Arizona State University Team Models Qubit Behavior With Volterra Equations

Jimmie Adriazola of Arizona State University and Katarzyna Roszak of the FZU, Institute of Physics of the Czech Academy of Sciences have developed a new framework for modeling qubit dynamics by representing the reduced density matrix as a four-dimensional state vector. This approach casts the dynamics as a Volterra equation, enabling the team to learn equations of motion for open quantum systems.

Their work demonstrates that using Padé approximants to model correlation functions captures complex temporal behaviors, including oscillatory memory and algebraic tails, even for systems like the non-rotating-wave quantum Rabi model where traditional analytical solutions fail. The results illustrate that data-driven rational approximation offers an effective route to identifying non-Markovian kernels relevant to quantum technologies.

Volterra Equations Model Qubit-Environment Interactions

A four-dimensional state vector streamlines the modeling of qubit dynamics within a newly developed framework, allowing researchers to represent the reduced density matrix and cast the system’s evolution as a Volterra equation. The team’s work builds on techniques used in molecular dynamics and statistical mechanics, adapting methods for extracting Volterra-type dynamics from time-series data. The framework employs Padé approximants to approximate bath correlation functions, using a non-local Crank-Nicolson method for forward evaluation of dynamics.