Evaluation of Decoherence for Quantum Control and Computing

TL;DR

This paper introduces a measure of decoherence based on the density matrix that quantifies environment-induced errors in quantum systems, with properties useful for analyzing multi-qubit quantum computing devices.

Contribution

It proposes a decoherence measure that is independent of initial conditions and internal dynamics, and demonstrates its additivity for multi-qubit systems, aiding quantum computer error estimation.

Findings

The measure is independent of initial conditions.

It is insensitive to internal system time scales.

Additivity allows error estimation in multi-qubit systems.

Abstract

Different approaches in quantifying environmentally-induced decoherence are considered. We identify a measure of decoherence, derived from the density matrix of the system of interest, that quantifies the environmentally induced error, i.e., deviation from the ideal isolated-system dynamics. This measure can be shown to have several useful features. Its behavior as a function of time has no dependence on the initial conditions, and is expected to be insensitive to the internal dynamical time scales of the system, thus only probing the decoherence-related time dependence. For a spin-boson model - a prototype of a qubit interacting with environment - we also demonstrate the property of additivity: in the regime of the onset of decoherence, the sum of the individual qubit error measures provides an estimate of the error for a several-qubit system, even if the qubits are entangled, as expected in quantum-computing applications. This makes it possible to estimate decoherence for several-qubits quantum computer gate designs for which explicit calculations are exceedingly difficult.