Essentially exact numerical modelling of flux qubit chains subject to charge and flux noise

TL;DR

This paper introduces an essentially exact numerical method using path integral formalism and tensor networks to model flux qubit chains affected by charge and flux noise, with controlled errors.

Contribution

It develops a novel, highly accurate numerical approach for simulating flux qubit chains, including an open-source Python implementation.

Findings

The method accurately captures non-Markovian dynamics.

The tensor network algorithm efficiently evaluates the path integral.

The approach reduces simulation errors to arbitrarily small levels.

Abstract

We present an essentially exact numerical method for modelling flux qubit chains subject to charge and flux noise. We define an essentially exact method as one that introduces errors that are completely controlled such that they can be made arbitrarily small by tuning the simulation parameters. The method adopts the quasi-adiabatic path integral formalism to express the system's reduced density matrix as a time-discretized path integral, comprising a series of influence functionals that encode the non-Markovian dynamics of the system. We present a detailed derivation of the path integral expression for the system's reduced density matrix and describe in detail the tensor network algorithm used to evaluate the path integral expression. We have implemented our method in an open-sourced Python library called "spinbosonchain". When appropriate, we draw connections between concepts covered in this manuscript and the library's code.