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quantum science seminar #56: Variational quantum algorithm for eigenvalue problems of a class of Schrödinger-type partial differential equations

15 July 2021 @ 6:00 PM 7:00 PM IDT

We develop a variational quantum algorithm to solve partial differential equations (PDE’s) using a space-efficient variational ansatz that merges structured quantum circuits for coarse-graining with Fourier-based interpolation. Variational circuits represent symmetrical smooth functions as the ansatz, and we combine them with different classical optimizers that differ on the gradient calculation: no gradient, numerical gradient and analytic gradient. As benchmark, we show the results for the computation of the ground state of the one-dimensional quantum harmonic oscillator. In idealized quantum computers, the infidelity is of order 10^{−5} with 3 qubits, and these fidelities can be approached in real noisy quantum computers, either directly or through error mitigation techniques. However, we find that the precision is sub-par with other classical methods, suggesting the need for better strategies in the optimization and the evaluation of the cost function itself.references

  1.  Paula García-Molina, Javier Rodríguez-Mediavilla, and Juan José García-RipollSolving partial differential equations in quantum computersarXiv 2104.02668 2021



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