Time-dependent Neural Galerkin Method for Quantum Dynamics

• URL: http://arxiv.org/abs/2412.11778v1
• Date: Mon, 16 Dec 2024 13:48:54 GMT
• Title: Time-dependent Neural Galerkin Method for Quantum Dynamics
• Authors: Alessandro Sinibaldi, Douglas Hendry, Filippo Vicentini, Giuseppe Carleo,
• Abstract summary: We introduce a classical computational method for quantum dynamics that relies on a global-in-time variational principle.<n>We showcase the method's effectiveness simulating global quantum quenches in the paradigmatic Transverse-Field Ising model in both 1D and 2D.<n>Overall, the method presented here shows competitive performance compared to state-of-the-art time-dependent variational approaches.
• Score: 42.81677042059531
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a classical computational method for quantum dynamics that relies on a global-in-time variational principle. Unlike conventional time-stepping approaches, our scheme computes the entire state trajectory over a finite time window by minimizing a physically motivated loss function that enforces the Schr\"odinger's equation. The variational state is parametrized with a Galerkin-inspired ansatz based on a time-dependent linear combination of time-independent Neural Quantum States. This structure effectively captures the relevant dynamical frequencies in the time evolution and is particularly well-suited for exploring long-time dynamics. We showcase the method's effectiveness by simulating global quantum quenches in the paradigmatic Transverse-Field Ising model in both 1D and 2D. By extracting the asymptotic long-time evolution, we uncover signatures of ergodicity breaking and absence of thermalization in two dimensions. Overall, the method presented here shows competitive performance compared to state-of-the-art time-dependent variational approaches and highlight the potential to explore previously inaccessible dynamical regimes of strongly interacting quantum systems.

Related papers

• Many-body dynamics with explicitly time-dependent neural quantum states [0.0]
  We introduce the time-dependent neural quantum state (t-NQS)<n>We optimize a single, time-independent set of parameters to solve the time-dependent Schr"odinger equation across an entire time interval.<n>Results establish t-NQS as a powerful framework for exploring quantum dynamics in strongly correlated systems.
  arXiv  Detail & Related papers  (2024-12-16T14:53:26Z)
• Thermalization slowing down of weakly nonintegrable quantum spin dynamics [0.0]
  We study thermalization slowing down of a quantum many-body system upon approach to two distinct integrability limits. Using a paradigmatic Quantum Ising chain we find that both timescales diverge upon approach to integrability.
  arXiv  Detail & Related papers  (2024-05-01T18:00:58Z)
• Real-time dynamics of false vacuum decay [49.1574468325115]
  We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
  arXiv  Detail & Related papers  (2023-10-06T12:44:48Z)
• Measurement events relative to temporal quantum reference frames [44.99833362998488]
  We compare two consistent approaches to the Page-Wootters formalism to clarify the operational meaning of evolution and measurements. We show that for non-ideal clocks, the purified measurement approach yields a time non-local evolution equation. We argue that these approaches describe operationally distinct situations.
  arXiv  Detail & Related papers  (2023-08-21T18:26:12Z)
• Dynamics with autoregressive neural quantum states: application to critical quench dynamics [41.94295877935867]
  We present an alternative general scheme that enables one to capture long-time dynamics of quantum systems in a stable fashion. We apply the scheme to time-dependent quench dynamics by investigating the Kibble-Zurek mechanism in the two-dimensional quantum Ising model.
  arXiv  Detail & Related papers  (2022-09-07T15:50:00Z)
• Out-of-equilibrium dynamics arising from slow round-trip variations of Hamiltonian parameters across quantum and classical critical points [0.0]
  We address the out-of-equilibrium dynamics of many-body systems subject to slow time-dependent round-trip protocols across quantum and classical (thermal) phase transitions. We consider protocols where one relevant parameter w is slowly changed across its critical point wc = 0, linearly in time with a large time scale ts.
  arXiv  Detail & Related papers  (2022-05-17T13:27:32Z)
• On optimization of coherent and incoherent controls for two-level quantum systems [77.34726150561087]
  This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr"odinger equation with coherent control. The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation.
  arXiv  Detail & Related papers  (2022-05-05T09:08:03Z)
• Shortcuts to adiabatic population inversion via time-rescaling: stability and thermodynamic cost [0.0]
  We study the problem of speeding up the population inversion of a two-level quantum system. The fidelity of the dynamics versus systematic errors in the control parameters are shown to be comparable with other STA schemes.
  arXiv  Detail & Related papers  (2022-04-29T20:27:02Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Exponentially accelerated approach to stationarity in Markovian open quantum systems through the Mpemba effect [0.0]
  We show that the relaxation dynamics of Markovian open quantum systems can be accelerated exponentially by devising an optimal unitary transformation. This initial "rotation" is engineered in such a way that the state of the quantum system becomes to the slowest decaying dynamical mode. We illustrate our idea by showing how to achieve an exponential speed-up in the convergence to stationarity in Dicke models.
  arXiv  Detail & Related papers  (2021-03-08T19:02:31Z)
• Fast and differentiable simulation of driven quantum systems [58.720142291102135]
  We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods. We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
  arXiv  Detail & Related papers  (2020-12-16T21:43:38Z)
• Floquet theory for temporal correlations and spectra in time-periodic open quantum systems: Application to squeezed parametric oscillation beyond the rotating-wave approximation [0.0]
  We propose a method to compute two-time correlations and corresponding spectral densities of time-periodic open quantum systems. We show how the quantum Langevin equations for the fluctuations can be efficiently integrated by partitioning the time domain into one-period duration intervals.
  arXiv  Detail & Related papers  (2020-05-17T13:25:04Z)

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.