Related papers: Importance Sampling Scheme for the Stochastic Simulation of Quantum Spin Dynamics

Importance Sampling Scheme for the Stochastic Simulation of Quantum Spin Dynamics

URL: http://arxiv.org/abs/2103.16468v2
Date: Wed, 30 Jun 2021 12:05:47 GMT
Title: Importance Sampling Scheme for the Stochastic Simulation of Quantum Spin Dynamics
Authors: Stefano De Nicola
Abstract summary: We develop an importance sampling scheme for the simulation of quantum spin dynamics. An exact transformation is then carried out to preferentially sample trajectories that are close to the dominant one. We demonstrate that this approach is capable of reducing the temporal growth of fluctuations in the quantities.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The numerical simulation of dynamical phenomena in interacting quantum systems is a notoriously hard problem. Although a number of promising numerical methods exist, they often have limited applicability due to the growth of entanglement or the presence of the so-called sign problem. In this work, we develop an importance sampling scheme for the simulation of quantum spin dynamics, building on a recent approach mapping quantum spin systems to classical stochastic processes. The importance sampling scheme is based on identifying the classical trajectory that yields the largest contribution to a given quantum observable. An exact transformation is then carried out to preferentially sample trajectories that are close to the dominant one. We demonstrate that this approach is capable of reducing the temporal growth of fluctuations in the stochastic quantities, thus extending the range of accessible times and system sizes compared to direct sampling. We discuss advantages and limitations of the proposed approach, outlining directions for further developments.

Related papers

Hybrid Stabilizer Matrix Product Operator [44.99833362998488]
We introduce a novel hybrid approach combining tensor network methods with the stabilizer formalism to address the challenges of simulating many-body quantum systems. We demonstrate the effectiveness of our method through applications to random Clifford T-doped circuits and Random Clifford Floquet Dynamics.
arXiv Detail & Related papers (2024-05-09T18:32:10Z)
Embedding memory-efficient stochastic simulators as quantum trajectories [0.0]
We show how continuous-time quantum simulators can be embedded in open quantum systems. We further show how such an embedding can be made exploiting for discrete-time processes.
arXiv Detail & Related papers (2024-02-07T09:54:11Z)
Variational dynamics of open quantum systems in phase space [0.0]
We present a method to simulate the dynamics of large driven-dissipative many-body open quantum systems. We present a proof of principle investigation into the physics of the driven-dissipative Bose-Hubbard model with weak nonlinearity.
arXiv Detail & Related papers (2023-07-14T15:48:31Z)
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)
Stochastic Representation of the Quantum Quartic Oscillator [0.0]
We show how to parameterize the time evolution of this model via the dynamics of a set of classical variables. We propose a novel way to numerically simulate the time evolution of the system.
arXiv Detail & Related papers (2022-11-03T16:04:26Z)
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)
Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
arXiv Detail & Related papers (2021-03-05T08:32:43Z)
Quantum Markov Chain Monte Carlo with Digital Dissipative Dynamics on Quantum Computers [52.77024349608834]
We develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. We evaluate the algorithm by simulating thermal states of the transverse Ising model.
arXiv Detail & Related papers (2021-03-04T18:21:00Z)
Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
arXiv Detail & Related papers (2021-02-18T20:55:04Z)
Dynamical replica analysis of quantum annealing [0.0]
An interesting alternative approach to the dynamics of quantum spin systems was proposed about a decade ago. It involves creating a proxy dynamics via the Suzuki-Trotter mapping of the quantum ensemble to a classical one. In this chapter we give an introduction to this approach, focusing on the ideas and assumptions behind the derivations.
arXiv Detail & Related papers (2020-10-23T12:17:38Z)

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