Quantum speed limit for robust state characterization and engineering

TL;DR

This paper introduces a new explicitly-computable quantum speed limit (QSL) to measure state robustness and formulates an efficient Hamiltonian engineering method to enhance robustness against decoherence in open quantum systems.

Contribution

It derives a tighter, explicitly-computable QSL applicable to Markovian open systems and formulates a convex optimization approach for Hamiltonian engineering to improve state robustness.

Findings

The new QSL is tighter than previous bounds in low decoherence regimes.

Hamiltonian engineering reduces decoherence effects effectively.

The approach is demonstrated with multiple quantum system examples.

Abstract

In this paper, we propose a concept to use a quantum speed limit (QSL) as a measure of robustness of states, defining that a state with bigger QSL is more robust. In this perspective, it is important to have an explicitly-computable QSL, because then we can formulate an engineering problem of Hamiltonian that makes a target state robust against decoherence. Hence we derive a new explicitly-computable QSL that is applicable to general Markovian open quantum systems. This QSL is tighter than another explicitly-computable QSL, in an important setup such that decoherence is small. Also the Hamiltonian engineering problem with this QSL is a quadratic convex optimization problem, and thus it is efficiently solvable. The idea of robust state characterization and the Hamiltonian engineering, in terms of QSL, is demonstrated with several examples.