# Query-optimal estimation of unitary channels in diamond distance

@article{Haah2023QueryoptimalEO, title={Query-optimal estimation of unitary channels in diamond distance}, author={Jeongwan Haah and Robin Kothari and Ryan O'Donnell and Ewin Tang}, journal={ArXiv}, year={2023}, volume={abs/2302.14066} }

We consider process tomography for unitary quantum channels. Given access to an unknown unitary channel acting on a $\textsf{d}$-dimensional qudit, we aim to output a classical description of a unitary that is $\varepsilon$-close to the unknown unitary in diamond norm. We design an algorithm achieving error $\varepsilon$ using $O(\textsf{d}^2/\varepsilon)$ applications of the unknown channel and only one qudit. This improves over prior results, which use $O(\textsf{d}^3/\varepsilon^2)$ [via…

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