True decoherence-free-subspace derived from a semiconductor double quantum dot Heisenberg spin-trimer

TL;DR

This paper derives a true decoherence-free subspace from a semiconductor double quantum dot spin-trimer, demonstrating protection against magnetic field fluctuations, which advances quantum information processing in solid-state systems.

Contribution

The authors derive and experimentally demonstrate a true DFS from a Heisenberg spin-1/2 trimer in a quantum dot system, protecting qubits from magnetic noise.

Findings

Protection of the DFS against short- and long-wavelength magnetic fluctuations.

Large magnetic field differences significantly alter the trimer's eigenspectrum.

Real-time Bayesian estimation confirms DFS energy gap stability.

Abstract

Spins in solid systems can inherently serve as qubits for quantum simulation or quantum information processing. Spin qubits are usually prone to environmental magnetic field fluctuations; however, a spin qubit encoded in a decoherence-free-subspace (DFS) can be protected from certain degrees of environmental noise depending on the specific structure of the DFS. Here, we derive the "true" DFS from an antiferromagnetic Heisenberg spin-1/2 trimer, which protects the qubit states against both short- and long-wavelength magnetic field fluctuations. We define the spin trimer with three electrons confined in a gate-defined GaAs double quantum dot (DQD) where we exploit Wigner-molecularization in one of the quantum dots. We first utilize the trimer for dynamic nuclear polarization (DNP), which generates a sizable magnetic field difference, $\Delta B_\mathrm{z}$, within the DQD. We show that large $\Delta B_\mathrm{z}$ significantly alters the eigenspectrum of the trimer and results in the "true" DFS in the DQD. Real-time Bayesian estimation of the DFS energy gap explicitly demonstrates protection of the DFS against short-wavelength magnetic field fluctuations in addition to long-wavelength ones. Our findings pave the way toward compact DFS structures for exchange-coupled quantum dot spin chains, the internal structure of which can be coherently controlled completely decoupled from environmental magnetic fields.