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, it is now timely to zoom out and take the whole picture: concerning applications that require user-driven evolutions, qubits should be assessed within the desired algorithm. This means to test qubits under external control while relaxation is 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 algorithms subject to relaxation. It is handled via a code, QBithm, which inputs gate sequences and relaxation rates thus connecting with the longstanding work devoted to their ab initio computation. We calculate fidelities against relaxation and imperfections, and implement well-known pulse sequences quantitatively agreeing with experimental data. Hopefully, this work will stimulate the study of many-qubit systems driven under relaxation and imperfections in quantum algorithms.
Added title and affiliation to SI.