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Boundary treatment for variational quantum simulations of partial differential equations on quantum computers
Citation Link: https://doi.org/10.15480/882.14303
Publikationstyp
Journal Article
Date Issued
2024-12-10
Sprache
English
Author(s)
Clerici, Francesco
Scandurra, Leonardo
de Villiers, Eugene
TORE-DOI
Journal
Volume
288
Article Number
106508
Citation
Computers and Fluids 288: 106508 (2024)
Publisher DOI
Scopus ID
Publisher
Elsevier
The paper presents a variational quantum algorithm to solve initial–boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum framework that is well suited for quantum computers of the current noisy intermediate-scale quantum era. The partial differential equation is initially translated into an optimal control problem with a modular control-to-state operator (ansatz). The objective function and its derivatives required by the optimizer can efficiently be evaluated on a quantum computer by measuring an ancilla qubit, while the optimization procedure employs classical hardware. The focal aspect of the study is the treatment of boundary conditions, which is tailored to the properties of the quantum hardware using a correction technique. For this purpose, the boundary conditions and the discretized terms of the partial differential equation are decomposed into a sequence of unitary operations and subsequently compiled into quantum gates. The accuracy and gate complexity of the approach are assessed for second-order partial differential equations by classically emulating the quantum hardware. The examples include steady and unsteady diffusive transport equations for a scalar property in combination with various Dirichlet, Neumann, or Robin conditions. The results of this flexible approach display a robust behavior and a strong predictive accuracy in combination with a remarkable polylog complexity scaling in the number of qubits of the involved quantum circuits. Remaining challenges refer to adaptive ansatz strategies that speed up the optimization procedure.
Subjects
Boundary conditions | Computational fluid dynamics | Quantum computing | Variational quantum algorithms
DDC Class
510: Mathematics
530: Physics
621.38: Electronics, Communications Engineering
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