Hyperfine interaction induced dephasing of coupled spin qubits in semiconductor double quantum dots

TL;DR

This paper provides a theoretical analysis of hyperfine-induced dephasing in coupled spin qubits within semiconductor double quantum dots, identifying dominant decoherence processes and evaluating their impact on quantum gate fidelity.

Contribution

It introduces an effective pure dephasing Hamiltonian and combines quantum and semiclassical methods to analyze hyperfine effects in various regimes, including different magnetic fields and material systems.

Findings

Dominant dephasing mechanisms depend on magnetic field and singlet-triplet splitting.

Hahn echo can mitigate certain hyperfine-induced dephasing effects.

Hyperfine interactions cause measurable exchange gate errors in quantum dots.

Abstract

We investigate theoretically the hyperfine-induced dephasing of two-electron-spin states in a double quantum dot with a finite singlet-triplet splitting J. In particular, we derive an effective pure dephasing Hamiltonian, which is valid when the hyperfine-induced mixing is suppressed due to the relatively large J and the external magnetic field. Using both a quantum theory based on resummation of ring diagrams and semiclassical methods, we identify the dominant dephasing processes in regimes defined by values of the external magnetic field, the singlet-triplet splitting, and inhomogeneity in the total effective magnetic field. We address both free induction and Hahn echo decay of superposition of singlet and unpolarized triplet states (both cases are relevant for singlet-triplet qubits realized in double quantum dots). We also study hyperfine-induced exchange gate errors for two single-spin qubits. Results for III-V semiconductors as well as silicon-based quantum dots are presented.