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

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

https://quinfog.hbar.es/