Environmental noise effects on entanglement fidelity of exchange-coupled semiconductor spin qubits

TL;DR

This study analyzes how magnetic and charge noise impact the creation of entanglement in semiconductor spin qubits, providing quantitative insights into noise effects and thresholds for quantum error correction.

Contribution

It offers an exact, quantitative analysis of magnetic and charge noise effects on entanglement fidelity in exchange-coupled spin qubits, guiding noise suppression requirements.

Findings

Charge noise causes faster decoherence than magnetic noise.

The impact of noise depends on the exchange coupling strength.

Quantitative noise thresholds for >99% fidelity are provided.

Abstract

We investigate the effect of magnetic field and charge noise on the generation of entanglement between two Heisenberg exchange-coupled electron spins in a double quantum dot. We focus on exchange-driven evolution that would ideally take an initial unentangled tensor product state to a maximally-entangled state in the absence of noise. The presence of noise obviously adversely affects the attainment of maximal entanglement, which we study quantitatively and exactly. To quantify the effects of noise, we calculate two-qubit coherence times and entanglement fidelity, both of which can be extracted from simulations or measurements of the return probability as a function of interaction time, i.e., the time period during which the exchange coupling remains effective between the two spins. We perform these calculations for a broad range of noise strengths that includes the regime of recent experiments. We find that the two types of noise reduce the amount of entanglement in qualitatively distinct ways and that, although charge noise generally leads to faster decoherence, the relative importance of the two types of noise in entanglement creation depends sensitively on the strength of the exchange coupling. Our results can be used to determine the level of noise suppression needed to reach quantum error correction thresholds. We provide quantitative guidance for the requisite noise constraints necessary to eventually reach the $>99\%$ fidelity consistent with the quantum error correction threshold.