Video URL http://pirsa.org/21120014
Quantum computers are expected to dramatically outperform classical computers for certain computational problems. While there has been extensive previous work for linear dynamics and discrete models, for more complex realistic problems arising in physical and social science, engineering, and medicine, the capability of quantum computing is far from well understood. One fundamental challenge is the substantial difference between the linear dynamics of a system of qubits and real-world systems with continuum, stochastic, and nonlinear behaviors. Utilizing advanced linear algebra techniques and nonlinear analysis, I attempt to build a bridge between classical and quantum mechanics, understand and optimize the power of quantum computation, and discover new quantum speedups over classical algorithms with provable guarantees. In this talk, I would like to cover quantum algorithms for scientific computational problems, including topics such as linear, nonlinear, and stochastic differential equations, with applications in areas such as quantum dynamics, biology and epidemiology, fluid dynamics, and finance.
Quantum spectral methods for differential equations, Communications in Mathematical Physics 375, 1427-1457 (2020), https://arxiv.org/abs/1901.00961
High-precision quantum algorithms for partial differential equations, Quantum 5, 574 (2021), https://arxiv.org/abs/2002.07868
Efficient quantum algorithm for dissipative nonlinear differential equations, Proceedings of the National Academy of Sciences 118, 35 (2021), https://arxiv.org/abs/2011.03185
Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance, Quantum 5, 481 (2021), https://arxiv.org/abs/2012.06283
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