QAFE$^2$: Quantum Accelerated Multiscale Finite Element Analysis

• URL: http://arxiv.org/abs/2604.06130v1
• Date: Tue, 07 Apr 2026 17:41:00 GMT
• Title: QAFE$^2$: Quantum Accelerated Multiscale Finite Element Analysis
• Abstract summary: We introduce a quantum-classical framework for multiscale finite element analysis (QAFE$2$)<n>At the single-RVE level, the proposed quantum solver attains polylogarithmic complexity with respect to the microscopic discretisation size.<n>QAFE$2$ exploits quantum superposition and entanglement to evaluate, in a single quantum execution, the entire ensemble of RVE problems associated with all macroscopic quadrature points.
• Score: 0.6383185503510568
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The computational cost of concurrent multiscale finite element methods is dominated by the repeated solution of microscopic representative volume element (RVE) problems at macroscopic quadrature points. In this work, we introduce a quantum-classical framework for multiscale finite element analysis (QAFE$^2$) that leverages quantum parallelism to fundamentally alter the scaling of RVE-based homogenisation. At the single-RVE level, the proposed quantum solver attains polylogarithmic complexity with respect to the microscopic discretisation size, yielding an exponential asymptotic speedup over the best available classical solvers. More importantly, QAFE$^2$ exploits quantum superposition and entanglement to evaluate, in a single quantum execution, the entire ensemble of RVE problems associated with all macroscopic quadrature points. This capability is a form of intrinsic quantum concurrency with no classical analogue. Numerical experiments on one- and two-dimensional model problems with known analytical solutions confirm the accuracy of the proposed formulation and verify the theoretical computational scaling and parallel performance.

Related papers

• Approximate Quantum Linear Solvers for Hybrid CFD: End-to-End Analysis with a Chebyshev-LCU Approach [0.0]
  We analyze how an approximate quantum linear solver affects the convergence of the overall CFD iteration.<n>We develop an approximate qubitization-based solver (Cheb-LCU) that can reduce quantum resource requirements.
  arXiv  Detail & Related papers  (2026-05-31T07:20:42Z)
• QAMA: Scalable Quantum Annealing Multi-Head Attention Operator for Deep Learning [48.12231190677108]
  Quantum Annealing Multi-Head Attention (QAMA) is proposed, a novel drop-in operator that reformulates attention as an energy-based Hamiltonian optimization problem.<n>In this framework, token interactions are encoded into binary quadratic terms, and quantum annealing is employed to search for low-energy configurations.<n> Empirically, evaluation on both natural language and vision benchmarks shows that, across tasks, accuracy deviates by at most 2.7 points from standard multi-head attention.
  arXiv  Detail & Related papers  (2025-04-15T11:29:09Z)
• An Implementation of the Finite Element Method in Hybrid Classical/Quantum Computers [0.0]
  This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum computers.<n>Q-FEM keeps the structure of the finite element discretization intact allowing for the use of variable element lengths and material coefficients in FEM discretization.
  arXiv  Detail & Related papers  (2024-11-13T21:32:30Z)
• Parallel Quantum Computing Simulations via Quantum Accelerator Platform Virtualization [44.99833362998488]
  We present a model for parallelizing simulation of quantum circuit executions. The model can take advantage of its backend-agnostic features, enabling parallel quantum circuit execution over any target backend.
  arXiv  Detail & Related papers  (2024-06-05T17:16:07Z)
• Towards Quantum Computational Mechanics [1.530480694206666]
  We show how quantum computing can be used to solve representative element volume (RVE) problems in computational homogenisation. Our quantum RVE solver attains exponential acceleration with respect to classical solvers.
  arXiv  Detail & Related papers  (2023-12-06T12:53:02Z)
• Approximation Algorithms for Quantum Max-$d$-Cut [42.248442410060946]
  The Quantum Max-$d$-Cut problem involves finding a quantum state that maximizes the expected energy associated with the projector onto the antisymmetric subspace of two, $d$-dimensional qudits over all local interactions. We develop an algorithm that finds product-state solutions of mixed states with bounded purity that achieve non-trivial performance guarantees.
  arXiv  Detail & Related papers  (2023-09-19T22:53:17Z)
• Quantum benefit of the quantum equation of motion for the strongly coupled many-body problem [0.0]
  The quantum equation of motion (qEOM) is a hybrid quantum-classical algorithm for computing excitation properties of a fermionic many-body system. We demonstrate explicitly that the qEOM exhibits a quantum benefit due to the independence of the number of required quantum measurements.
  arXiv  Detail & Related papers  (2023-09-18T22:10:26Z)
• 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)
• A Quantum Approach for Stochastic Constrained Binary Optimization [2.6803492658436032]
  Quantum-based algorithms have been shown to generate high-quality solutions to hard problems. This work puts forth quantum vectors to cope with binary quadratically constrained programs. The method builds upon dual decomposition and entails solving a sequence of judiciously modified standard VQE tasks.
  arXiv  Detail & Related papers  (2023-01-04T04:24:26Z)
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive [52.77024349608834]
  We present a self consistent field approach (SCF) within the Adaptive Derivative-Assembled Problem-Assembled Ansatz Variational Eigensolver (ADAPTVQE) This framework is used for efficient quantum simulations of chemical systems on nearterm quantum computers.
  arXiv  Detail & Related papers  (2022-12-21T23:15:17Z)
• Towards Neural Variational Monte Carlo That Scales Linearly with System Size [67.09349921751341]
  Quantum many-body problems are central to demystifying some exotic quantum phenomena, e.g., high-temperature superconductors. The combination of neural networks (NN) for representing quantum states, and the Variational Monte Carlo (VMC) algorithm, has been shown to be a promising method for solving such problems. We propose a NN architecture called Vector-Quantized Neural Quantum States (VQ-NQS) that utilizes vector-quantization techniques to leverage redundancies in the local-energy calculations of the VMC algorithm.
  arXiv  Detail & Related papers  (2022-12-21T19:00:04Z)
• Analyzing Prospects for Quantum Advantage in Topological Data Analysis [35.423446067065576]
  We analyze and optimize an improved quantum algorithm for topological data analysis. We show that super-quadratic quantum speedups are only possible when targeting a multiplicative error approximation. We argue that quantum circuits with tens of billions of Toffoli can solve seemingly classically intractable instances.
  arXiv  Detail & Related papers  (2022-09-27T17:56:15Z)
• VQE Method: A Short Survey and Recent Developments [5.9640499950316945]
  The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues and eigenvalues of a Hamiltonian. VQE has been successfully applied to solve the electronic Schr"odinger equation for a variety of small molecules. Modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatze.
  arXiv  Detail & Related papers  (2021-03-15T16:25:36Z)

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.