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arXiv Machine Learning By Mikhail Gennadievich Belov, Victor Victorovich Dubov, Vadim Konstantinovich Ivanov, Alexander Yurievich Maslov, Olga Vladimirovna Proshina, Vladislav Gennadievich Malyshkin

Semidefinite Programming for Quantum Channel Learning

Read the original on arXiv Machine Learning →

The paper studies how to reconstruct a quantum channel from classical data by formulating the fidelity optimization as a semidefinite program (SDP). When the fidelity can be expressed as a ratio of two quadratic forms—such as in mapping mixed to pure states, projective operators, or unitary learning—the SDP approach yields a convex optimization that can be efficiently solved with commercial solvers. Experiments show that the resulting channels often have a Kraus rank far below the maximum, indicating that a small Kraus rank suffices to capture the observed data, and the method is also applied to reconstruct projective operators and a classical computational model based on quantum channel transformation.

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