Analysis of measurement errors for a superconducting phase qubit

TL;DR

This paper investigates various sources of measurement errors in superconducting flux-biased phase qubits, analyzing how pulse duration, tunneling rate ratios, and relaxation times affect measurement fidelity through analytical and numerical methods.

Contribution

It provides a detailed analysis of measurement error mechanisms in phase qubits, combining analytical models with numerical simulations to improve understanding.

Findings

Nonadiabatic transitions occur with short measurement pulses.

Incomplete discrimination due to tunneling rate ratios affects accuracy.

Repopulation of the quantum well impacts measurement reliability.

Abstract

We analyze several mechanisms leading to errors in a course of measurement of a superconducting flux-biased phase qubit. Insufficiently long measurement pulse may lead to nonadiabatic transitions between qubit states $|1>$ and $|0>$, before tunneling through a reduced barrier is supposed to distinguish the qubit states. Finite (though large) ratio of tunneling rates for these states leads to incomplete discrimination between $|1>$ and $|0>$. Insufficiently fast energy relaxation after the tunneling of state $|1>$ may cause the repopulation of the quantum well in which only the state $|0>$ is supposed to remain. We analyze these types of measurement errors using analytical approaches as well as numerical solution of the time-dependent Schr\"{o}dinger equation.