Optimally Band-Limited Noise Filtering for Single Qubit Gates

TL;DR

This paper presents a quantum control protocol using optimally concentrated sequences to design smooth, experimentally feasible control filters that suppress correlated noise in single qubit systems, enhancing fidelity.

Contribution

It introduces a novel filter design method based on discrete prolate spheroidal sequences and filter function formalism for optimized noise suppression in quantum control.

Findings

Identifies regimes of optimal noise suppression related to control bandwidth.

Develops control sequences that balance noise filtering and high fidelity operations.

Provides principles for designing filters tailored to specific noise environments.

Abstract

We introduce a quantum control protocol that produces smooth, experimentally implementable control sequences optimized to combat temporally correlated noise for single qubit systems. The control ansatz is specifically chosen to be a functional expansion of discrete prolate spheroidal sequences, a discrete time basis known to be optimally concentrated in time and frequency, and quite attractive when faced with experimental control hardware constraints. We leverage the filter function formalism to transform the control problem into a filter design problem, and show that the frequency response of a quantum system can be carefully tailored to avoid the most relevant dynamical contributions of noise processes. Using gradient ascent, we obtain optimized filter functions and exploit them to elucidate important details about the relationship between filter function design, control bandwidth, and noise characteristics. In particular, we identify regimes of optimal noise suppression and in turn, optimal control bandwidth directly proportional to the size of the frequency bands where the noise power is large. In addition to providing guiding principles for filter design, our approach enables the development of controls that simultaneously yield robust noise filtering and high fidelity single qubit logic operations in a wide variety of complex noise environments.