Quantum Information and Foundations Group – CSIC


Work statistics and symmetry breaking in an excited-state quantum phase transition

Publications from 2021
Z. Mzaouali, R. Puebla, J. Goold, M. El Baz, and S. Campbell
We examine how the presence of an excited state quantum phase transition manifests in the dynamics of a many-body system subject to a sudden quench. Focusing on the Lipkin-Meshkov-Glick model initialized in the ground state of the ferromagnetic phase, we demonstrate that the work probability distribution displays non-Gaussian behavior for quenches in the vicinity of the excited state critical point. Furthermore, we show that the entropy of the diagonal ensemble is highly susceptible to critical regions, making it a robust and practical indicator of the associated spectral characteristics. We assess the role that symmetry breaking has on the ensuing dynamics, highlighting that its effect is only present for quenches beyond the critical point. Finally, we show that similar features persist when the system is initialized in an excited state and briefly explore the behavior for initial states in the paramagnetic phase.

Solving partial differential equations in quantum computers

Publications from 2021
Paula García-Molina, Javier Rodríguez-Mediavilla, Juan José García-Ripoll
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.