Quantum algorithm for nonlinear Burgers' equation for high-speed compressible flows

被引:0
|
作者
Esmaeilifar, Esmaeil [1 ,2 ]
Ahn, Doyeol [3 ]
Myong, Rho Shin [1 ,2 ]
机构
[1] Gyeongsang Natl Univ, Sch Mech & Aerosp Engn, 501Jinjudaero, Jinju 52828, Gyeongnam, South Korea
[2] Gyeongsang Natl Univ, CTRC, 501 Jinjudaero, Jinju 52828, Gyeongnam, South Korea
[3] Univ Seoul, Dept Elect & Comp Engn, 163 Seoulsiripdae Ro, Seoul 02504, South Korea
关键词
MODELS;
D O I
10.1063/5.0231994
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
Recent advances in quantum hardware and quantum computing algorithms promise significant breakthroughs in computational capabilities. Quantum computers can achieve exponential improvements in speed vs classical computers by employing principles of quantum mechanics like superposition and entanglement. However, designing quantum algorithms to solve the nonlinear partial differential equations governing fluid dynamics is challenging due to the inherent linearity of quantum mechanics, which requires unitary transformation. In this study, we first address in detail several challenges that arise when trying to deal with nonlinearity using quantum algorithms and then propose a novel pure quantum algorithm for solving a nonlinear Burgers' equation. We employed multiple copies of the state vector to calculate the nonlinear term, which is necessary due to the no-cloning theorem. By reusing qubits from the previous time steps, we significantly reduced the number of qubits required for multi-step simulations, from exponential/quadratic scaling in earlier studies to linear scaling in time in the current study. We also employed various advanced quantum techniques, including block-encoding, quantum Hadamard product, and the linear combination of unitaries, to design a quantum circuit for the proposed quantum algorithm. The quantum circuit was executed on quantum simulators, and the obtained results demonstrated excellent agreement with those from classical simulations.
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页数:17
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