A practical approach to determine minimal quantum gate durations using amplitude-bounded quantum controls

TL;DR

This paper introduces an iterative method to estimate the shortest possible duration for quantum gate operations under amplitude constraints, using scaled optimal control cycles to approach the quantum speed limit.

Contribution

The authors develop a practical, system-agnostic iterative scheme that efficiently finds minimal gate durations respecting hardware amplitude bounds.

Findings

Fast convergence to near quantum speed limit durations

Applicable to various quantum systems and target gates

Effective in reducing quantum gate operation times

Abstract

We present an iterative scheme to estimate the minimal duration in which a quantum gate can be realized while satisfying hardware constraints on the control pulse amplitudes. The scheme performs a sequence of unconstrained numerical optimal control cycles that each minimize the gate fidelity for a given gate duration alongside an additional penalty term for the control pulse amplitudes. After each cycle, the gate duration is adjusted based on the inverse of the resulting maximum control pulse amplitudes, by re-scaling the dynamics to a new duration where control pulses satisfy the amplitude constraints. Those scaled controls then serve as an initial guess for the next unconstrained optimal control cycle, using the adjusted gate duration. We provide multiple numerical examples that each demonstrate fast convergence of the scheme towards a gate duration that is close to the quantum speed limit, given the control pulse amplitude bound. The proposed technique is agnostic to the underlying system and control Hamiltonian models, as well as the target unitary gate operation, making the time-scaling iteration an easy to implement and practically useful scheme for reducing the durations of quantum gate operations.