Quantum Speed Limits from Symmetries in Quantum Control

TL;DR

This paper establishes fundamental quantum speed limits based on symmetries in control Hamiltonians, providing practical bounds for implementing unitaries and Hamiltonians in quantum systems without solving complex dynamics.

Contribution

It introduces a Lie algebraic framework linking symmetries to quantum speed limits and offers calculable bounds applicable to various physical quantum systems.

Findings

Derived bounds for control time to implement target unitaries.

Established bounds for the time to realize target Hamiltonian dynamics.

Validated bounds on systems like qubits, spin chains, and Rydberg atoms.

Abstract

In quantum control, quantum speed limits provide fundamental lower bounds on the time that is needed to implement certain unitary transformations. Using Lie algebraic methods, we link these speed limits to symmetries of the control Hamiltonians and provide quantitative bounds that can be calculated without solving the controlled system dynamics. In particular we focus on two scenarios: On one hand, we provide bounds on the time that is needed for a control system to implement a given target unitary $U$ and on the other hand we bound the time that is needed to implement the dynamics of a target Hamiltonian $H$ in the worst case. We apply our abstract bounds on physically relevant systems like coupled qubits, spin chains, globally controlled Rydberg atoms and NMR molecules and compare our results to the existing literature. We hope that our bounds can aid experimentalists to identify bottlenecks and design faster quantum control systems.