Shishaev G.Yu.
shishaevgy@hw.tpu.ru
Graduated from Tomsk State University (2006), specialization "Mathematical Methods in Economics".PhD.
Deputy Director for Research Activities of the National Research Tomsk Polytechnic University; Center for Training and Retraining of Oil and Gas Specialists.
Geological simulation and issues of petroleum fields development
| Article # 24_2026 | submitted on 06/29/2026 displayed on website on 09/21/2026 |
| 14 p. | Amirkhanov D.S., Merzlikin B.S., Shishaev G.Yu., Shirokov A.V., Matveev I.V. |
| Analysis of the applicability of the variational quantum linear solver to fluid filtration modeling in a core sample | |
| This paper assesses the applicability of quantum linear-system algorithms – the Harrow–Hassidim–Lloyd algorithm and the variational quantum linear solver – to the steady-state filtration of an incompressible fluid in a porous medium. In the eikonal (quasi-stationary) approximation, the initial–boundary value problem for the pressure diffusivity equation reduces to the Poisson equation for pressure, which is discretized by the finite-difference method into a system of linear algebraic equations. The structural correspondences between the problem formulation and the requirements of the quantum algorithms are analyzed, and the issues of data encoding, quantum state preparation, and result extraction are discussed. The approach is validated on a tomographic image of a real core sample slice: for an 8×8 node region, the solutions obtained by the variational quantum linear solver and by a classical direct matrix-decomposition method are compared in terms of the pressure and filtration-velocity fields, with an estimate of the absolute error. The variational quantum linear solver is shown to reproduce a pressure distribution and velocity field consistent with the classical solution, confirming the correct operation of the hybrid quantum-classical approach on a model example. The results demonstrate the feasibility of using variational quantum linear-solver algorithms for digital core modeling, outline their advantages and fundamental limitations in the context of subsurface hydrodynamics, and define the direction of further research on larger models. Keywords: porous-media fluid filtration, systems of linear equations, variational quantum algorithms, variational quantum linear solver, Harrow–Hassidim–Lloyd algorithm, finite-difference method, Poisson equation, digital core modeling. |
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| article citation | Amirkhanov D.S., Merzlikin B.S., Shishaev G.Yu., Shirokov A.V., Matveev I.V. Analysis of the applicability of the variational quantum linear solver to fluid filtration modeling in a core sample. Neftegazovaya Geologiya. Teoriya I Praktika, 2026, vol. 21, no. 3, available at: https://www.ngtp.ru/rub/2026/24_2026.html EDN: SLOFKA |
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Amaral C.A., Oliveira V.L., Salazar J.P.L.C., Duzzioni E.I. A review of quantum machine learning and quantum-inspired applied methods to computational fluid dynamics. Brazilian Journal of Physics, 2026, vol. 56, no. 1, p. 39. DOI: 10.1007/s13538-025-01959-8
Bravo-Prieto C., LaRose R., Cerezo M., Subasi Y., Cincio L., Coles P. J. Variational quantum linear solver. Quantum, 2023, vol. 7, p. 1188. DOI: 10.22331/q-2023-11-22-1188
Harrow A.W., Hassidim A., Lloyd S. Quantum algorithm for linear systems of equations. Physical Review Letters, 2009, vol. 103, no. 15, p. 150502. DOI: 10.1103/PhysRevLett.103.150502
Liu Y.Y., Chen Z., Shu C., Rebentrost P., Liu Y.G., Chew S.C., Khoo B.C., Cui Y.D. A variational quantum algorithm-based numerical method for solving potential and Stokes flows. Ocean Engineering, 2024, vol. 292, p. 116494. DOI: 10.1016/j.oceaneng.2023.116494
Rao X. Performance study of variational quantum linear solver with an improved ansatz for reservoir flow equations. Physics of Fluids, 2024a, vol. 36, no. 4, p. 047104. DOI: 10.1063/5.0201739
Rao X. Quantum computing implementation for solving pressure equations in reservoir numerical simulation. 6th Asia Pacific Meeting on Near Surface Geoscience and Engineering. Tsukuba, Japan: EAGE, 2024b, pp. 1-5. DOI: 10.3997/2214-4609.202472014
Rao X. The first application of quantum computing algorithm in streamline-based simulation of water-flooding reservoirs. Abu Dhabi International Petroleum Exhibition and Conference (ADIPEC). Abu Dhabi: SPE, 2024c, paper SPE-221850-MS. DOI: 10.2118/221850-MS
Sahimi M., Tahmasebi P. The potential of quantum computing for geoscience. Transport in Porous Media, 2022, vol. 145, no. 2, pp. 367-387. DOI: 10.1007/s11242-022-01855-8
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Trahan C.J., Loveland M., Davis N., Ellison E. A variational quantum linear solver application to discrete finite-element methods. Entropy, 2023, vol. 25, no. 4. 580 p. DOI: 10.3390/e25040580