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

• URL: http://arxiv.org/abs/2312.01311v1
• Date: Sun, 3 Dec 2023 07:44:17 GMT
• Title: Using non-convex optimization in quantum process tomography: Factored gradient descent is tough to beat
• Authors: David A. Quiroga, Anastasios Kyrillidis
• Abstract summary: Our algorithm converges faster and achieves higher fidelities than state the art, both in terms of settings and noise tolerance. We find our algorithm converges faster and achieves higher fidelities than state the art, both in terms of settings and noise tolerance.
• Score: 11.893324664457552
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a non-convex optimization algorithm, based on the Burer-Monteiro (BM) factorization, for the quantum process tomography problem, in order to estimate a low-rank process matrix $\chi$ for near-unitary quantum gates. In this work, we compare our approach against state of the art convex optimization approaches based on gradient descent. We use a reduced set of initial states and measurement operators that require $2 \cdot 8^n$ circuit settings, as well as $\mathcal{O}(4^n)$ measurements for an underdetermined setting. We find our algorithm converges faster and achieves higher fidelities than state of the art, both in terms of measurement settings, as well as in terms of noise tolerance, in the cases of depolarizing and Gaussian noise models.

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