Multi-particle quantum systems within the Worldline Monte Carlo formalism

• URL: http://arxiv.org/abs/2512.24942v1
• Date: Wed, 31 Dec 2025 16:07:06 GMT
• Title: Multi-particle quantum systems within the Worldline Monte Carlo formalism
• Authors: Ivan Ahumada, Max Badcott, James P. Edwards, Craig McNeile, Filippo Ricchetti, Federico Grasselli, Guido Goldoni, Olindo Corradini, Marco Palomino,
• Abstract summary: We extend the Worldline Monte Carlo approach to computationally simulating non-relativistic quantum-mechanical systems.<n>We show how to generate an arbitrary number of worldlines distributed according to the (free) kinetic part of the multi-particle quantum dynamics.<n>We validate our approach with numerically exact solutions obtained via straightforward diagonalisation of the Hamiltonian.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We extend the Worldline Monte Carlo approach to computationally simulating the Feynman path integral of non-relativistic multi-particle quantum-mechanical systems. We show how to generate an arbitrary number of worldlines distributed according to the (free) kinetic part of the multi-particle quantum dynamics and how to simulate interactions between worldlines in the ensemble. We test this formalism with two- and three-particle quantum mechanical systems, with both long range Coulomb-like interactions between the particles and external fields acting separately on the particles, in various spatial dimensionality. We extract accurate estimations of the ground state energy of these systems using the late-time behaviour of the propagator, validating our approach with numerically exact solutions obtained via straightforward diagonalisation of the Hamiltonian. Systematic benchmarking of the new approach, presented here for the first time, shows that the computational complexity of Wordline Monte Carlo scales more favourably with respect to standard numerical alternatives. The method, which is general, numerically exact, and computationally not intensive, can easily be generalised to relativistic systems.

Related papers

• Variational approach to open quantum systems with long-range competing interactions [0.0]
  We introduce an efficient and scalable approach to dissipative quantum lattices in one and two dimensions.<n>We showcase the versatility, effectiveness, and unique methodological advantages of our algorithm by simulating the non-equilibrium dynamics and steady states of spin-$frac12$ lattices.<n>This approach offers promising prospects for advancing our understanding of the complex non-equilibrium properties of a diverse variety of experimentally-realizable quantum systems with long-ranged interactions.
  arXiv  Detail & Related papers  (2025-10-02T00:29:00Z)
• Unraveling Open Quantum Dynamics with Time-Dependent Variational Monte Carlo [0.0]
  We introduce a method to simulate open quantum many-body dynamics by combining time-dependent variational Monte Carlo (VMC) with quantum trajectory techniques.<n>Our approach unravels the Lindblad master equation into an ensemble of Schr"odinger equations for a variational ansatz.<n>This work enables large-scale simulations of complex, dissipative quantum systems in higher dimensions, with broad implications for quantum technology and fundamental science.
  arXiv  Detail & Related papers  (2025-06-30T14:56:01Z)
• Infinite-dimensional Extension of the Linear Combination of Hamiltonian Simulation: Theorems and Applications [3.6320083572773507]
  We extend the Linear Combination of Hamiltonian Simulation (LCHS) formula to simulate time-evolution operators in infinite-dimensional spaces.<n>We demonstrate the applicability of the Inf-LCHS theorem to a wide range of non-Hermitian dynamics.<n>Our analysis provides insights into simulating general linear dynamics using a finite number of quantum dynamics.
  arXiv  Detail & Related papers  (2025-02-27T01:58:32Z)
• Simulating continuous-space systems with quantum-classical wave functions [0.0]
  Non-relativistic interacting quantum many-body systems are naturally described in terms of continuous-space Hamiltonians. Current algorithms require discretization, which usually amounts to choosing a finite basis set, inevitably introducing errors. We propose an alternative, discretization-free approach that combines classical and quantum resources in a global variational ansatz.
  arXiv  Detail & Related papers  (2024-09-10T10:54:59Z)
• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• Unbiasing time-dependent Variational Monte Carlo by projected quantum evolution [44.99833362998488]
  We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate quantum systems classically. We prove that the most used scheme, the time-dependent Variational Monte Carlo (tVMC), is affected by a systematic statistical bias. We show that a different scheme based on the solution of an optimization problem at each time step is free from such problems.
  arXiv  Detail & Related papers  (2023-05-23T17:38:10Z)
• Calculating non-linear response functions for multi-dimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion [68.8204255655161]
  We present a methodology for simulating multi-dimensional electronic spectra of molecular aggregates with coupling electronic excitation to a structured environment. A crucial aspect of our approach is that we propagate the NMQSD equation in a doubled system Hilbert space but with the same noise.
  arXiv  Detail & Related papers  (2022-07-06T15:30:38Z)
• Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
  We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity. For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
  arXiv  Detail & Related papers  (2021-12-22T15:27:30Z)
• Effective two-level approximation of a multi-level system driven by coherent and incoherent fields [0.0]
  We describe a multi-level system (MLS) by an effective two-level system (TLS) that best reproduces the coherent and total scattering properties in any saturation regime. The trust interval of the model is quantified for the D2-line of 87Rb atoms but it could be generalized to any closed transition of a multi-level quantum system.
  arXiv  Detail & Related papers  (2021-10-17T19:03:24Z)
• From geometry to coherent dissipative dynamics in quantum mechanics [68.8204255655161]
  We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation. We describe quantum decays in a 2-level system as coherent and continuous processes.
  arXiv  Detail & Related papers  (2021-07-29T18:27:38Z)
• 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)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)

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.