Quantum neurocomputation and signal processing (original) (raw)

In this paper we consider a Quantum computational algorithm that can be used to determine (probabilistically) how close a given signal is to one of a set of previously observed signal stored in the state of a quantum neurocomputional machine. The realization of a new quantum algorithm for factorization of integers by Shor and its implication to cryptography has created a rapidly growing field of investigation. Although no physical realization of quantum computer is available, a number of software systems simulating a quantum computation process exist. In light of the rapidly increasing power of desktop computers and their ability to carry out these simulations, it is worthwhile to investigate possible advantages as well as realizations of quantum algorithms in signal processing applications. The algorithm presented in this paper offers a glimpse of the potentials of this approach. Neural Networks (NN) provide a natural paradigm for parallel and distributed processing of a wide class of signals. Neural Networks within the context of classical computation have been used for approximation and classification tasks with some success. In this paper we propose a model for Quantum Neurocomputation (QN) and explore some of its properties and potential applications to signal processing in an information-theoretic context. A Quantum Computer can evolve a coherent superposition of many possible input states, to an output state through a series of unitary transformations that simultaneously affect each element of the superposition. This construction generates a massively parallel data processing system existing within a single piece of hardware. Our model of QN consists of a set of Quantum Neurons and Quantum interconnections. Quantum neurons represent a normalized element of the n-dimensional Hilbert space-a state of a finite dimensional quantum mechanical system. Quantum connections provide a realization of probability distribution over the set of state that combined with the Quantum Neurons provide a density matrix representation of the system. A second layer with a similar architecture interrogates the system through a series of random state descriptions to obtain an average state description. We discuss the application of this paradigm to the quantum analog of independent states using the quantum version of the Kullback-Leibler distance.