A General Transfer-Function Approach to Noise Filtering in Open-Loop Quantum Control

TL;DR

This paper introduces a comprehensive transfer-function framework for noise filtering in open-loop quantum control, enabling systematic design and analysis of error suppression in quantum systems.

Contribution

It develops a general, computationally manageable set of fundamental filter functions for quantum noise filtering, surpassing traditional recursive approaches.

Findings

Fundamental filter functions can be combined to achieve high-order noise suppression.

The approach characterizes error suppression in both time and frequency domains.

Filtering order offers new insights beyond traditional error cancellation measures.

Abstract

We present a general transfer-function approach to noise filtering in open-loop Hamiltonian engineering protocols for open quantum systems. We show how to identify a computationally tractable set of fundamental filter functions, out of which arbitrary transfer filter functions may be assembled up to arbitrary high order in principle. Besides avoiding the infinite recursive hierarchy of filter functions that arises in general control scenarios, this fundamental filter-functions set suffices to characterize the error suppression capabilities of the control protocol in both the time and frequency domain. We prove that the resulting notion of filtering order reveals conceptually distinct, albeit complementary, features of the controlled dynamics as compared to the order of error cancellation, traditionally defined in the Magnus sense. Examples and implications are discussed.