Probabilistic Quantum Memories

Abstract

Typical address-oriented computer memories cannot recognize incomplete or noisy information. Associative (content-addressable) memories solve this problem but suffer from severe capacity shortages. I propose a model of a quantum memory that solves both problems. The storage capacity is exponential in the number of qbits and thus optimal. The retrieval mechanism for incomplete or noisy inputs is probabilistic, with postselection of the measurement result. The output is determined by a probability distribution on the memory which is peaked around the stored patterns closest in Hamming distance to the input.