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Variational quantum Monte Carlo (VMC) combined with neural-network quantum states offers a novel angle of attack on the curse-of-dimensionality encountered in a particular class of partial differential equations (PDEs); namely, the real- and imaginary time-dependent Schr\"odinger equation.
A variational solution of the time-dependent Schrodinger equation
AD McLachlan · 1964
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Solving high-dimensional partial differential equations using deep learning
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John Preskill · 2018
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Variational quantum algorithms
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Joan Bruna, Benjamin Peherstorfer, and Eric Vanden-Eijnden · 2022
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