From Vlasov-Poisson to Schr\"odinger-Poisson: dark matter simulation with a quantum variational time evolution algorithm

• URL: http://arxiv.org/abs/2307.06032v3
• Date: Fri, 26 Jan 2024 13:38:50 GMT
• Title: From Vlasov-Poisson to Schr\"odinger-Poisson: dark matter simulation with a quantum variational time evolution algorithm
• Authors: Luca Cappelli, Francesco Tacchino, Giuseppe Murante, Stefano Borgani and Ivano Tavernelli
• Abstract summary: We introduce a quantum algorithm for simulating the Schr"odinger-Poisson (SP) equation by adapting a variational real-time evolution approach to a self-consistent, non-linear, problem. This approach holds the potential to serve as an efficient alternative for solving the Vlasov-Poisson (VP) equation by means of classical algorithms.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Cosmological simulations describing the evolution of density perturbations of a self-gravitating collisionless Dark Matter (DM) fluid in an expanding background, provide a powerful tool to follow the formation of cosmic structures over wide dynamic ranges. The most widely adopted approach, based on the N-body discretization of the collisionless Vlasov-Poisson (VP) equations, is hampered by an unfavorable scaling when simulating the wide range of scales needed to cover at the same time the formation of single galaxies and of the largest cosmic structures. The dynamics described by the VP equations is limited by the rapid increase of the number of resolution elements which is required to simulate an ever growing range of scales. Recent studies showed an interesting mapping of the 6-dimensional+1 (6D+1) VP problem into a more amenable 3D+1 non-linear Schr\"odinger-Poisson (SP) problem for simulating the evolution of DM perturbations. This opens up the possibility of improving the scaling of time propagation simulations using quantum computing. In this paper, we introduce a quantum algorithm for simulating the (SP) equation by adapting a variational real-time evolution approach to a self-consistent, non-linear, problem. To achieve this, we designed a novel set of quantum circuits that establish connections between the solution of the original Poisson equation and the solution of the corresponding time-dependent Schr\"odinger equation. We also analyzed how nonlinearity impacts the variance of observables. Furthermore, we explored how the spatial resolution behaves as the SP dynamics approaches the classical limit and discovered an empirical logarithmic relationship between the required number of qubits and the scale of the SP equation. This entire approach holds the potential to serve as an efficient alternative for solving the Vlasov-Poisson (VP) equation by means of classical algorithms.

Related papers

• Real-time Dynamics of the Schwinger Model as an Open Quantum System with Neural Density Operators [1.0713888959520208]
  This work develops machine learning algorithms to overcome the difficulty of approximating exact quantum states with neural network parametrisations. As a proof of principle demonstration in a QCD-like theory, the approach is applied to solve the Lindblad master equation in the 1+1d lattice Schwinger Model as an open quantum system.
  arXiv  Detail & Related papers  (2024-02-09T18:36:17Z)
• Variational Quantum Simulation of Partial Differential Equations: Applications in Colloidal Transport [0.0]
  We show that real-amplitude ansaetze with full circular entangling layers lead to higher-fidelity solutions. To efficiently encode impulse functions, we propose a graphical mapping technique for quantum states.
  arXiv  Detail & Related papers  (2023-07-14T05:51:57Z)
• Machine learning of hidden variables in multiscale fluid simulation [77.34726150561087]
  Solving fluid dynamics equations often requires the use of closure relations that account for missing microphysics. In our study, a partial differential equation simulator that is end-to-end differentiable is used to train judiciously placed neural networks. We show that this method enables an equation based approach to reproduce non-linear, large Knudsen number plasma physics.
  arXiv  Detail & Related papers  (2023-06-19T06:02:53Z)
• A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules [62.997667081978825]
  We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix. We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
  arXiv  Detail & Related papers  (2023-04-12T18:10:47Z)
• Potential quantum advantage for simulation of fluid dynamics [1.4046104514367475]
  We show that a potential quantum exponential speedup can be achieved to simulate the Navier-Stokes equations governing turbulence using quantum computing. This work suggests that an exponential quantum advantage may exist for simulating nonlinear multiscale transport phenomena.
  arXiv  Detail & Related papers  (2023-03-29T09:14:55Z)
• Quantum algorithm for collisionless Boltzmann simulation of self-gravitating systems [0.0]
  We propose an efficient quantum algorithm to solve the collisionless Boltzmann equation (CBE) We extend the algorithm to perform quantum simulations of self-gravitating systems, incorporating the method to calculate gravity. It will allow us to perform large-scale CBE simulations on future quantum computers.
  arXiv  Detail & Related papers  (2023-03-29T06:59:00Z)
• A quantum algorithm for the linear Vlasov equation with collisions [0.0]
  We present a quantum algorithm that simulates the linearized Vlasov equation with and without collisions. We show that a quadratic speedup in system size is attainable.
  arXiv  Detail & Related papers  (2023-03-06T19:19:30Z)
• 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)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• 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)
• The role of boundary conditions in quantum computations of scattering observables [58.720142291102135]
  Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution. As with present-day calculations, quantum computation strategies still require the restriction to a finite system size. We quantify the volume effects for various $1+1$D Minkowski-signature quantities and show that these can be a significant source of systematic uncertainty.
  arXiv  Detail & Related papers  (2020-07-01T17:43:11Z)

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.