Extracting the lifetime of a synthetic two-level system

TL;DR

This paper investigates methods to accurately determine the lifetime of states in a noisy Kerr Parametric Oscillator, a synthetic two-level system, by comparing rate counting techniques and analyzing phase space fluctuations.

Contribution

It introduces a novel approach using Allan variance peaks to estimate state lifetime, enhancing characterization of KPO networks for simulated annealing.

Findings

Peak in Allan variance indicates state lifetime

Rate counting methods provide consistent lifetime estimates

Enhanced understanding of noise-induced switching in KPOs

Abstract

The Kerr Parametric Oscillator (KPO) is a nonlinear resonator system that is often described as a synthetic two-level system. In the presence of noise, the system switches between two states via a fluctuating trajectory in phase space, instead of following a straight path. The presence of such fluctuating trajectories makes it hard to establish a precise count or even a useful definition, of the "lifetime" of the state. Addressing this issue, we compare several rate counting methods that allow to estimate a lifetime for the levels. In particular, we establish that a peak in the Allan variance of fluctuations can also be used to determine the levels' lifetime. Our work provides a basis for characterizing KPO networks for simulated annealing where an accurate determination of the state lifetime is of fundamental importance.