A new quantum algorithm can estimate the diamond distance between two unknown unitary channels of dimension d to within additive error ε, using O(√d/ε) queries to the channels and their inverses. The diamond distance is the relevant measure for determining the optimal probability of distinguishing two quantum channels from a single use, making it a central tool for verifying quantum gates and devices.

The diamond distance is hard to compute: in general, evaluating it exactly is costly even when the full description of the channels is known. The new method addresses the case of d-dimensional unitary channels, the typical scenario when characterising logical gates on a quantum processor, and provides an estimate with controlled error through a query procedure.

The algorithm achieves a query complexity of O(√d/ε), a result that turns out to be optimal. The corresponding lower bound was established by Jeon and Oh (npj Quantum Inf. 2026), so no query-based strategy can improve, in order of magnitude, the number of calls needed to reach the same precision.

The practical relevance lies in device characterisation: having a cost-optimal method to estimate the diamond distance eases the validation of unitary gates without resorting to full tomography. It remains open whether similar techniques can be extended to non-unitary channels, where the structure of the problem is substantially richer.