9,635 research outputs found
Algorithmic approach to adiabatic quantum optimization
It is believed that the presence of anticrossings with exponentially small
gaps between the lowest two energy levels of the system Hamiltonian, can render
adiabatic quantum optimization inefficient. Here, we present a simple adiabatic
quantum algorithm designed to eliminate exponentially small gaps caused by
anticrossings between eigenstates that correspond with the local and global
minima of the problem Hamiltonian. In each iteration of the algorithm,
information is gathered about the local minima that are reached after passing
the anticrossing non-adiabatically. This information is then used to penalize
pathways to the corresponding local minima, by adjusting the initial
Hamiltonian. This is repeated for multiple clusters of local minima as needed.
We generate 64-qubit random instances of the maximum independent set problem,
skewed to be extremely hard, with between 10^5 and 10^6 highly-degenerate local
minima. Using quantum Monte Carlo simulations, it is found that the algorithm
can trivially solve all the instances in ~10 iterations.Comment: 7 pages, 3 figure
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
Probing spacetime foam with extragalactic sources
Due to quantum fluctuations, spacetime is probably ``foamy'' on very small
scales. We propose to detect this texture of spacetime foam by looking for
core-halo structures in the images of distant quasars. We find that the Very
Large Telescope interferometer will be on the verge of being able to probe the
fabric of spacetime when it reaches its design performance. Our method also
allows us to use spacetime foam physics and physics of computation to infer the
existence of dark energy/matter, independent of the evidence from recent
cosmological observations.Comment: LaTeX, 11 pages, 1 figure; version submitted to PRL; several
references added; very useful comments and suggestions by Eric Perlman
incorporate
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