Error channels in quantum nondemolition measurements on spin systems

TL;DR

This paper develops a theoretical framework to analyze errors in quantum nondemolition measurements on spin systems, highlighting how deviations from ideal QND processes cause bit flip errors and applying the model to various spin qubit platforms.

Contribution

The paper introduces a comprehensive model for QND measurement errors in spin qubits, including exchange-coupled and electron-nuclear systems, validated against experimental data.

Findings

Model accurately predicts measurement errors in silicon donor nuclear spins.

Deviations from perfect QND cause quantum jumps and bit flip errors.

Analysis of anisotropic spin couplings extends the model's applicability.

Abstract

Quantum nondemolition (QND) measurements are a precious resource for quantum information processing. Repetitive QND measurements can boost the fidelity of qubit preparation and measurement, even when the underlying single-shot measurements are of low fidelity. However, this fidelity boost is limited by the degree in which the physical system allows for a truly QND process -- slight deviations from ideal QND measurement result in bit flip errors (`quantum jumps') if the measurement is repeated too often. Here, we develop a theoretical framework to understand and quantify the resulting error arising from deviation from perfect QND measurement in model spin qubit systems. We first develop our model on the ubiquitous example of exchange-coupled electron spins qubits tunnel-coupled to a charge reservoir. We then extend it to electron-nuclear spin systems, to illustrate the crucial similarities and differences between the two limits. Applied to the well-understood platform of a donor nuclear spin in silicon, the model shows excellent agreement with experiments. For added generality, we conclude the work by considering the effect of anisotropic spin couplings.