期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 65, 期 9, 页码 5931-5944出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2019.2916646
关键词
Quantum machine learning; quantum state discrimination; representation theory; supervised learning
We consider the problem of correctly classifying a given quantum two-level system (qubit) which is known to be in one of two equally probable quantum states. We assume that this task should be performed by a quantum machine which does not have at its disposal a complete classical description of the two template states, but can only have partial prior information about their level of purity and mutual overlap. Moreover, similarly to the classical supervised learning paradigm, we assume that the machine can be trained by n qubits prepared in the first template state and by n more qubits prepared in the second template state. In this situation, we are interested in the optimal process which correctly classifies the input qubit with the largest probability allowed by quantum mechanics. The problem is studied in its full generality for a number of different prior information scenarios and for an arbitrary size n of the training data. Finite size corrections around the asymptotic limit n -> infinity are derived. When the states are assumed to be pure, with known overlap, the problem is also solved in the case of d-level systems.
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