Towards the coherent control of robust spin qubits in quantum algorithms

TL;DR

This paper develops an analytical framework and a computational tool to evaluate and optimize the fidelity of spin qubit quantum algorithms under realistic conditions including relaxation and imperfections.

Contribution

It introduces a master equation approach and the QBithm code to simulate one-spin-qubit gate sequences with relaxation, aiding the design of robust spin qubits.

Findings

Quantitative assessment of relaxation effects on qubit fidelity.

Validation of pulse sequences against experimental data.

Framework for improving spin qubit robustness in quantum algorithms.

Abstract

Many efforts have succeeded over the last decade at lengthening the timescale in which spin qubits loss quantum information under free evolution. With these design principles at a mature stage, it is now timely to widen the scope and take the whole picture: concerning applications that require user-driven coherent evolutions, qubits should be assessed operating within the desired algorithm. This means to test qubits under external control while relaxation and imperfections are active, and to maximize the algorithm fidelity as the actual figure of merit. Herein, we pose and analytically solve a master equation devised to run one-spin-qubit gate-based algorithms subject to relaxation. It is handled via a home-made code, QBithm, which inputs gate sequences and relaxation rates thus connecting with the longstanding work devoted to their $\textit{ab initio}$ computation. We evaluate the impact of relaxation and potential experimental imperfections in the calculated fidelities, and implement well-known pulse sequences quantitatively agreeing with experimental data. Hopefully, this work will stimulate the study of many-spin-qubit systems in quantum algorithms, and will serve as a help to design robust spin qubits against decoherence and to perform better-characterized experiments.