Spin qubit shuttling between coupled quantum dots with inhomogeneous Land\'e g-tensors

TL;DR

This paper investigates the non-adiabatic dynamics of spin qubit shuttling between coupled quantum dots with inhomogeneous g-tensors, analyzing how to achieve high-fidelity transfer and quantum gate operations through controlled ramping and shuttling protocols.

Contribution

It provides a detailed analysis of spin dynamics during shuttling with inhomogeneous g-tensors, including conditions for high-fidelity transfer and methods to implement quantum gates.

Findings

High-fidelity inter-dot spin transfer depends on ramping time and tunnel-coupling strength.

Multiple shuttling rounds can be modeled with an operator matrix for gate implementation.

Tuning idling times enables realization of Hadamard and other single-qubit gates.

Abstract

By utilizing the site-dependent spin quantization axis in semiconductor quantum dot (QD) arrays, shuttling-based spin qubit gates have become an appealing approach to realize scalable quantum computing due to the circumvention of using high-frequency driving fields. The emergence of a spin deviation from the local quantization axis of one residing QD is the prerequisite to implement the qubit gates. In this work, we study the non-adiabatic dynamics of a spin qubit shuttling between coupled QDs with inhomogeneous Land\'e g-tensors and a small magnetic field. The spin dynamics is analyzed through solving the time-dependent Schr\"odinger equation of the qubit under the effects of spin-orbit interaction and rapid ramping inter-dot detuning. The precondition, imposed on the ramping time and the tunnel-coupling strength, to ensure a high-fidelity inter-dot transfer is estimated. We then calculate the change in the spin orientation of a transferred qubit, and study the dependences of the spin deviation on the difference in the quantization axes of the two QDs, the tunnel-coupling strength, and the ramping time. We also demonstrate that the effect of multiple rounds of inter-dot bidirectional shuttling can be captured by an operator matrix, and evaluate the idling times required for realizing the single-qubit Pauli-X and Pauli-Y gates. Intriguingly, it is confirmed that a generalized Hadamard gate can be achieved through tuning the idling times.