Quantum Associative Pattern Retrieval

Associative pattern retrieval, one of the hallmarks of intelligence, cannot only be realized by the traditional attractor dynamics of the Hopfield model but also by a reversible, unitary evolution of quantum bits (qubits). We will show that qubit networks with long-range interactions governed by the Hebb rule can be used as quantum associative memories. Starting from a uniform superposition, the unitary evolution generated by these interactions drives the network through a quantum phase transition at a critical computation time, after which ferromagnetic order guarantees that a measurement retrieves the stored patterns. The memory capacity of these qubit networks depends on the computation time: the maximum capacity is reached at a memory density α = p/n = 1, after which a phase transition to a quantum spin glass state implies total amnesia. At these loading factors, however the retrieval quality is poor; admitting only a few percent of errors requires lower memory loading factors, comparable with the classical Hopfield model.