Non-Markovian quantum input-output networks

TL;DR

This paper extends quantum input-output network theory to include non-Markovian effects, enabling analysis of complex mesoscopic quantum networks like superconducting qubits with finite bandwidths.

Contribution

It introduces a non-Markovian formalism for quantum input-output networks, expanding the analysis capabilities beyond Markovian assumptions.

Findings

Analyzed non-Markovian effects in superconducting qubit networks

Demonstrated how finite cavity bandwidths influence network behavior

Showed applications to open- and closed-loop control systems

Abstract

Quantum input-output response analysis is a useful method for modeling the dynamics of complex quantum networks, such as those for communication or quantum control via cascade connections. Non-Markovian effects have not yet been studied in such networks. Here we extend the Markovian input-output network formalism developed in optical systems to non-Markovian cascaded networks which can be used, e.g., to analyze the input-output response of mesoscopic quantum networks. We use this formalism to explore the behavior of superconducting qubit networks, where we examine the effect of finite cavity bandwidths. We also discuss its application to open- and closed-loop control networks, and show how these networks create effective Hamiltonians for the controlled system.