Finite-Size Scaling on a Digital Quantum Simulator using Quantum Restricted Boltzmann Machine

• URL: http://arxiv.org/abs/2202.00112v1
• Date: Mon, 31 Jan 2022 21:58:01 GMT
• Title: Finite-Size Scaling on a Digital Quantum Simulator using Quantum Restricted Boltzmann Machine
• Authors: Bilal Khalid, Shree Hari Sureshbabu, Arnab Banerjee, Sabre Kais
• Abstract summary: The critical point and the critical exponents for a phase transition can be determined using the Finite-Size Scaling analysis. We propose an alternative FSS method in which the truncation of the system is done in the Hilbert space instead of the physical space.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The critical point and the critical exponents for a phase transition can be determined using the Finite-Size Scaling (FSS) analysis. This method assumes that the phase transition occurs only in the infinite size limit. However, there has been a lot of interest recently in quantum phase transitions occuring in finite size systems such as a single two-level system interacting with a single bosonic mode e.g. in the Quantum Rabi Model (QRM). Since, these phase transitions occur at a finite system size, the traditional FSS method is rendered inapplicable for these cases. For cases like this, we propose an alternative FSS method in which the truncation of the system is done in the Hilbert space instead of the physical space. This approach has previously been used to calculate the critical parameters for stability and symmetry breaking of electronic structure configurations of atomic and molecular systems. We calculate the critical point for the quantum phase transition of the QRM using this approach. We also provide a protocol to implement this method on a digital quantum simulator using the Quantum Restricted Boltzmann Machine algorithm. Our work opens up a new direction in the study of quantum phase transitions on quantum devices.

Related papers

• Thermalization and Criticality on an Analog-Digital Quantum Simulator [133.58336306417294]
  We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions. We digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization.
  arXiv  Detail & Related papers  (2024-05-27T17:40:39Z)
• Qubit-assisted quantum metrology [2.4927008953071725]
  We propose a quantum metrology protocol based on a two-step joint evolution of the probe system and an ancillary qubit. We find that QFI can approach the Heisenberg scaling $N2$ with respect to the quantum number $N$, even when the probe system is prepared in a classical state.
  arXiv  Detail & Related papers  (2024-04-19T06:25:13Z)
• Quantum Classical Algorithm for the Study of Phase Transitions in the Hubbard Model via Dynamical Mean-Field Theory [0.0]
  We propose a workflow that synergizes quantum computing, many-body theory, and quantum machine learning for studying strongly correlated systems. We generate a database of zero-temperature wavefunctions of the Hubbard model within the DMFT approximation. We then use a QML algorithm to distinguish between the metallic phase and the Mott insulator phase to capture the metal-to-Mott insulator phase transition.
  arXiv  Detail & Related papers  (2023-08-02T19:11:04Z)
• Measurement-induced entanglement and teleportation on a noisy quantum processor [105.44548669906976]
  We investigate measurement-induced quantum information phases on up to 70 superconducting qubits. We use a duality mapping, to avoid mid-circuit measurement and access different manifestations of the underlying phases. Our work demonstrates an approach to realize measurement-induced physics at scales that are at the limits of current NISQ processors.
  arXiv  Detail & Related papers  (2023-03-08T18:41:53Z)
• Quantum Computation of Phase Transition in Interacting Scalar Quantum Field Theory [0.0]
  It has been demonstrated that the critical point of the phase transition in scalar quantum field theory can be approximated via a Gaussian Effective Potential (GEP) We perform quantum computations with various lattice sizes and obtain evidence of a transition from a symmetric to a symmetry-broken phase. We implement the ten-site case on IBM quantum hardware using the Variational Quantum Eigensolver (VQE) algorithm to minimize the GEP.
  arXiv  Detail & Related papers  (2023-03-04T14:11:37Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Coherent quantum annealing in a programmable 2000-qubit Ising chain [1.2472275770062884]
  We show coherent evolution through a quantum phase transition in the paradigmatic setting of the 1D transverse-field Ising chain. Results are in quantitative agreement with analytical solutions to the closed-system quantum model. These experiments demonstrate that large-scale quantum annealers can be operated coherently.
  arXiv  Detail & Related papers  (2022-02-11T19:00:00Z)
• Enhanced nonlinear quantum metrology with weakly coupled solitons and particle losses [58.720142291102135]
  We offer an interferometric procedure for phase parameters estimation at the Heisenberg (up to 1/N) and super-Heisenberg scaling levels. The heart of our setup is the novel soliton Josephson Junction (SJJ) system providing the formation of the quantum probe. We illustrate that such states are close to the optimal ones even with moderate losses.
  arXiv  Detail & Related papers  (2021-08-07T09:29:23Z)
• Observation of a quantum phase transition in the quantum Rabi model with a single trapped ion [0.0]
  Quantum phase transitions (QPTs) are usually associated with many-body systems with large degrees of freedom approaching the thermodynamic limit. It has been realized that a QPT can occur in a simple system composed of only a two-level atom and a single-mode bosonic field. We report the first experimental demonstration of a QPT in the quantum Rabi model using a single trapped ion.
  arXiv  Detail & Related papers  (2021-02-10T13:03:37Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.