A useful fundamental speed limit for the imaginary-time Schrodinger equation

TL;DR

This paper establishes a fundamental speed limit for the imaginary-time Schrödinger equation, extending quantum speed limit concepts to imaginary-time dynamics and analyzing implications for quantum annealing.

Contribution

It derives a new speed limit for the imaginary-time Schrödinger equation inspired by recent quantum speed limit work, applicable to quantum annealing.

Findings

The speed limit bounds the optimal computational time in imaginary-time quantum annealing.

The lower bound for the Grover problem in imaginary-time quantum annealing is proportional to log N.

The result aligns with previous studies on quantum annealing efficiency.

Abstract

The quantum speed limit (QSL), or the energy-time uncertainty relation, gives a fundamental speed limit for quantum dynamics. Recently, Kieu [arXiv:1702.00603] derived a new class of QSL which is not only formal but also suitable for actually evaluating the speed limit. Inspired by his work, we obtain a similar speed limit for the imaginary-time Schr\"odinger equation. Using this new bound, we show that the optimal computational time of the Grover problem in imaginary-time quantum annealing is bounded from below by $\log N$, which is consistent with a result of previous study.