Extension to the Quantum Langevin Equation in the Incoherent Hopping Regime

TL;DR

This paper extends the quantum Langevin equation to include quantum tunneling events in the incoherent hopping regime, aiding in more accurate modeling of superconducting qubits.

Contribution

It introduces a systematic extension of the quantum Langevin equation with stochastic variables for tunneling, valid in the incoherent hopping regime.

Findings

Incorporates quantum tunneling into Langevin dynamics.

Provides a systematic derivation and regime of validity.

Aims to improve error analysis in superconducting qubits.

Abstract

An extension to the quantum Langevin equation is derived, that is valid in the incoherent hopping regime, and which allows one to incorporate quantum tunneling events. This is achieved by the inclusion of additional stochastic variables in the Langevin equation representing the tunneling events. A systematic derivation of this extension and of its regime of validity is presented. The study is motivated by efforts to determine the error in reading the state of a super-conducting quantum bit.