7,112 research outputs found
Neutrix Calculus and Finite Quantum Field Theory
In general, quantum field theories (QFT) require regularizations and infinite
renormalizations due to ultraviolet divergences in their loop calculations.
Furthermore, perturbation series in theories like QED are not convergent
series, but are asymptotic series. We apply neutrix calculus, developed in
connection with asymptotic series and divergent integrals, to QFT,obtaining
finite renormalizations. While none of the physically measurable results in
renormalizable QFT is changed, quantum gravity is rendered more manageable in
the neutrix framework.Comment: 10 pages; LaTeX; version to appear in J. Phys. A: Math. Gen. as a
Letter to the Edito
Experimental implementation of an adiabatic quantum optimization algorithm
We report the realization of a nuclear magnetic resonance computer with three
quantum bits that simulates an adiabatic quantum optimization algorithm.
Adiabatic quantum algorithms offer new insight into how quantum resources can
be used to solve hard problems. This experiment uses a particularly well suited
three quantum bit molecule and was made possible by introducing a technique
that encodes general instances of the given optimization problem into an easily
applicable Hamiltonian. Our results indicate an optimal run time of the
adiabatic algorithm that agrees well with the prediction of a simple
decoherence model.Comment: REVTeX, 5 pages, 4 figures, improved lay-out; accepted for
publication in Physical Review Letter
Relativistic Partial Wave Analysis Using the Velocity Basis of the Poincare Group
The velocity basis of the Poincare group is used in the direct product space
of two irreducible unitary representations of the Poincare group. The velocity
basis with total angular momentum j will be used for the definition of
relativistic Gamow vectors.Comment: 14 pages; revte
Enhanced Peculiar Velocities in Brane-Induced Gravity
The mounting evidence for anomalously large peculiar velocities in our
Universe presents a challenge for the LCDM paradigm. The recent estimates of
the large scale bulk flow by Watkins et al. are inconsistent at the nearly 3
sigma level with LCDM predictions. Meanwhile, Lee and Komatsu have recently
estimated that the occurrence of high-velocity merging systems such as the
Bullet Cluster (1E0657-57) is unlikely at a 6.5-5.8 sigma level, with an
estimated probability between 3.3x10^{-11} and 3.6x10^{-9} in LCDM cosmology.
We show that these anomalies are alleviated in a broad class of
infrared-modifed gravity theories, called brane-induced gravity, in which
gravity becomes higher-dimensional at ultra large distances. These theories
include additional scalar forces that enhance gravitational attraction and
therefore speed up structure formation at late times and on sufficiently large
scales. The peculiar velocities are enhanced by 24-34% compared to standard
gravity, with the maximal enhancement nearly consistent at the 2 sigma level
with bulk flow observations. The occurrence of the Bullet Cluster in these
theories is 10^4 times more probable than in LCDM cosmology.Comment: 15 pages, 6 figures. v2: added reference
Noise Thresholds for Higher Dimensional Systems using the Discrete Wigner Function
For a quantum computer acting on d-dimensional systems, we analyze the
computational power of circuits wherein stabilizer operations are perfect and
we allow access to imperfect non-stabilizer states or operations. If the noise
rate affecting the non-stabilizer resource is sufficiently high, then these
states and operations can become simulable in the sense of the Gottesman-Knill
theorem, reducing the overall power of the circuit to no better than classical.
In this paper we find the depolarizing noise rate at which this happens, and
consequently the most robust non-stabilizer states and non-Clifford gates. In
doing so, we make use of the discrete Wigner function and derive facets of the
so-called qudit Clifford polytope i.e. the inequalities defining the convex
hull of all qudit Clifford gates. Our results for robust states are provably
optimal. For robust gates we find a critical noise rate that, as dimension
increases, rapidly approaches the the theoretical optimum of 100%. Some
connections with the question of qudit magic state distillation are discussed.Comment: 14 pages, 1 table; Minor changes vs. version
Critical collapse of a massive vector field
We perform numerical simulations of the critical gravitational collapse of a
massive vector field. The result is that there are two critical solutions. One
is equivalent to the Choptuik critical solution for a massless scalar field.
The other is periodic.Comment: 7 pages, 4 figure
Mass for the graviton
Can we give the graviton a mass? Does it even make sense to speak of a
massive graviton? In this essay I shall answer these questions in the
affirmative. I shall outline an alternative to Einstein Gravity that satisfies
the Equivalence Principle and automatically passes all classical weak-field
tests (GM/r approx 10^{-6}). It also passes medium-field tests (GM/r approx
1/5), but exhibits radically different strong-field behaviour (GM/r approx 1).
Black holes in the usual sense do not exist in this theory, and large-scale
cosmology is divorced from the distribution of matter. To do all this we have
to sacrifice something: the theory exhibits {*prior geometry*}, and depends on
a non-dynamical background metric.Comment: 12 pages, plain LaTeX. Major revisions: (1) Inconsistency in
equations of motion fixed. (2) More discussion of the problems associated
with quantization. (3) Many more references adde
Optimization by Quantum Annealing: Lessons from hard 3-SAT cases
The Path Integral Monte Carlo simulated Quantum Annealing algorithm is
applied to the optimization of a large hard instance of the Random 3-SAT
Problem (N=10000). The dynamical behavior of the quantum and the classical
annealing are compared, showing important qualitative differences in the way of
exploring the complex energy landscape of the combinatorial optimization
problem. At variance with the results obtained for the Ising spin glass and for
the Traveling Salesman Problem, in the present case the linear-schedule Quantum
Annealing performance is definitely worse than Classical Annealing.
Nevertheless, a quantum cooling protocol based on field-cycling and able to
outperform standard classical simulated annealing over short time scales is
introduced.Comment: 10 pages, 6 figures, submitted to PR
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