we have verified the accordance between our measures and the expected results for these states. Finally, we validate the two measures in two cases of multipartite states. The first is a generalization to three qubits of the Werner state, the second is a one-parameter three qubits mixed state interpolating between a bi-separable state and a genuine multipartite state, passing through a fully separable state.
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Affiliation(s)
- Arthur Vesperini
- grid.9024.f0000 0004 1757 4641DSFTA, University of Siena, Via Roma 56, Siena, 53100 Italy ,grid.470215.5INFN Sezione di Perugia, Perugia, 06123 Italy ,grid.425378.f0000 0001 2097 1574QSTAR & CNR - Istituto Nazionale di Ottica, Largo Enrico Fermi 2, Firenze, 50125 Italy
| | - Ghofrane Bel-Hadj-Aissa
- grid.9024.f0000 0004 1757 4641DSFTA, University of Siena, Via Roma 56, Siena, 53100 Italy ,grid.470215.5INFN Sezione di Perugia, Perugia, 06123 Italy ,grid.425378.f0000 0001 2097 1574QSTAR & CNR - Istituto Nazionale di Ottica, Largo Enrico Fermi 2, Firenze, 50125 Italy
| | - Roberto Franzosi
- DSFTA, University of Siena, Via Roma 56, Siena, 53100, Italy. .,INFN Sezione di Perugia, Perugia, 06123, Italy. .,QSTAR & CNR - Istituto Nazionale di Ottica, Largo Enrico Fermi 2, Firenze, 50125, Italy.
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27
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Suzuki Y, Watabe S, Kawabata S, Masuda S. Measurement-based preparation of stable coherent states of a Kerr parametric oscillator. Sci Rep 2023; 13:1606. [PMID: 36709379 PMCID: PMC9884232 DOI: 10.1038/s41598-023-28682-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2022] [Accepted: 01/23/2023] [Indexed: 01/30/2023] Open
Abstract
Kerr parametric oscillators (KPOs) have attracted increasing attention in terms of their application to quantum information processing and quantum simulations. The state preparation and measurement of KPOs are typical requirements when used as qubits. The methods previously proposed for state preparations of KPOs utilize modulation of external fields such as a pump and drive fields. We study the stochastic state preparation of stable coherent states of a KPO with homodyne detection, which does not require modulation of external fields, and thus can reduce experimental efforts and exclude unwanted effects of possible imperfection in control of external fields. We quantitatively show that the detection data, if averaged over an optimal averaging time to decrease the effect of measurement noise, has a strong correlation with the state of the KPO, and therefore can be used to estimate the state (stochastic state preparation). We examine the success probability of the state estimation taking into account the measurement noise and bit flips. Moreover, the proper range of the averaging time to realize a high success probability is obtained by developing a binomial-coherent-state model, which describes the stochastic dynamics of the KPO under homodyne detection.
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Affiliation(s)
- Yuta Suzuki
- grid.143643.70000 0001 0660 6861Department of Physics, Faculty of Science Division I, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601 Japan ,grid.208504.b0000 0001 2230 7538Research Center for Emerging Computing Technologies (RCECT), National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1, Umezono, Tsukuba, Ibaraki 305-8568 Japan
| | - Shohei Watabe
- grid.143643.70000 0001 0660 6861Department of Physics, Faculty of Science Division I, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601 Japan ,grid.419152.a0000 0001 0166 4675Department of Computer Science and Engineering, College of Engineering, Shibaura Institute of Technology, 3-7-5 Toyosu, Koto-ku, Tokyo 135-8548 Japan
| | - Shiro Kawabata
- grid.208504.b0000 0001 2230 7538Research Center for Emerging Computing Technologies (RCECT), National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1, Umezono, Tsukuba, Ibaraki 305-8568 Japan ,grid.208504.b0000 0001 2230 7538NEC-AIST Quantum Technology Cooperative Research Laboratory, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568 Japan
| | - Shumpei Masuda
- grid.208504.b0000 0001 2230 7538Research Center for Emerging Computing Technologies (RCECT), National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1, Umezono, Tsukuba, Ibaraki 305-8568 Japan ,grid.208504.b0000 0001 2230 7538NEC-AIST Quantum Technology Cooperative Research Laboratory, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568 Japan
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28
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Abaach S, Mzaouali Z, El Baz M. Long distance entanglement and high-dimensional quantum teleportation in the Fermi-Hubbard model. Sci Rep 2023; 13:964. [PMID: 36653438 DOI: 10.1038/s41598-023-28180-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2022] [Accepted: 01/13/2023] [Indexed: 01/19/2023] Open
Abstract
The long distance entanglement in finite size open Fermi-Hubbard chains, together with the end-to-end quantum teleportation are investigated. We show the peculiarity of the ground state of the Fermi-Hubbard model to support maximum long distance entanglement, which allows it to operate as a quantum resource for high fidelity long distance quantum teleportation. We determine the physical properties and conditions for creating scalable long distance entanglement and analyze its stability under the effect of the Coulomb interaction and the hopping amplitude. Furthermore, we show that the choice of the measurement basis in the protocol can drastically affect the fidelity of quantum teleportation and we argue that perfect information transfer can be attained by choosing an adequate basis reflecting the salient properties of the quantum channel, i.e. Hubbard projective measurements.
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29
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Deng X, Stadler KM, Haule K, Lee SB, Weichselbaum A, von Delft J, Kotliar G. Author Correction: Reply to: Extracting Kondo temperature of strongly-correlated systems from the inverse local magnetic susceptibility. Nat Commun 2023; 14:206. [PMID: 36639391 DOI: 10.1038/s41467-023-35946-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
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30
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Abstract
One of the most important properties of classical neural networks is how surprisingly trainable they are, though their training algorithms typically rely on optimizing complicated, nonconvex loss functions. Previous results have shown that unlike the case in classical neural networks, variational quantum models are often not trainable. The most studied phenomenon is the onset of barren plateaus in the training landscape of these quantum models, typically when the models are very deep. This focus on barren plateaus has made the phenomenon almost synonymous with the trainability of quantum models. Here, we show that barren plateaus are only a part of the story. We prove that a wide class of variational quantum models-which are shallow, and exhibit no barren plateaus-have only a superpolynomially small fraction of local minima within any constant energy from the global minimum, rendering these models untrainable if no good initial guess of the optimal parameters is known. We also study the trainability of variational quantum algorithms from a statistical query framework, and show that noisy optimization of a wide variety of quantum models is impossible with a sub-exponential number of queries. Finally, we numerically confirm our results on a variety of problem instances. Though we exclude a wide variety of quantum algorithms here, we give reason for optimism for certain classes of variational algorithms and discuss potential ways forward in showing the practical utility of such algorithms.
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Affiliation(s)
- Eric R. Anschuetz
- grid.116068.80000 0001 2341 2786MIT Center for Theoretical Physics, 77 Massachusetts Avenue, Cambridge, MA 02139 USA
| | - Bobak T. Kiani
- grid.116068.80000 0001 2341 2786MIT Department of Electrical Engineering and Computer Science, 77 Massachusetts Avenue, Cambridge, MA 02139 USA
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31
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Watson JD, Onorati E, Cubitt TS. Uncomputably complex renormalisation group flows. Nat Commun 2022; 13:7618. [PMID: 36494351 PMCID: PMC9734166 DOI: 10.1038/s41467-022-35179-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2021] [Accepted: 11/22/2022] [Indexed: 12/13/2022] Open
Abstract
Renormalisation group methods are among the most important techniques for analysing the physics of many-body systems: by iterating a renormalisation group map, which coarse-grains the description of a system and generates a flow in the parameter space, physical properties of interest can be extracted. However, recent work has shown that important physical features, such as the spectral gap and phase diagram, may be impossible to determine, even in principle. Following these insights, we construct a rigorous renormalisation group map for the original undecidable many-body system that appeared in the literature, which reveals a renormalisation group flow so complex that it cannot be predicted. We prove that each step of this map is computable, and that it converges to the correct fixed points, yet the resulting flow is uncomputable. This extreme form of unpredictability for renormalisation group flows had not been shown before and goes beyond the chaotic behaviour seen previously.
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Affiliation(s)
- James D. Watson
- grid.83440.3b0000000121901201Department of Computer Science, University College London, London, UK
| | - Emilio Onorati
- grid.83440.3b0000000121901201Department of Computer Science, University College London, London, UK
| | - Toby S. Cubitt
- grid.83440.3b0000000121901201Department of Computer Science, University College London, London, UK
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32
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Chan A, Shivam S, Huse DA, De Luca A. Many-body quantum chaos and space-time translational invariance. Nat Commun 2022; 13:7484. [PMID: 36470877 PMCID: PMC9722696 DOI: 10.1038/s41467-022-34318-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2021] [Accepted: 10/18/2022] [Indexed: 12/12/2022] Open
Abstract
We study the consequences of having translational invariance in space and time in many-body quantum chaotic systems. We consider ensembles of random quantum circuits as minimal models of translational invariant many-body quantum chaotic systems. We evaluate the spectral form factor as a sum over many-body Feynman diagrams in the limit of large local Hilbert space dimension q. At sufficiently large t, diagrams corresponding to rigid translations dominate, reproducing the random matrix theory (RMT) behaviour. At finite t, we show that translational invariance introduces additional mechanisms via two novel Feynman diagrams which delay the emergence of RMT. Our analytics suggests the existence of exact scaling forms which describe the approach to RMT behavior in the scaling limit where both t and L are large while the ratio between L and LTh(t), the many-body Thouless length, is fixed. We numerically demonstrate, with simulations of two distinct circuit models, that the resulting scaling functions are universal in the scaling limit.
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Affiliation(s)
- Amos Chan
- grid.16750.350000 0001 2097 5006Princeton Center for Theoretical Science, Princeton University, Princeton, NJ 08544 USA ,Physics Department, Lancaster University, Lancaster, LA1 4YW USA
| | - Saumya Shivam
- grid.16750.350000 0001 2097 5006Department of Physics, Princeton University, Princeton, NJ 08544 USA
| | - David A. Huse
- grid.16750.350000 0001 2097 5006Department of Physics, Princeton University, Princeton, NJ 08544 USA
| | - Andrea De Luca
- grid.507676.5Laboratoire de Physique Théorique et Modélisation, CY Cergy Paris Université, CNRS, F-95302 Cergy-Pontoise, France
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33
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Tindall J, Searle A, Alhajri A, Jaksch D. Quantum physics in connected worlds. Nat Commun 2022; 13:7445. [PMID: 36460651 PMCID: PMC9718787 DOI: 10.1038/s41467-022-35090-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2022] [Accepted: 11/17/2022] [Indexed: 12/03/2022] Open
Abstract
Theoretical research into many-body quantum systems has mostly focused on regular structures which have a small, simple unit cell and where a vanishingly small fraction of the pairs of the constituents directly interact. Motivated by advances in control over the pairwise interactions in many-body simulators, we determine the fate of spin systems on more general, arbitrary graphs. Placing the minimum possible constraints on the underlying graph, we prove how, with certainty in the thermodynamic limit, such systems behave like a single collective spin. We thus understand the emergence of complex many-body physics as dependent on 'exceptional', geometrically constrained structures such as the low-dimensional, regular ones found in nature. Within the space of dense graphs we identify hitherto unknown exceptions via their inhomogeneity and observe how complexity is heralded in these systems by entanglement and highly non-uniform correlation functions. Our work paves the way for the discovery and exploitation of a whole class of geometries which can host uniquely complex phases of matter.
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Affiliation(s)
- Joseph Tindall
- grid.430264.70000 0004 4648 6763Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, NY 10010 USA ,grid.4991.50000 0004 1936 8948Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU UK
| | - Amy Searle
- grid.4991.50000 0004 1936 8948Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU UK
| | - Abdulla Alhajri
- grid.4991.50000 0004 1936 8948Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU UK ,grid.510500.10000 0004 8306 7226Technology Innovation Institute, Masdar City, 9639 Abu Dhabi United Arab Emirates
| | - Dieter Jaksch
- grid.4991.50000 0004 1936 8948Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU UK ,grid.9026.d0000 0001 2287 2617The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany ,grid.9026.d0000 0001 2287 2617Institut für Laserphysik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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34
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Nandy DK, Sowiński T. Sudden quench of harmonically trapped mass-imbalanced fermions. Sci Rep 2022; 12:19710. [PMID: 36385321 DOI: 10.1038/s41598-022-24228-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2022] [Accepted: 11/11/2022] [Indexed: 11/17/2022] Open
Abstract
Dynamical properties of two-component mass-imbalanced few-fermion systems confined in a one-dimensional harmonic trap following a sudden quench of interactions are studied. It is assumed that initially the system is prepared in the non-interacting ground state and then, after a sudden quench of interactions, the unitary evolution is governed by interacting many-body Hamiltonian. By careful analysis of the evolution of the Loschmidt echo, density distributions of the components, and entanglement entropy between them, the role of mass imbalance and particle number imbalance on the system's evolution stability are investigated. All the quantities studied manifest a dramatic dependence on the number of heavy and lighter fermions in each component at a given quench strength. The results may have implications for upcoming experiments on fermionic mixtures with a well-defined and small number of particles.
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Alba-Arroyo JE, Caballero-Benitez SF, Jáuregui R. Weber number and the outcome of binary collisions between quantum droplets. Sci Rep 2022; 12:18467. [PMID: 36323755 DOI: 10.1038/s41598-022-22904-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2022] [Accepted: 10/20/2022] [Indexed: 11/25/2022] Open
Abstract
A theoretical analysis of binary collisions of quantum droplets under feasible experimental conditions is reported. Droplets formed from degenerate dilute Bose gases made up from binary mixtures of ultracold atoms are considered. Reliable expressions for the surface tension of the droplets are introduced based on a study of low energy excitations of their ground state within the random phase approximation. Their relevance is evaluated considering an estimation of the expected excitation energy having in mind the Thouless variational theorem. The surface tension expressions allow calculating the Weber number of the droplets involved in the collisions. Several regimes on the outcomes of the binary frontal collisions that range from the coalescence of the quantum droplets to their disintegration into smaller droplets are identified. Atoms losses of the droplets derived from self-evaporation and three-body scattering are quantified for both homo- and hetero-nuclear mixtures. Their control is mandatory for the observation of some interesting effects arising from droplets collisions.
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36
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Donvil B, Muratore-Ginanneschi P. Quantum trajectory framework for general time-local master equations. Nat Commun 2022; 13:4140. [PMID: 35842427 PMCID: PMC9288492 DOI: 10.1038/s41467-022-31533-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2021] [Accepted: 06/10/2022] [Indexed: 11/09/2022] Open
Abstract
Master equations are one of the main avenues to study open quantum systems. When the master equation is of the Lindblad-Gorini-Kossakowski-Sudarshan form, its solution can be "unraveled in quantum trajectories" i.e., represented as an average over the realizations of a Markov process in the Hilbert space of the system. Quantum trajectories of this type are both an element of quantum measurement theory as well as a numerical tool for systems in large Hilbert spaces. We prove that general time-local and trace-preserving master equations also admit an unraveling in terms of a Markov process in the Hilbert space of the system. The crucial ingredient is to weigh averages by a probability pseudo-measure which we call the "influence martingale". The influence martingale satisfies a 1d stochastic differential equation enslaved to the ones governing the quantum trajectories. We thus extend the existing theory without increasing the computational complexity.
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Affiliation(s)
- Brecht Donvil
- University of Helsinki, Department of Mathematics and Statistics, P.O. Box 68, FIN-00014, Helsinki, Finland.
- Institute for Complex Quantum Systems and IQST, Ulm University, Albert-Einstein-Allee 11, D-89069, Ulm, Germany.
| | - Paolo Muratore-Ginanneschi
- University of Helsinki, Department of Mathematics and Statistics, P.O. Box 68, FIN-00014, Helsinki, Finland.
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37
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Rodríguez I, Valladares RM, Valladares A, Hinojosa-Romero D, Valladares AA. Ab initio studies of magnetism and topology in solid Pd-rich [Formula: see text]-PdSi alloys. Sci Rep 2022; 12:4624. [PMID: 35302061 PMCID: PMC8931064 DOI: 10.1038/s41598-022-08656-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2021] [Accepted: 02/28/2022] [Indexed: 11/09/2022] Open
Abstract
In 1965 Duwez et al. reported having generated an amorphous, stable phase of palladium-silicon in the region 15 to 23 atomic percent, at.%, silicon. These pioneering efforts have led to the development of solid materials that are now known as Bulk Metallic Glasses, BMG. In 2019 Rodríguez et al. discovered, computationally, that bulk amorphous Pd becomes magnetic, and so does porous/amorphous Pd. Puzzled by these results, the study of several solid binary systems in the Pd-rich zone was undertaken; in particular, the study of the glassy metallic alloy a-Pd[Formula: see text]Si[Formula: see text], for [Formula: see text], (c in at.%) to see what their topology is, what their electronic properties are and to inquire about their magnetism. In this work it is shown that this metallic glass is in fact magnetic in the region [Formula: see text]. Collaterally [Formula: see text] and [Formula: see text] magnetization curves are shown where the net magnetic moment is presented. The topology and the position of the first few peaks of the pair distribution functions, which agrees well with experiment, are also discussed. The BMGs produced experimentally so far are limited in size, but despite this limitation, recent industrial efforts have developed some useful devices that may revolutionize technology.
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Affiliation(s)
- Isaías Rodríguez
- Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Apartado Postal 70-360, 04510 Ciudad Universitaria, CDMX, Mexico
| | - Renela M. Valladares
- Facultad de Ciencias, Universidad Nacional Autónoma de México, Apartado Postal 70-542, 04510 Ciudad Universitaria, CDMX, Mexico
| | - Alexander Valladares
- Facultad de Ciencias, Universidad Nacional Autónoma de México, Apartado Postal 70-542, 04510 Ciudad Universitaria, CDMX, Mexico
| | - David Hinojosa-Romero
- Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Apartado Postal 70-360, 04510 Ciudad Universitaria, CDMX, Mexico
| | - Ariel A. Valladares
- Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Apartado Postal 70-360, 04510 Ciudad Universitaria, CDMX, Mexico
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38
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Kovács IA, Iglói F. Geometry of rare regions behind Griffiths singularities in random quantum magnets. Sci Rep 2022; 12:1074. [PMID: 35058527 PMCID: PMC8776845 DOI: 10.1038/s41598-022-05096-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Accepted: 12/24/2021] [Indexed: 12/04/2022] Open
Abstract
In many-body systems with quenched disorder, dynamical observables can be singular not only at the critical point, but in an extended region of the paramagnetic phase as well. These Griffiths singularities are due to rare regions, which are locally in the ordered phase and contribute to a large susceptibility. Here, we study the geometrical properties of rare regions in the transverse Ising model with dilution or with random couplings and transverse fields. In diluted models, the rare regions are percolation clusters, while in random models the ground state consists of a set of spin clusters, which are calculated by the strong disorder renormalization method. We consider the so called energy cluster, which has the smallest excitation energy and calculate its mass and linear extension in one-, two- and three-dimensions. Both average quantities are found to grow logarithmically with the linear size of the sample. Consequently, the energy clusters are not compact: for the diluted model they are isotropic and tree-like, while for the random model they are quasi-one-dimensional.
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Affiliation(s)
- István A Kovács
- Department of Physics and Astronomy, Northwestern University, Evanston, IL, 60208, USA.
- Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL, 60208, USA.
| | - Ferenc Iglói
- Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, Budapest, 1525, Hungary
- Institute of Theoretical Physics, Szeged University, Szeged, 6720, Hungary
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39
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Peng B, Bouhon A, Monserrat B, Slager RJ. Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates. Nat Commun 2022; 13:423. [PMID: 35058473 PMCID: PMC8776786 DOI: 10.1038/s41467-022-28046-9] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2021] [Accepted: 12/29/2021] [Indexed: 11/08/2022] Open
Abstract
Topological phases of matter have revolutionised the fundamental understanding of band theory and hold great promise for next-generation technologies such as low-power electronics or quantum computers. Single-gap topologies have been extensively explored, and a large number of materials have been theoretically proposed and experimentally observed. These ideas have recently been extended to multi-gap topologies with band nodes that carry non-Abelian charges, characterised by invariants that arise by the momentum space braiding of such nodes. However, the constraints placed by the Fermi-Dirac distribution to electronic systems have so far prevented the experimental observation of multi-gap topologies in real materials. Here, we show that multi-gap topologies and the accompanying phase transitions driven by braiding processes can be readily observed in the bosonic phonon spectra of known monolayer silicates. The associated braiding process can be controlled by means of an electric field and epitaxial strain, and involves, for the first time, more than three bands. Finally, we propose that the band inversion processes at the Γ point can be tracked by following the evolution of the Raman spectrum, providing a clear signature for the experimental verification of the band inversion accompanied by the braiding process.
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Affiliation(s)
- Bo Peng
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge, CB3 0HE, United Kingdom.
| | - Adrien Bouhon
- Nordic Institute for Theoretical Physics (Nordita), Stockholm University and KTH Royal Institute of Technology, Hannes Alfvéns väg 12, Stockholm, SE-106 91, Sweden.
| | - Bartomeu Monserrat
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge, CB3 0HE, United Kingdom.
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge, CB3 0FS, United Kingdom.
| | - Robert-Jan Slager
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge, CB3 0HE, United Kingdom.
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40
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Abstract
Hyperinvariant tensor networks (hyMERA) were introduced as a way to combine the successes of perfect tensor networks (HaPPY) and the multiscale entanglement renormalization ansatz (MERA) in simulations of the AdS/CFT correspondence. Although this new class of tensor network shows much potential for simulating conformal field theories arising from hyperbolic bulk manifolds with quasiperiodic boundaries, many issues are unresolved. In this manuscript we analyze the challenges related to optimizing tensors in a hyMERA with respect to some quasiperiodic critical spin chain, and compare with standard approaches in MERA. Additionally, we show two new sets of tensor decompositions which exhibit different properties from the original construction, implying that the multitensor constraints are neither unique, nor difficult to find, and that a generalization of the analytical tensor forms used up until now may exist. Lastly, we perform randomized trials using a descending superoperator with several of the investigated tensor decompositions, and find that the constraints imposed on the spectra of local descending superoperators in hyMERA are compatible with the operator spectra of several minimial model CFTs.
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Affiliation(s)
- Matthew Steinberg
- QuTech, Delft University of Technology, Delft, The Netherlands.
- Quantum and Computer Engineering Department, Delft University of Technology, Delft, The Netherlands.
| | - Javier Prior
- Departamento de Física Aplicada, Universidad Politécnica de Cartagena, 30202, Cartagena, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071, Granada, Spain
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41
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Contreras-Tejada P, Scarpa G, Kubicki AM, Brandenburger A, La Mura P. Observers of quantum systems cannot agree to disagree. Nat Commun 2021; 12:7021. [PMID: 34857739 PMCID: PMC8640027 DOI: 10.1038/s41467-021-27134-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2021] [Accepted: 11/05/2021] [Indexed: 11/16/2022] Open
Abstract
Is the world quantum? An active research line in quantum foundations is devoted to exploring what constraints can rule out the postquantum theories that are consistent with experimentally observed results. We explore this question in the context of epistemics, and ask whether agreement between observers can serve as a physical principle that must hold for any theory of the world. Aumann's seminal Agreement Theorem states that two observers (of classical systems) cannot agree to disagree. We propose an extension of this theorem to no-signaling settings. In particular, we establish an Agreement Theorem for observers of quantum systems, while we construct examples of (postquantum) no-signaling boxes where observers can agree to disagree. The PR box is an extremal instance of this phenomenon. These results make it plausible that agreement between observers might be a physical principle, while they also establish links between the fields of epistemics and quantum information that seem worthy of further exploration.
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Affiliation(s)
| | - Giannicola Scarpa
- Escuela Técnica Superior de Ingeniería de Sistemas Informáticos, Universidad Politécnica de Madrid, 28031, Madrid, Spain.
| | - Aleksander M Kubicki
- Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, 28040, Madrid, Spain
| | - Adam Brandenburger
- Stern School of Business, Tandon School of Engineering, NYU Shanghai, New York University, New York, NY, 10012, USA
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42
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Denner MM, Skurativska A, Schindler F, Fischer MH, Thomale R, Bzdušek T, Neupert T. Exceptional topological insulators. Nat Commun 2021; 12:5681. [PMID: 34584085 PMCID: PMC8478920 DOI: 10.1038/s41467-021-25947-z] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2021] [Accepted: 09/08/2021] [Indexed: 11/23/2022] Open
Abstract
We introduce the exceptional topological insulator (ETI), a non-Hermitian topological state of matter that features exotic non-Hermitian surface states which can only exist within the three-dimensional topological bulk embedding. We show how this phase can evolve from a Weyl semimetal or Hermitian three-dimensional topological insulator close to criticality when quasiparticles acquire a finite lifetime. The ETI does not require any symmetry to be stabilized. It is characterized by a bulk energy point gap, and exhibits robust surface states that cover the bulk gap as a single sheet of complex eigenvalues or with a single exceptional point. The ETI can be induced universally in gapless solid-state systems, thereby setting a paradigm for non-Hermitian topological matter.
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Affiliation(s)
- M Michael Denner
- Department of Physics, University of Zurich, Winterthurerstrasse 190, 8057, Zurich, Switzerland.
| | - Anastasiia Skurativska
- Department of Physics, University of Zurich, Winterthurerstrasse 190, 8057, Zurich, Switzerland
| | - Frank Schindler
- Department of Physics, University of Zurich, Winterthurerstrasse 190, 8057, Zurich, Switzerland
- Princeton Center for Theoretical Science, Princeton University, Princeton, NJ, 08544, USA
| | - Mark H Fischer
- Department of Physics, University of Zurich, Winterthurerstrasse 190, 8057, Zurich, Switzerland
| | - Ronny Thomale
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074, Würzburg, Germany
| | - Tomáš Bzdušek
- Department of Physics, University of Zurich, Winterthurerstrasse 190, 8057, Zurich, Switzerland
- Condensed Matter Theory Group, Paul Scherrer Institute, 5232, Villigen PSI, Switzerland
| | - Titus Neupert
- Department of Physics, University of Zurich, Winterthurerstrasse 190, 8057, Zurich, Switzerland
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43
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Petruzziello L, Illuminati F. Quantum gravitational decoherence from fluctuating minimal length and deformation parameter at the Planck scale. Nat Commun 2021; 12:4449. [PMID: 34294717 PMCID: PMC8298405 DOI: 10.1038/s41467-021-24711-7] [Citation(s) in RCA: 26] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2020] [Accepted: 06/25/2021] [Indexed: 02/06/2023] Open
Abstract
Schemes of gravitationally induced decoherence are being actively investigated as possible mechanisms for the quantum-to-classical transition. Here, we introduce a decoherence process due to quantum gravity effects. We assume a foamy quantum spacetime with a fluctuating minimal length coinciding on average with the Planck scale. Considering deformed canonical commutation relations with a fluctuating deformation parameter, we derive a Lindblad master equation that yields localization in energy space and decoherence times consistent with the currently available observational evidence. Compared to other schemes of gravitational decoherence, we find that the decoherence rate predicted by our model is extremal, being minimal in the deep quantum regime below the Planck scale and maximal in the mesoscopic regime beyond it. We discuss possible experimental tests of our model based on cavity optomechanics setups with ultracold massive molecular oscillators and we provide preliminary estimates on the values of the physical parameters needed for actual laboratory implementations.
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Affiliation(s)
- Luciano Petruzziello
- Dipartimento di Ingegneria Industriale, Università degli Studi di Salerno, Fisciano, (SA), Italy.
- INFN, Sezione di Napoli, Gruppo collegato di Salerno, Fisciano, (SA), Italy.
| | - Fabrizio Illuminati
- Dipartimento di Ingegneria Industriale, Università degli Studi di Salerno, Fisciano, (SA), Italy.
- INFN, Sezione di Napoli, Gruppo collegato di Salerno, Fisciano, (SA), Italy.
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44
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Kozubov AV, Gaidash AA, Kiselev AD, Miroshnichenko GP. Filtration mapping as complete Bell state analyzer for bosonic particles. Sci Rep 2021; 11:14236. [PMID: 34244596 PMCID: PMC8270949 DOI: 10.1038/s41598-021-93679-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2021] [Accepted: 06/21/2021] [Indexed: 11/09/2022] Open
Abstract
In this paper, we present the approach to complete Bell state analysis based on filtering mapping. The key distinctive feature of this appoach is that it avoids complications related to using either hyperentanglement or representation of the Bell states as concatenated Greenber-Horne-Zeilinger (C-GHZ) state to perform discrimination procedure. We describe two techniques developed within the suggested approach and based on two-step algorithms with two different types of filtration mapping which can be called the non-demolition and semi-demolition filtrations. In the method involving non-demolition filtration measurement the filtration process employs cross-Kerr nonlinearity and the probe mode to distinguish between the two pairs of the Bell states. In the case of semi-demolition measurement, the two states are unambiguously discriminated and hence destroyed, whereas filtraton keeps the other two states intact. We show that the measurement that destroys the single photon subspace in every mode and preserves the superposition of zero and two photons can be realized with discrete photodetection based on microresonator with atoms.
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Affiliation(s)
- A V Kozubov
- Department of Mathematical Methods for Quantum Technologies, Steklov Mathematical Institute of Russian Academy of Sciences, 119991, Moscow, Russia.
- Laboratory of Quantum Processes and Measurements, ITMO University, Kadetskaya Line 3b, 199034, Saint Petersburg, Russia.
| | - A A Gaidash
- Department of Mathematical Methods for Quantum Technologies, Steklov Mathematical Institute of Russian Academy of Sciences, 119991, Moscow, Russia
- Laboratory of Quantum Processes and Measurements, ITMO University, Kadetskaya Line 3b, 199034, Saint Petersburg, Russia
| | - A D Kiselev
- Laboratory of Quantum Processes and Measurements, ITMO University, Kadetskaya Line 3b, 199034, Saint Petersburg, Russia
- Faculty of Physics, St. Petersburg State University, 199034, Saint Petersburg, Russia
| | - G P Miroshnichenko
- Faculty of Laser Photonics and Optoelectronics, ITMO University, 49 Kronverksky Pr., 197101, Saint Petersburg, Russia
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45
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Magnifico G, Felser T, Silvi P, Montangero S. Lattice quantum electrodynamics in (3+1)-dimensions at finite density with tensor networks. Nat Commun 2021; 12:3600. [PMID: 34127658 PMCID: PMC8203653 DOI: 10.1038/s41467-021-23646-3] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2020] [Accepted: 05/07/2021] [Indexed: 02/05/2023] Open
Abstract
Gauge theories are of paramount importance in our understanding of fundamental constituents of matter and their interactions. However, the complete characterization of their phase diagrams and the full understanding of non-perturbative effects are still debated, especially at finite charge density, mostly due to the sign-problem affecting Monte Carlo numerical simulations. Here, we report the Tensor Network simulation of a three dimensional lattice gauge theory in the Hamiltonian formulation including dynamical matter: Using this sign-problem-free method, we simulate the ground states of a compact Quantum Electrodynamics at zero and finite charge densities, and address fundamental questions such as the characterization of collective phases of the model, the presence of a confining phase at large gauge coupling, and the study of charge-screening effects.
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Affiliation(s)
- Giuseppe Magnifico
- Dipartimento di Fisica e Astronomia G. Galilei, Università di Padova, Padova, Italy.
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova, Padova, Italy.
| | - Timo Felser
- Dipartimento di Fisica e Astronomia G. Galilei, Università di Padova, Padova, Italy
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova, Padova, Italy
- Theoretische Physik, Universität des Saarlandes, Saarbrücken, Germany
| | - Pietro Silvi
- Center for Quantum Physics, Institute for Experimental Physics, University of Innsbruck, Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck, Austria
| | - Simone Montangero
- Dipartimento di Fisica e Astronomia G. Galilei, Università di Padova, Padova, Italy
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova, Padova, Italy
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Kirichenko EV, Stephanovich VA. The influence of Coulomb interaction screening on the excitons in disordered two-dimensional insulators. Sci Rep 2021; 11:11956. [PMID: 34099801 PMCID: PMC8184999 DOI: 10.1038/s41598-021-91414-w] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2021] [Accepted: 05/21/2021] [Indexed: 11/19/2022] Open
Abstract
We study the joint effect of disorder and Coulomb interaction screening on the exciton spectra in two-dimensional (2D) structures. These can be van der Waals structures or heterostructures of organic (polymeric) semiconductors as well as inorganic substances like transition metal dichalcogenides. We consider 2D screened hydrogenic problem with Rytova-Keldysh interaction by means of so-called fractional Scrödinger equation. Our main finding is that above synergy between screening and disorder either destroys the exciton (strong screening) or promote the creation of a bound state, leading to its collapse in the extreme case. Our second finding is energy levels crossing, i.e. the degeneracy (with respect to index [Formula: see text]) of the exciton eigenenergies at certain discrete value of screening radius. Latter effects may also be related to the quantum manifestations of chaotic exciton behavior in above 2D semiconductor structures. Hence, they should be considered in device applications, where the interplay between dielectric screening and disorder is important.
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Affiliation(s)
- E V Kirichenko
- Institute of Physics, Opole University, Oleska 48, 45-052, Opole, Poland
| | - V A Stephanovich
- Institute of Physics, Opole University, Oleska 48, 45-052, Opole, Poland.
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Schwonnek R, Goh KT, Primaatmaja IW, Tan EYZ, Wolf R, Scarani V, Lim CCW. Device-independent quantum key distribution with random key basis. Nat Commun 2021; 12:2880. [PMID: 34001885 PMCID: PMC8128898 DOI: 10.1038/s41467-021-23147-3] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2020] [Accepted: 04/19/2021] [Indexed: 11/09/2022] Open
Abstract
Device-independent quantum key distribution (DIQKD) is the art of using untrusted devices to distribute secret keys in an insecure network. It thus represents the ultimate form of cryptography, offering not only information-theoretic security against channel attacks, but also against attacks exploiting implementation loopholes. In recent years, much progress has been made towards realising the first DIQKD experiments, but current proposals are just out of reach of today's loophole-free Bell experiments. Here, we significantly narrow the gap between the theory and practice of DIQKD with a simple variant of the original protocol based on the celebrated Clauser-Horne-Shimony-Holt (CHSH) Bell inequality. By using two randomly chosen key generating bases instead of one, we show that our protocol significantly improves over the original DIQKD protocol, enabling positive keys in the high noise regime for the first time. We also compute the finite-key security of the protocol for general attacks, showing that approximately 108-1010 measurement rounds are needed to achieve positive rates using state-of-the-art experimental parameters. Our proposed DIQKD protocol thus represents a highly promising path towards the first realisation of DIQKD in practice.
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Affiliation(s)
- René Schwonnek
- Department of Electrical & Computer Engineering, National University of Singapore, Singapore, Singapore
| | - Koon Tong Goh
- Department of Electrical & Computer Engineering, National University of Singapore, Singapore, Singapore
| | | | - Ernest Y-Z Tan
- Institute for Theoretical Physics, ETH Zürich, Zürich, Switzerland
| | - Ramona Wolf
- Institut für Theoretische Physik, Leibniz Universität Hannover, Hannover, Germany
| | - Valerio Scarani
- Centre for Quantum Technologies, National University of Singapore, Singapore, Singapore
- Department of Physics, National University of Singapore, Singapore, Singapore
| | - Charles C-W Lim
- Department of Electrical & Computer Engineering, National University of Singapore, Singapore, Singapore.
- Centre for Quantum Technologies, National University of Singapore, Singapore, Singapore.
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Abstract
Discrete-time quantum walks are known to exhibit exotic topological states and phases. Physical realization of quantum walks in a lossy environment may destroy these phases. We investigate the behaviour of topological states in quantum walks in the presence of a lossy environment. The environmental effects in the quantum walk dynamics are addressed using the non-Hermitian Hamiltonian approach. We show that the topological phases of the quantum walks are robust against moderate losses. The topological order in one-dimensional split-step quantum walk persists as long as the Hamiltonian respects exact [Formula: see text]-symmetry. Although the topological nature persists in two-dimensional quantum walks as well, the [Formula: see text]-symmetry has no role to play there. Furthermore, we observe topological phase transition in two-dimensional quantum walks that is induced by losses in the system.
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Affiliation(s)
- Vikash Mittal
- Department of Physical Sciences, Indian Institute of Science Education & Research (IISER) Mohali, Sector 81 SAS Nagar, PO 140306, Manauli, Punjab, India
| | - Aswathy Raj
- Okinawa Institute of Science and Technology Graduate University, Okinawa, 904-0495, Japan
| | - Sanjib Dey
- Department of Physical Sciences, Indian Institute of Science Education & Research (IISER) Mohali, Sector 81 SAS Nagar, PO 140306, Manauli, Punjab, India
| | - Sandeep K Goyal
- Department of Physical Sciences, Indian Institute of Science Education & Research (IISER) Mohali, Sector 81 SAS Nagar, PO 140306, Manauli, Punjab, India.
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49
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Maslova NS, Arseyev PI, Mantsevich VN. Tunneling current and noise of entangled electrons in correlated double quantum dot. Sci Rep 2021; 11:9336. [PMID: 33927283 PMCID: PMC8085215 DOI: 10.1038/s41598-021-88721-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2020] [Accepted: 04/16/2021] [Indexed: 11/10/2022] Open
Abstract
We developed general approach for the analysis of tunneling current and its zero frequency noise for a wide class of systems where electron transport occurs through the intermediate structure with localized electrons. Proposed approach opens the possibility to study electron transport through multi-electron correlated states and allows to reveal the influence of spatial and spin symmetry of the total system on the electron transport. This approach is based on Keldysh diagram technique in pseudo-particle representation taking into account the operator constraint on the number of pseudo-particles, which gives the possibility to exclude non-physical states. It was shown that spatial and spin symmetry of the total system can block some channels for electron transport through the correlated quantum dots. Moreover, it was demonstrated that the stationary tunneling current and zero frequency noise in correlated coupled quantum dots depend on initial state of the system. In the frame of the proposed approach it was also shown that for the parallel coupling of two correlated quantum dots to the reservoirs tunneling current and its zero frequency noise are suppressed if tunneling occurs through the entangled triplet state with zero total spin projection on the z axis or enhanced for the tunneling through the singlet state in comparison with electron transport through the uncorrelated localized single-electron state. Obtained results demonstrate that two-electron entangled states in correlated quantum dots give the possibility to tune the zero frequency noise amplitude by blocking some channels for electron transport that is very promising in the sense of two-electron entangled states application in quantum communication and logic devices. The obtained nonmonotonic behavior of Fano factor as a function of applied bias is the direct manifestation of the possibility to control the noise to signal ration in correlated quantum dots. We also provide detailed calculations of current and noise for both single type of carriers and two different types of carriers in the presence and in the absence of Coulomb interaction in Supplementary materials.
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Affiliation(s)
- N S Maslova
- Quantum Technology Center and Quantum electronics department, Faculty of Physics, Lomonosov Moscow State University, Moscow, 119991, Russia
| | - P I Arseyev
- P.N. Lebedev Physical Institute RAS, 119991, Moscow, Russia
| | - V N Mantsevich
- Quantum Technology Center and department of Semiconductor physics and Cryoelectronics, Faculty of Physics, Lomonosov Moscow State University, Moscow, 119991, Russia.
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Pietraszewicz J, Seweryn A, Witkowska E. Multifaceted phase ordering kinetics of an antiferromagnetic spin-1 condensate. Sci Rep 2021; 11:9296. [PMID: 33927249 PMCID: PMC8085072 DOI: 10.1038/s41598-021-88454-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2020] [Accepted: 04/07/2021] [Indexed: 11/18/2022] Open
Abstract
We study phase domain coarsening in the long time limit after a quench of magnetic field in a quasi one-dimensional spin-1 antiferromagnetic condensate. We observe that the growth of correlation length obeys scaling laws predicted by the two different models of phase ordering kinetics, namely the binary mixture and vector field. We derive regimes of clear realization for both of them. We demonstrate appearance of atypical scaling laws, which emerge in intermediate regions.
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Affiliation(s)
- Joanna Pietraszewicz
- Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, 02668, Warsaw, Poland
| | - Aleksandra Seweryn
- Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, 02668, Warsaw, Poland
| | - Emilia Witkowska
- Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, 02668, Warsaw, Poland.
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