The methodology of resonant equiangular composite quantum gates

TL;DR

This paper introduces a systematic method for designing composite quantum gates that depend on a parameter, enabling precise control and optimization for applications like metrology and spectroscopy, by linking quantum gate design with classical signal processing techniques.

Contribution

The authors develop a comprehensive, efficient methodology for constructing and decomposing composite quantum gates of arbitrary length, fully characterizing their capabilities and optimal approximations.

Findings

Provides an algorithm for shortest gate sequences implementing desired unitaries.

Characterizes the family of realizable parameter-dependent unitaries.

Demonstrates construction of optimized, bandwidth-limited gates for single spin rotations.

Abstract

The creation of composite quantum gates that implement quantum response functions $\hat{U}(\theta)$ dependent on some parameter of interest $\theta$ is often more of an art than a science. Through inspired design, a sequence of $L$ primitive gates also depending on $\theta$ can engineer a highly nontrivial $\hat{U}(\theta)$ that enables myriad precision metrology, spectroscopy, and control techniques. However, discovering new, useful examples of $\hat{U}(\theta)$ requires great intuition to perceive the possibilities, and often brute-force to find optimal implementations. We present a systematic and efficient methodology for composite gate design of arbitrary length, where phase-controlled primitive gates all rotating by $\theta$ act on a single spin. We fully characterize the realizable family of $\hat{U}(\theta)$, provide an efficient algorithm that decomposes a choice of $\hat{U}(\theta)$ into its shortest sequence of gates, and show how to efficiently choose an achievable $\hat{U}(\theta)$ that for fixed $L$, is an optimal approximation to objective functions on its quadratures. A strong connection is forged with \emph{classical} discrete-time signal processing, allowing us to swiftly construct, as examples, compensated gates with optimal bandwidth that implement arbitrary single spin rotations with sub-wavelength spatial selectivity.