Protocols to measure the non-Abelian Berry phase by pumping a spin qubit through a quantum-dot loop

TL;DR

This paper proposes protocols to measure the non-Abelian Berry phase in spin qubits within quantum-dot loops, which could enable robust quantum gates for quantum computing, and analyzes their feasibility with current technology.

Contribution

It introduces specific protocols for measuring the non-Abelian Berry phase in spin qubits, advancing holonomic quantum gate implementation in semiconductor systems.

Findings

Protocols can characterize local Zeeman fields in quantum dots.

All key elements for experiments have been demonstrated.

Protocols are feasible for near-term experimental realization.

Abstract

A quantum system constrained to a degenerate energy eigenspace can undergo a nontrival time evolution upon adiabatic driving, described by a non-Abelian Berry phase. This type of dynamics may provide logical gates in quantum computing that are robust against timing errors. A strong candidate to realize such holonomic quantum gates is an electron or hole spin qubit trapped in a spin-orbit-coupled semiconductor, whose twofold Kramers degeneracy is protected by time-reversal symmetry. Here, we propose and quantitatively analyze protocols to measure the non-Abelian Berry phase by pumping a spin qubit through a loop of quantum dots. One of these protocols allows to characterize the local internal Zeeman field directions in the dots of the loop. We expect a near-term realisation of these protocols, as all key elements have been already demonstrated in spin-qubit experiments. These experiments would be important to assess the potential of holonomic quantum gates for spin-based quantum information processing.