History and Definition of Quantum Computing Components

Jack D. Hidary

Jack D. Hidary

David Deutsch, Adriano Barenco, Artur Ekert

We show that in quantum computation almost every gate that operates on two or more bits is a universal gate. We discuss various physical considerations bearing on the proper definition of universality for computational components such as logic gates. Introduction It has been known for several years that the theory of quantum computers --- i.e. machines that rely on characteristically quantum phenomena to perform computations [1] --- is substantially different from the classical theory of computation, which is essentially the theory of the universal Turing machine. We may identify three important differences. Firstly, the properties of quantum computers are not postulated in abstracto but are deduced entirely from the laws of physics. Logically, this was already true of the classical theory, as Landauer [2] has pointed out, but the intuitive nature of the classically-available computational operations, and the millennia-long history of their study, allowed pioneers such as Turing, Chu...

Leonardo Castellani

Abstract A formalism is proposed to describe entangled quantum histories, and their entanglement entropy. We define a history vector, living in a tensor space with basis elements corresponding to the allowed histories, i.e. histories with nonvanishing amplitudes. The amplitudes are the components of the history vector, and contain the dynamical information. Probabilities of measurement sequences, and resulting collapse, are given by generalized Born rules: they are all expressed by means of projections and scalar products involving the history vector. Entangled history states are introduced, and a history density matrix is defined in terms of ensembles of history vectors. The corresponding history entropies (and history entanglement entropies for composite systems) are explicitly computed in two examples taken from quantum computation circuits.

W R Matson

This chapter starts with a brief review of the history of science culminating in providing the definitions of wave components to be used throughout the balance of the book. The wave equation is used to formally derive wave expressions in space and time. These are then used to discuss several interference phenomena.

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