Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Probabilistic Engineering Mechanics

Eigenvalue analysis of stochastic structural systems: A quantum computing approach

Leonidas Taliadouros, Ilias G. Mavromatis, Ioannis A. Kougioumtzoglou

Published Jul 1, 2025• 3 citations
Publisher
DOI
10.1016/j.probengmech.2025.103814

Related papers

Quantum algorithms for the generalized eigenvalue problem

Jin‐Min Liang, Shu‐Qian Shen, Ming Li +1 more

arXiv:2112.02554•Quantum Information Processing•Dec 28, 2021•16 citations

Decomposition‐Free Variational Quantum Eigensolvers for Natural Frequency Analysis in Structural Engineering

Yongchun Xu, Heng Hu

ABSTRACT The analysis of natural frequency is an important problem of structural engineering, where complex structures often lead to expensive eigenvalue problems. Variational quantum eigensolvers provide a potentially efficient solution by using quantum computing, but their application is limited by the costly need to decompose system matrices into a linear combination of unitaries. In this work, we apply a recently proposed decomposition‐free method from linear systems to eigenvalue problems in structural engineering. Specifically, we develop two algorithms based on this method, the decomposition‐free variational quantum eigensolver (DF‐VQE) and generalized eigensolver (DF‐VQGE) for the standard eigenvalue problems and the generalized eigenvalue problems, respectively. In these algorithms, the Rayleigh Quotient and generalized Rayleigh Quotient cost evaluations are reformulated so that the need for matrix decomposition is bypassed. The central technical step in this application is to use vectorization to encode the system matrices directly into quantum state vectors, allowing their properties to be computed via a standard swap test quantum circuit. The proposed methods are validated on a quantum simulator with three representative structural engineering problems, including a 1D bar, a 2D beam, and a 3D truss bridge, obtaining results that align well with reference solutions from classical finite element analysis. We also discuss the quantum state preparation challenge that must be addressed before this formulation can be connected to meaningful quantum advantage.

International Journal for Numerical Methods in Engineering•Aug 21, 2026•0 citations

A Recursive Method of the Stochastic State Selection for Quantum Spin Systems

Tomo Munehisa, Yasuko Munehisa

In this paper we propose the recursive stochastic state selection method, an extension of the recently developed stochastic state selection method in Monte Carlo calculations for quantum spin systems. In this recursive method we use intermediate states to define probability functions for stochastic state selections. Then we can diminish variances of samplings when we calculate expectation values of the powers of the Hamiltonian. In order to show the improvement we perform numerical calculations of the spin-1/2 anti-ferromagnetic Heisenberg model on the triangular lattice. Examining results on the ground state of the 21-site system we confide this method in its effectiveness. We also calculate the lowest and the excited energy eigenvalues as well as the static structure factor for the 36-site system. The maximum number of basis states kept in a computer memory for this system is about 3.6 x 10**7. Employing a translationally invariant initial trial state, we evaluate the lowest energy eigenvalue within 0.5 % of the statistical errors.

arXiv:cond-mat/0312418•Journal of the Physical Society of Japan•Aug 15, 2004•7 citations

Quantum techniques for eigenvalue problems

Dean Lee

arXiv:2307.03889•The European Physical Journal A•Nov 20, 2023•4 citations

Contour Integral-based Quantum Algorithm for Estimating Matrix Eigenvalue Density

Yasunori Futamura, Xiucai Ye, Tetsuya Sakurai

The eigenvalue density of a matrix plays an important role in various types of scientific computing such as electronic-structure calculations. In this paper, we propose a quantum algorithm for computing the eigenvalue density in a given interval. Our quantum algorithm is based on a method that approximates the eigenvalue counts by applying the numerical contour integral and the stochastic trace estimator applied to a matrix involving resolvent matrices. As components of our algorithm, the HHL solver is applied to an augmented linear system of the resolvent matrices, and the quantum Fourier transform (QFT) is adopted to represent the operation of the numerical contour integral. To reduce the size of the augmented system, we exploit a certain symmetry of the numerical integration. We also introduce a permutation formed by CNOT gates to make the augmented system solution consistent with the QFT input. The eigenvalue count in a given interval is derived as the probability of observing a bit pattern in a fraction of the qubits of the output state.

arXiv:2112.05395•Dec 10, 2021•0 citations

Stochastic Methods and Computer Techniques in Quantum Dynamics

Springer eBooks•Jan 1, 1984•6 citations
ABSTRACT The analysis of natural frequency is an important problem of structural engineering, where complex structures often lead to expensive eigenvalue problems. Variational quantum eigensolvers provide a potentially efficient solution by using quantum computing, but their application is limited by the costly need to decompose system matrices into a linear combination of unitaries. In this work, we apply a recently proposed decomposition‐free method from linear systems to eigenvalue problems in structural engineering. Specifically, we develop two algorithms based on this method, the decomposition‐free variational quantum eigensolver (DF‐VQE) and generalized eigensolver (DF‐VQGE) for the standard eigenvalue problems and the generalized eigenvalue problems, respectively. In these algorithms, the Rayleigh Quotient and generalized Rayleigh Quotient cost evaluations are reformulated so that the need for matrix decomposition is bypassed. The central technical step in this application is to use vectorization to encode the system matrices directly into quantum state vectors, allowing their properties to be computed via a standard swap test quantum circuit. The proposed methods are validated on a quantum simulator with three representative structural engineering problems, including a 1D bar, a 2D beam, and a 3D truss bridge, obtaining results that align well with reference solutions from classical finite element analysis. We also discuss the quantum state preparation challenge that must be addressed before this formulation can be connected to meaningful quantum advantage.
In this paper we propose the recursive stochastic state selection method, an extension of the recently developed stochastic state selection method in Monte Carlo calculations for quantum spin systems. In this recursive method we use intermediate states to define probability functions for stochastic state selections. Then we can diminish variances of samplings when we calculate expectation values of the powers of the Hamiltonian. In order to show the improvement we perform numerical calculations of the spin-1/2 anti-ferromagnetic Heisenberg model on the triangular lattice. Examining results on the ground state of the 21-site system we confide this method in its effectiveness. We also calculate the lowest and the excited energy eigenvalues as well as the static structure factor for the 36-site system. The maximum number of basis states kept in a computer memory for this system is about 3.6 x 10**7. Employing a translationally invariant initial trial state, we evaluate the lowest energy eigenvalue within 0.5 % of the statistical errors.
The eigenvalue density of a matrix plays an important role in various types of scientific computing such as electronic-structure calculations. In this paper, we propose a quantum algorithm for computing the eigenvalue density in a given interval. Our quantum algorithm is based on a method that approximates the eigenvalue counts by applying the numerical contour integral and the stochastic trace estimator applied to a matrix involving resolvent matrices. As components of our algorithm, the HHL solver is applied to an augmented linear system of the resolvent matrices, and the quantum Fourier transform (QFT) is adopted to represent the operation of the numerical contour integral. To reduce the size of the augmented system, we exploit a certain symmetry of the numerical integration. We also introduce a permutation formed by CNOT gates to make the augmented system solution consistent with the QFT input. The eigenvalue count in a given interval is derived as the probability of observing a bit pattern in a fraction of the qubits of the output state.