Quantum Robots Plus Environments

A quantum robot is a mobile quantum system including an on bord quantum computer and ancillary systems, that interact with an environment of quantum systems. Quantum robots carry out tasks whose goals include carrying out measurements and physical experiments on the environment. Environments considered so far in the literature: oracles, data bases, and quantum registers, are shown to be special cases of environments considered here. It is noted that quantum robots should include a quantum computer and cannot be simply a multistate head. A model is discussed in which each task, as a sequence of computation and action phases, is described by a unitary step operator. Overall system dynamics is described in terms of a Feynman sum over paths of completed computation and action phases. A simple task example, measuring the distance between the quantum robot and a particle on a 1D space lattice, with quantum phase path and time duration dispersion present, is analyzed.Comment: 10 pages Latex, 1 postscript figur

New Gauge Fields from Extension of Parallel Transport of Vector Spaces to Underlying Scalar Fields

Gauge theories can be described by assigning a vector space V(x) to each space time point x. A common set of complex numbers, C, is usually assumed to be the set of scalars for all the V{x}. This is expanded here to assign a separate set of scalars, C{x}, to V{x} for each x. The freedom of choice of bases, expressed by the action of a gauge group operator on the V{x}, is expanded here to include the freedom of choice of complex scale factors, c_{y,x}, as elements of GL(1,C) that relate C{y} to C{x}. A gauge field representation of c_{y,x} gives two gauge fields, A(x) and iB(x). Inclusion of these fields in the covariant derivatives of Lagrangians results in A(x) appearing as a gauge boson for which mass is optional and B(x) as a massless gauge boson. B(x) appears to be the photon field. The nature of A(x) is not known at present. One does know that the coupling constant of A(x) to matter fields is very small compared to the fine structure constant.Comment: 16 pages,1 figure, paper for talk at SPIE conference, April 27-29, 201

Quantum Robots and Quantum Computers

Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and experiments. The description of quantum computers is under active development. No description of systems to carry out experiments has been given. A small step in this direction is taken here by giving a description of quantum robots as mobile systems with on board quantum computers that interact with environments. Some properties of these systems are discussed. A specific model based on the literature descriptions of quantum Turing machines is presented.Comment: 18 pages, RevTex, one postscript figure. Paper considerably revised and enlarged. submitted to Phys. Rev.

The Representation of Numbers by States in Quantum Mechanics

The representation of numbers by tensor product states of composite quantum systems is examined. Consideration is limited to k-ary representations of length L and arithmetic modulo k^{L}. An abstract representation on an L fold tensor product Hilbert space H^{arith} of number states and operators for the basic arithmetic operations is described. Unitary maps onto a physical parameter based tensor product space H^{phy} are defined and the relations between these two spaces and the dependence of algorithm dynamics on the unitary maps is discussed. The important condition of efficient implementation by physically realizable Hamiltonians of the basic arithmetic operations is also discussed.Comment: Paper, 8 pages, for Proceedings, QCM&C 3, O Hirota and P. Tombesi, Editors, Kluver/Plenum, publisher