Exact analytical treatment of multiqubit noisy dynamics in exchange-coupled semiconductor spin qubits

TL;DR

This paper provides an exact analytical analysis of how quasistatic charge noise affects the coherence and dynamics of exchange-coupled semiconductor spin qubits, revealing key dependencies and decay behaviors.

Contribution

It introduces an exact analytical method to study charge noise effects on multiqubit spin systems, including coherence times and oscillation decay, with quantitative insights for quantum gate performance.

Findings

Decoherence time T2* depends only on disorder strength.

Return probability exhibits multiple Gaussian-decaying oscillations.

Decoherence time decreases as the number of qubits increases.

Abstract

Charge noise remains the primary obstacle to the development of quantum information technologies with semiconductor spin qubits. We use an exact analytical calculation to determine the effects of quasistatic charge noise on a ring of three equally spaced exchange-coupled quantum dots. We calculate the disorder-averaged return probability from a specific initial state, and use it to determine the coherence time T2* and show that it depends only on the disorder strength and not the mean interaction strength. We also use a perturbative approach to investigate other arrangements of three or four qubits, finding that the return probability contains multiple oscillation frequencies. These oscillations decay in a Gaussian manner, determined by differences in energy levels of the Hamiltonian. We give quantitative values for gate times resulting in several target fidelities. We find that the decoherence time decreases with increasing number of qubits. Our work provides useful analytical insight into the charge noise dynamics of coupled spin qubits.