Sound and Efficient Certification of High-Quality Qubit Operations: Theory and Experiment

• URL: http://arxiv.org/abs/2608.17005v1
• Date: Mon, 17 Aug 2026 18:03:00 GMT
• Title: Sound and Efficient Certification of High-Quality Qubit Operations: Theory and Experiment
• Abstract summary: We introduce a sound black-box certification protocol for a single-qubit gate based on a small set of fixed, deterministic sequences.<n>From the data, the protocol derives finite-sample bounds on the gate's rotation eigenvalue, a gauge-invariant property.<n>We prove that these spectral constraints imply, up to a physically meaningful unitary change of basis, a rigorous average gate-fidelity lower bound for every time-independent qubit model.
• Score: 23.48673361417131
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Can a high-quality quantum gate be certified when uncharacterized state-preparation and measurement errors are dominant? Can this be achieved with low experimental overhead? Here, we introduce a sound black-box certification protocol for a single-qubit gate based on a small set of fixed, deterministic sequences. From the data, the protocol derives finite-sample bounds on the gate's rotation eigenvalue, a gauge-invariant property. Its phase reveals the accuracy of the rotation angle, while its modulus quantifies the loss of coherence under repeated gate applications. We implement the protocol on a $^{40}\mathrm{Ca}^{+}$ trapped-ion processor and certify the $\sqrt{\mathrm{X}}$-gate rotation eigenvalue using $22\,000$ circuit executions, and demonstrate the robustness of certification to state-preparation and measurement errors by deliberately degrading the readout. Finally, we prove that these spectral constraints imply, up to a physically meaningful unitary change of basis, a rigorous average gate-fidelity lower bound for every time-independent qubit model compatible with the data. In both readout settings, the spectral bounds yield the same fidelity certificate of $99.94(3)\%$ with $99\%$ confidence. Our results establish a new standard for quantum-gate certification by combining soundness and experimental efficiency without requiring trusted reference operations, randomized circuits, or model fitting.

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