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We propose a non-convex optimization algorithm, based on the Burer-Monteiro(BM) factorization, for the quantum process tomography problem, in order toestimate a low-rank process matrix $\chi$ for near-unitary quantum gates. Inthis work, we compare our approach against state of the art convex optimizationapproaches based on gradient descent. We use a reduced set of initial statesand measurement operators that require $2 \cdot 8^n$ circuit settings, as wellas $\mathcal{O}(4^n)$ measurements for an underdetermined setting. We find ouralgorithm converges faster and achieves higher fidelities than state of theart, both in terms of measurement settings, as well as in terms of noisetolerance, in the cases of depolarizing and Gaussian noise models.

Using non-convex optimization in quantum process tomography: Factored gradient descent is tough to beat