Speeding up quantum adiabatic processes with dynamical quantum geometric tensor

TL;DR

This paper introduces the dynamical quantum geometric tensor as a metric to optimize control protocols, enabling faster quantum adiabatic processes with minimal non-adiabatic transitions, demonstrated through two models.

Contribution

It proposes a novel metric-based approach to accelerate quantum adiabatic processes, reducing the need for slow parameter variation.

Findings

Optimal protocols follow geodesic paths in control space.

Transition probability is bounded by a function of adiabatic length and operation time.

Validated approach with Landau-Zener and transverse Ising models.

Abstract

For adiabatic controls of quantum systems, the non-adiabatic transitions are reduced by increasing the operation time of processes. Perfect quantum adiabaticity usually requires the infinitely slow variation of control parameters. In this paper, we propose the dynamical quantum geometric tensor, as a metric in the control parameter space, to speed up quantum adiabatic processes and reach quantum adiabaticity in relatively short time. The optimal protocol to reach quantum adiabaticity is to vary the control parameter with a constant velocity along the geodesic path according to the metric. For the system initiated from the n-th eigenstate, the transition probability in the optimal protocol is bounded by P_{n}(t)\leq4\mathcal{L}_{n}^{2}/\tau^{2} with the operation time \tau and the quantum adiabatic length \mathcal{L}_{n} induced by the metric. Our optimization strategy is illustrated via two explicit models, the Landau-Zener model and the one-dimensional transverse Ising model.