General framework for quantum associative memory

The classification of inputs into a set of categories is a fundamental task in data science and machine learning. Associative memory (AM) is a particular example of attractor networks whose temporal evolution settles on stable solutions. Here, a system stores a set of memory states in the form of stable fixed points. The system, through its dynamics, identifies the stored pattern most similar to the clue according to a properly defined distance. While extensions to the quantum domain have been explored, a comprehensive framework is yet to be fully established. In this work, we define the theoretical prerequisites for executing associative memory tasks through a completely positive, trace-preserving (CPTP) map. We demonstrate the feasibility of encoding non-orthogonal states and achieving enhanced storage capacity compared to classical models. Our findings lay the groundwork for advancing quantum associative memory systems, holding promise for applications in quantum machine learning or quantum error correction. 

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