Optimal suppression of defect generation during a passage across a quantum critical point

TL;DR

This paper develops a gradient-based optimal control method to minimize defect formation during quantum phase transitions, demonstrating that power law quenches are effective and robust, and identifying a critical speed limit for quantum evolution.

Contribution

It introduces a deterministic optimal control approach to suppress defects in quantum critical dynamics, highlighting the effectiveness of power law quenches and their robustness against noise.

Findings

Power law quenches minimize defect density effectively.

Optimized quenches are robust against noise.

A critical ratio of quench duration to system size marks a speed limit.

Abstract

The dynamics of quantum phase transitions are inevitably accompanied by the formation of defects when crossing a quantum critical point. For a generic class of quantum critical systems, we solve the problem of minimizing the production of defects through the use of a gradient-based deterministic optimal control algorithm. By considering a finite size quantum Ising model with a tunable global transverse field, we show that an optimal power law quench of the transverse field across the Ising critical point works well at minimizing the number of defects, in spite of being drawn from a subset of quench profiles. These power law quenches are shown to be inherently robust against noise. The optimized defect density exhibits a transition at a critical ratio of the quench duration to the system size, which we argue coincides with the intrinsic speed limit for quantum evolution.