Quantum Neural Networks

Abstract

This chapter outlines the research, development and perspectives of quantum neural networks-a burgeoning new field which integrates classical neurocomputing with quantum computation [1]. It is argued that the study of quantum neural networks may give us both new undestanding of brain function as well as unprecedented possibilities in creating new systems for information processing, including solving classically intractable problems, associative memory with exponential capacity and possibly overcoming the limitations posed by the Church-Turing thesis. Why quantum neural networks? There are two main reasons to discuss quantum neural networks. One has its origin in arguments for the essential role which quantum processes play in the living brain. For example, Roger Penrose has argued that a new physics binding quantum phenomena with general relativity can explain such mental abilities as understanding, awareness and consciousness [2]. However, this approach advocates the study of intracellular structures, such as microtubules rather than that of the networks of neurons themselves [3]. A second motivation is the possibility that the field of classical artificial neural networks can be generalized to the quantum domain by eclectic combination of that field with the promising new field of quantum computing [4]. Both considerations suggest new understanding of mind and brain function as well as new unprecedented abilities in information processing. Here we consider quantum neural networks as the next natural step in the evolution of neurocomputing systems, focusing our attention on artificial rather than biological systems. We outline different approaches to the