BEGIN:VCALENDAR
VERSION:2.0
METHOD:PUBLISH
CALSCALE:GREGORIAN
PRODID:-//WordPress - MECv5.20.0//EN
X-ORIGINAL-URL:http://mlqx.quantumexcellence.org/
BEGIN:VEVENT
UID:MEC-ac1dd209cbcc5e5d1c6e28598e8cbbe8@mlqx.quantumexcellence.org
DTSTART:20210707T150000Z
DTEND:20210707T152000Z
DTSTAMP:20210610T120300Z
CREATED:20210610
LAST-MODIFIED:20210629
SUMMARY:Paula García-Molina (IFF-CSIC)

**Variational quantum algorithm for eigenvalue problems of a class of Schrödinger-type partial differential equations**
DESCRIPTION:In this work, 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. We implement variational circuits to represent symmetrical smooth functions as the ansatz and combine them with classical optimizers that differ on the gradient calculation: no gradient, numerical gradient and analytic gradient. We apply this method to the computation of the ground state of the one-dimensional quantum harmonic oscillator and the transmon qubit. In idealized quantum computers, we show that the harmonic oscillator can be solved with an infidelity of order 10^{−5} with 3 qubits and the transmon qubit with an error of order 10^{−4} with 4 qubits. We find that these fidelities can be approached in real noisy quantum computers, either directly or through error mitigation techniques. However, we also find that the precision in the estimate of the eigenvalues is still sub-par with other classical methods, suggesting the need for better strategies in the optimization and the evaluation of the cost function itself.\n
URL:http://mlqx.quantumexcellence.org/index.php/events/poster-session/
ORGANIZER;CN=:MAILTO:
END:VEVENT
END:VCALENDAR