Frame-Based Filter-Function Formalism for Quantum Characterization and Control

TL;DR

This paper presents a novel, flexible filter-function formalism for efficiently characterizing and controlling non-Markovian quantum systems, accommodating experimental constraints and enabling advanced noise spectroscopy and model reduction.

Contribution

It introduces a control-adapted, frame-based filter-function framework that generalizes standard methods and overcomes key limitations for quantum system characterization and control.

Findings

Allows efficient representation of control matrix elements

Enables quantum noise spectroscopy with nonstationary noise

Facilitates control-driven model reduction for quantum gates

Abstract

We introduce a theoretical framework for resource-efficient characterization and control of non-Markovian open quantum systems, which naturally allows for the integration of given, experimentally motivated, control capabilities and constraints. This is achieved by developing a transfer filter-function formalism based on the general notion of a frame and by appropriately tying the choice of frame to the available control. While recovering the standard frequency-based filter-function formalism as a special instance, this control-adapted generalization affords intrinsic flexibility and, crucially, it permits an efficient representation of the relevant control matrix elements and dynamical integrals if an appropriate finite-size frame condition is obeyed. Our frame-based formulation overcomes important limitations of existing approaches. In particular, we show how to implement quantum noise spectroscopy in the presence of nonstationary noise sources, and how to effectively achieve control-driven model reduction for noise-optimized prediction and quantum gate design.