Solving wave equation problems on D-Wave quantum annealers

• URL: http://arxiv.org/abs/2507.13724v1
• Date: Fri, 18 Jul 2025 08:06:43 GMT
• Title: Solving wave equation problems on D-Wave quantum annealers
• Authors: Aigerim Bazarkhanova, Alejandro J. Castro, Antonio A. Valido,
• Abstract summary: We solve the one-dimensional Helmholtz equation in several scenarios using the quantum annealer provided by the D-Wave systems within a pseudospectral scheme.<n>We assess the performance of different strategies of encoding based on algebraic arguments and the adiabatic condition.
• Score: 44.99833362998488
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We solve the one-dimensional Helmholtz equation in several scenarios using the quantum annealer provided by the D-Wave systems within a pseudospectral scheme, where its solution is encoded into certain set of suitable basis functions. We assess the performance of different strategies of encoding based on algebraic arguments and the adiabatic condition, and benchmark these against the classical heuristic simulating annealing algorithm. In particular, we compute the minimum energy gap, the so-called dynamic range and the mean squared error to assess the numerical stability, consistency and accuracy of the solutions returned by each strategy. Our work stresses out the importance of developing custom embedded techniques ensuring well-conditioned algebraic systems. In particular, we find out that encoding strategies retrieving algebraic systems exhibiting full-rank and small dynamic ranges enhance the performance of the quantum annealer even under polychromatic driving and for intricate initial conditions. We further discuss the prospect of developing hybrid quantum-classical schemes enable to meet suitable algebraic and adiabatic conditions simultaneously.

Related papers

• Self-Supervised Coarsening of Unstructured Grid with Automatic Differentiation [55.88862563823878]
  In this work, we present an original algorithm to coarsen an unstructured grid based on the concepts of differentiable physics.<n>We demonstrate performance of the algorithm on two PDEs: a linear equation which governs slightly compressible fluid flow in porous media and the wave equation.<n>Our results show that in the considered scenarios, we reduced the number of grid points up to 10 times while preserving the modeled variable dynamics in the points of interest.
  arXiv  Detail & Related papers  (2025-07-24T11:02:13Z)
• Practical Application of the Quantum Carleman Lattice Boltzmann Method in Industrial CFD Simulations [44.99833362998488]
  This work presents a practical numerical assessment of a hybrid quantum-classical approach to CFD based on the Lattice Boltzmann Method (LBM)<n>We evaluate this method on three benchmark cases featuring different boundary conditions, periodic, bounceback, and moving wall.<n>Our results confirm the validity of the approach, achieving median error fidelities on the order of $10-3$ and success probabilities sufficient for practical quantum state sampling.
  arXiv  Detail & Related papers  (2025-04-17T15:41:48Z)
• Quantum Wave Simulation with Sources and Loss Functions [0.0]
  We present a quantum algorithmic framework for simulating linear, anti-Hermitian (lossless) wave equations in heterogeneous media.<n>Our framework is compatible with standard numerical discretization schemes.<n>We show that subspace energies can be extracted and wave fields compared through an $l$ loss function.
  arXiv  Detail & Related papers  (2024-11-26T17:42:55Z)
• Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions [39.58317527488534]
  We propose a variational strategy based on symmetry-preserving cost functions to iteratively construct a reduced subspace for extraction of low-lying energy states.<n>As a proof of concept, we test the proposed algorithms on H4 chain and ring, targeting both the ground-state energy and the charge gap.
  arXiv  Detail & Related papers  (2024-11-25T20:33:47Z)
• Towards Variational Quantum Algorithms for generalized linear and nonlinear transport phenomena [0.0]
  This article proposes a Variational Quantum Algorithm to solve linear and nonlinear thermofluid dynamic transport equations.<n>The hybrid classical-quantum framework is applied to problems governed by the heat, wave, and Burgers' equation in combination with different engineering boundary conditions.
  arXiv  Detail & Related papers  (2024-11-22T13:39:49Z)
• Demonstration of Scalability and Accuracy of Variational Quantum Linear Solver for Computational Fluid Dynamics [0.0]
  This paper presents an exploration of quantum methodologies aimed at achieving high accuracy in solving such a large system of equations. We consider the 2D, transient, incompressible, viscous, non-linear coupled Burgers equation as a test problem. Our findings demonstrate that our quantum methods yield results comparable in accuracy to traditional approaches.
  arXiv  Detail & Related papers  (2024-09-05T04:42:24Z)
• Solving reaction dynamics with quantum computing algorithms [42.408991654684876]
  We study quantum algorithms for response functions, relevant for describing different reactions governed by linear response.<n>We focus on nuclear-physics applications and consider a qubit-efficient mapping on the lattice, which can efficiently represent the large volumes required for realistic scattering simulations.
  arXiv  Detail & Related papers  (2024-03-30T00:21:46Z)
• Hybrid quantum-classical and quantum-inspired classical algorithms for solving banded circulant linear systems [0.8192907805418583]
  We present an efficient algorithm based on convex optimization of combinations of quantum states to solve for banded circulant linear systems. By decomposing banded circulant matrices into cyclic permutations, our approach produces approximate solutions to such systems with a combination of quantum states linear to $K$. We validate our methods with classical simulations and actual IBM quantum computer implementation, showcasing their applicability for solving physical problems such as heat transfer.
  arXiv  Detail & Related papers  (2023-09-20T16:27:16Z)
• A quantum-classical decomposition of Gaussian quantum environments: a stochastic pseudomode model [0.8258451067861933]
  We show that the effect of a Bosonic environment linearly coupled to a quantum system can be simulated by a Gaussian Lindblad master equation. For a subset of rational spectral densities, all parameters are explicitly specified without the need of any fitting procedure.
  arXiv  Detail & Related papers  (2023-01-18T14:17:17Z)
• Quadratic Unconstrained Binary Optimisation via Quantum-Inspired Annealing [58.720142291102135]
  We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. We benchmark our approach for large scale problem instances with tuneable hardness and planted solutions.
  arXiv  Detail & Related papers  (2021-08-18T09:26:17Z)
• 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)
• Adaptive variational quantum eigensolvers for highly excited states [4.038971004196936]
  Highly excited states of quantum many-body systems are central objects in the study of quantum dynamics and thermalization. We propose an adaptive variational algorithm, adaptive VQE-X, that self-generates a variational ansatz for arbitrary eigenstates of a many-body Hamiltonian $H$.
  arXiv  Detail & Related papers  (2021-04-26T15:03:51Z)
• 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)

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.