214 research outputs found
The Mammoth “earthquake fault” and related features in Mono County, California
In undertaking this work it was our intention to investigate the well-known
"Earthquake Fault" situated about two miles northwest of the town of Mammoth
in Mono County, California. In working in the surrounding region we
found, however, that this is only a part of an extensive system of similar features.
The locations of those which have been found thus far are shown on the
map (fig. 1), which is reproduced from U. S. Geological Survey topographical
maps, Mount Lyell and Mount Morrison quadrangles. We consider that the
southern and eastern limits of the features shown are real, whereas in the
northern and western directions they represent only the extent of our investigations
to date
Quantum Robots and Environments
Quantum robots and their interactions with environments of quantum systems
are described and their study justified. A quantum robot is a mobile quantum
system that includes a quantum computer and needed ancillary systems on board.
Quantum robots carry out tasks whose goals include specified changes in the
state of the environment or carrying out measurements on the environment. Each
task is a sequence of alternating computation and action phases. Computation
phase activities include determination of the action to be carried out in the
next phase and possible recording of information on neighborhood environmental
system states. Action phase activities include motion of the quantum robot and
changes of neighborhood environment system states. Models of quantum robots and
their interactions with environments are described using discrete space and
time. To each task is associated a unitary step operator T that gives the
single time step dynamics. T = T_{a}+T_{c} is a sum of action phase and
computation phase step operators. Conditions that T_{a} and T_{c} should
satisfy are given along with a description of the evolution as a sum over paths
of completed phase input and output states. A simple example of a task carrying
out a measurement on a very simple environment is analyzed. A decision tree for
the task is presented and discussed in terms of sums over phase paths. One sees
that no definite times or durations are associated with the phase steps in the
tree and that the tree describes the successive phase steps in each path in the
sum.Comment: 30 Latex pages, 3 Postscript figures, Minor mathematical corrections,
accepted for publication, Phys Rev
Cyclic networks of quantum gates
In this article initial steps in an analysis of cyclic networks of quantum
logic gates is given. Cyclic networks are those in which the qubit lines are
loops. Here we have studied one and two qubit systems plus two qubit cyclic
systems connected to another qubit on an acyclic line. The analysis includes
the group classification of networks and studies of the dynamics of the qubits
in the cyclic network and of the perturbation effects of an acyclic qubit
acting on a cyclic network. This is followed by a discussion of quantum
algorithms and quantum information processing with cyclic networks of quantum
gates, and a novel implementation of a cyclic network quantum memory. Quantum
sensors via cyclic networks are also discussed.Comment: 14 pages including 11 figures, References adde
Quantum Ballistic Evolution in Quantum Mechanics: Application to Quantum Computers
Quantum computers are important examples of processes whose evolution can be
described in terms of iterations of single step operators or their adjoints.
Based on this, Hamiltonian evolution of processes with associated step
operators is investigated here. The main limitation of this paper is to
processes which evolve quantum ballistically, i.e. motion restricted to a
collection of nonintersecting or distinct paths on an arbitrary basis. The main
goal of this paper is proof of a theorem which gives necessary and sufficient
conditions that T must satisfy so that there exists a Hamiltonian description
of quantum ballistic evolution for the process, namely, that T is a partial
isometry and is orthogonality preserving and stable on some basis. Simple
examples of quantum ballistic evolution for quantum Turing machines with one
and with more than one type of elementary step are discussed. It is seen that
for nondeterministic machines the basis set can be quite complex with much
entanglement present. It is also proved that, given a step operator T for an
arbitrary deterministic quantum Turing machine, it is decidable if T is stable
and orthogonality preserving, and if quantum ballistic evolution is possible.
The proof fails if T is a step operator for a nondeterministic machine. It is
an open question if such a decision procedure exists for nondeterministic
machines. This problem does not occur in classical mechanics.Comment: 37 pages Latexwith 2 postscript figures tar+gzip+uuencoded, to be
published in Phys. Rev.
Global Seismic Oscillations in Soft Gamma Repeaters
There is evidence that soft gamma repeaters (SGRs) are neutron stars which
experience frequent starquakes, possibly driven by an evolving, ultra-strong
magnetic field. The empirical power-law distribution of SGR burst energies,
analogous to the Gutenberg-Richter law for earthquakes, exhibits a turn-over at
high energies consistent with a global limit on the crust fracture size. With
such large starquakes occurring, the significant excitation of global seismic
oscillations (GSOs) seems likely. Moreover, GSOs may be self-exciting in a
stellar crust that is strained by many, randomly-oriented stresses. We explain
why low-order toroidal modes, which preserve the shape of the star and have
observable frequencies as low as ~ 30 Hz, may be especially susceptible to
excitation. We estimate the eigenfrequencies as a function of stellar mass and
radius, and their magnetic and rotational shiftings/splittings. We also
describes ways in which these modes might be detected and damped. There is
marginal evidence for 23 ms oscillations in the hard initial pulse of the 1979
March 5th event. This could be due to the mode in a neutron star with B
~ 10^{14} G or less; or it could be the fundamental toroidal mode if the field
in the deep crust of SGR 0526-66 is ~ 4 X 10^{15} G, in agreement with other
evidence. If confirmed, GSOs would give corroborating evidence for
crust-fracturing magnetic fields in SGRs: B >~ 10^{14} G.Comment: 12 pages, AASTeX, no figures. Accepted for Astrophysical Journal
Letter
Efficient Implementation and the Product State Representation of Numbers
The relation between the requirement of efficient implementability and the
product state representation of numbers is examined. Numbers are defined to be
any model of the axioms of number theory or arithmetic. Efficient
implementability (EI) means that the basic arithmetic operations are physically
implementable and the space-time and thermodynamic resources needed to carry
out the implementations are polynomial in the range of numbers considered.
Different models of numbers are described to show the independence of both EI
and the product state representation from the axioms. The relation between EI
and the product state representation is examined. It is seen that the condition
of a product state representation does not imply EI. Arguments used to refute
the converse implication, EI implies a product state representation, seem
reasonable; but they are not conclusive. Thus this implication remains an open
question.Comment: Paragraph in page proof for Phys. Rev. A revise
The Representation of Natural Numbers in Quantum Mechanics
This paper represents one approach to making explicit some of the assumptions
and conditions implied in the widespread representation of numbers by composite
quantum systems. Any nonempty set and associated operations is a set of natural
numbers or a model of arithmetic if the set and operations satisfy the axioms
of number theory or arithmetic. This work is limited to k-ary representations
of length L and to the axioms for arithmetic modulo k^{L}. A model of the
axioms is described based on states in and operators on an abstract L fold
tensor product Hilbert space H^{arith}. Unitary maps of this space onto a
physical parameter based product space H^{phy} are then described. Each of
these maps makes states in H^{phy}, and the induced operators, a model of the
axioms. Consequences of the existence of many of these maps are discussed along
with the dependence of Grover's and Shor's Algorithms on these maps. The
importance of the main physical requirement, that the basic arithmetic
operations are efficiently implementable, is discussed. This conditions states
that there exist physically realizable Hamiltonians that can implement the
basic arithmetic operations and that the space-time and thermodynamic resources
required are polynomial in L.Comment: Much rewrite, including response to comments. To Appear in Phys. Rev.
Decoherence in Ion Trap Quantum Computers
The {\it intrinsic} decoherence from vibrational coupling of the ions in the
Cirac-Zoller quantum computer [Phys. Rev. Lett. {\bf 74}, 4091 (1995)] is
considered. Starting from a state in which the vibrational modes are at a
temperature , and each ion is in a superposition of an excited and a ground
state, an adiabatic approximation is used to find the inclusive probability
for the ions to evolve as they would without the vibrations, and for the
vibrational modes to evolve into any final state. An analytic form is found for
at , and the decoherence time is found for all . The decoherence
is found to be quite small, even for 1000 ions.Comment: 11 pages, no figures, uses revte
Quantum search without entanglement
Entanglement of quantum variables is usually thought to be a prerequisite for
obtaining quantum speed-ups of information processing tasks such as searching
databases. This paper presents methods for quantum search that give a speed-up
over classical methods, but that do not require entanglement. These methods
rely instead on interference to provide a speed-up. Search without entanglement
comes at a cost: although they outperform analogous classical devices, the
quantum devices that perform the search are not universal quantum computers and
require exponentially greater overhead than a quantum computer that operates
using entanglement. Quantum search without entanglement is compared to
classical search using waves.Comment: 9 pages, TeX, submitted to Physical Review Letter
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