Dynamical decoupling methods in nanoscale NMR

Publications from 2021
C. Munuera-Javaloy, R. Puebla, J. Casanova
Nuclear magnetic resonance (NMR) schemes can be applied to micron-, and nanometer-sized samples by the aid of quantum sensors such as nitrogen vacancy (NV) color centers in diamond. These minute devices allow for magnetometry of nuclear spin ensembles with high spatial and frequency resolution at ambient conditions, thus having a clear impact in different areas such as chemistry, biology, medicine, and material sciences. In practice, NV quantum sensors are driven by microwave (MW) control fields with a twofold objective: On the one hand, MW fields bridge the energy gap between NV and nearby nuclei which enables a coherent and selective coupling among them while, on the other hand, MW fields remove environmental noise on the NV leading to enhanced interrogation time. In this work we review distinct MW radiation patterns, or dynamical decoupling techniques, for nanoscale NMR applications.

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.

A perspective on scaling up quantum computation with molecular spins

Publications from 2021
S. Carretta, D. Zueco, A. Chiesa, Á. Gómez-León and F. Luis
Artificial magnetic molecules can contribute to progressing toward large scale quantum computation by (a) integrating multiple quantum resources and (b) reducing the computational costs of some applications. Chemical design, guided by theoretical proposals, allows embedding nontrivial quantum functionalities in each molecular unit, which then acts as a microscopic quantum processor able to encode error protected logical qubits or to implement quantum simulations. Scaling up even further requires “wiring-up” multiple molecules. We discuss how to achieve this goal by the coupling to on-chip superconducting resonators. The potential advantages of this hybrid approach and the challenges that still lay ahead are critically reviewed.