1,872 research outputs found
Sufficient conditions for convergence of the Sum-Product Algorithm
We derive novel conditions that guarantee convergence of the Sum-Product
algorithm (also known as Loopy Belief Propagation or simply Belief Propagation)
to a unique fixed point, irrespective of the initial messages. The
computational complexity of the conditions is polynomial in the number of
variables. In contrast with previously existing conditions, our results are
directly applicable to arbitrary factor graphs (with discrete variables) and
are shown to be valid also in the case of factors containing zeros, under some
additional conditions. We compare our bounds with existing ones, numerically
and, if possible, analytically. For binary variables with pairwise
interactions, we derive sufficient conditions that take into account local
evidence (i.e., single variable factors) and the type of pair interactions
(attractive or repulsive). It is shown empirically that this bound outperforms
existing bounds.Comment: 15 pages, 5 figures. Major changes and new results in this revised
version. Submitted to IEEE Transactions on Information Theor
Truncating the loop series expansion for Belief Propagation
Recently, M. Chertkov and V.Y. Chernyak derived an exact expression for the
partition sum (normalization constant) corresponding to a graphical model,
which is an expansion around the Belief Propagation solution. By adding
correction terms to the BP free energy, one for each "generalized loop" in the
factor graph, the exact partition sum is obtained. However, the usually
enormous number of generalized loops generally prohibits summation over all
correction terms. In this article we introduce Truncated Loop Series BP
(TLSBP), a particular way of truncating the loop series of M. Chertkov and V.Y.
Chernyak by considering generalized loops as compositions of simple loops. We
analyze the performance of TLSBP in different scenarios, including the Ising
model, regular random graphs and on Promedas, a large probabilistic medical
diagnostic system. We show that TLSBP often improves upon the accuracy of the
BP solution, at the expense of increased computation time. We also show that
the performance of TLSBP strongly depends on the degree of interaction between
the variables. For weak interactions, truncating the series leads to
significant improvements, whereas for strong interactions it can be
ineffective, even if a high number of terms is considered.Comment: 31 pages, 12 figures, submitted to Journal of Machine Learning
Researc
Quantum state detection of a superconducting flux qubit using a DC-SQUID in the inductive mode
We present a readout method for superconducting flux qubits. The qubit
quantum flux state can be measured by determining the Josephson inductance of
an inductively coupled DC superconducting quantum interference device
(DC-SQUID). We determine the response function of the DC-SQUID and its
back-action on the qubit during measurement. Due to driving, the qubit energy
relaxation rate depends on the spectral density of the measurement circuit
noise at sum and difference frequencies of the qubit Larmor frequency and SQUID
driving frequency. The qubit dephasing rate is proportional to the spectral
density of circuit noise at the SQUID driving frequency. These features of the
backaction are qualitatively different from the case when the SQUID is used in
the usual switching mode. For a particular type of readout circuit with
feasible parameters we find that single shot readout of a superconducting flux
qubit is possible.Comment: 11 pages, 3 figures; submitted to Phys. Rev.
Parametric coupling for superconducting qubits
We propose a scheme to couple two superconducting charge or flux qubits
biased at their symmetry points with unequal energy splittings. Modulating the
coupling constant between two qubits at the sum or difference of their two
frequencies allows to bring them into resonance in the rotating frame.
Switching on and off the modulation amounts to switching on and off the
coupling which can be realized at nanosecond speed. We discuss various physical
implementations of this idea, and find that our scheme can lead to rapid
operation of a two-qubit gate.Comment: 6 page
Coherent Quantum Dynamics of a Superconducting Flux Qubit
We have observed coherent time evolution between two quantum states of a
superconducting flux qubit comprising three Josephson junctions in a loop. The
superposition of the two states carrying opposite macroscopic persistent
currents is manipulated by resonant microwave pulses. Readout by means of
switching-event measurement with an attached superconducting quantum
interference device revealed quantum-state oscillations with high fidelity.
Under strong microwave driving it was possible to induce hundreds of coherent
oscillations. Pulsed operations on this first sample yielded a relaxation time
of 900 nanoseconds and a free-induction dephasing time of 20 nanoseconds. These
results are promising for future solid-state quantum computing.Comment: submitted 2 December 2002; accepted 4 February 200
Characterising exo-ringsystems around fast-rotating stars using the Rossiter-McLaughlin effect
Planetary rings produce a distinct shape distortion in transit lightcurves.
However, to accurately model such lightcurves the observations need to cover
the entire transit, especially ingress and egress, as well as an out-of-transit
baseline. Such observations can be challenging for long period planets, where
the transits may last for over a day. Planetary rings will also impact the
shape of absorption lines in the stellar spectrum, as the planet and rings
cover different parts of the rotating star (the Rossiter-McLaughlin effect).
These line-profile distortions depend on the size, structure, opacity,
obliquity and sky projected angle of the ring system. For slow rotating stars,
this mainly impacts the amplitude of the induced velocity shift, however, for
fast rotating stars the large velocity gradient across the star allows the line
distortion to be resolved, enabling direct determination of the ring
parameters. We demonstrate that by modeling these distortions we can recover
ring system parameters (sky-projected angle, obliquity and size) using only a
small part of the transit. Substructure in the rings, e.g. gaps, can be
recovered if the width of the features () relative to the size of the
star is similar to the intrinsic velocity resolution (set by the width of the
local stellar profile, ) relative to the stellar rotation velocity (
sin, i.e. sin/). This opens up a new
way to study the ring systems around planets with long orbital periods, where
observations of the full transit, covering the ingress and egress, are not
always feasible.Comment: Accepted for publication in MNRA
Nondestructive readout for a superconducting flux qubit
We present a new readout method for a superconducting flux qubit, based on
the measurement of the Josephson inductance of a superconducting quantum
interference device that is inductively coupled to the qubit. The intrinsic
flux detection efficiency and back-action are suitable for a fast and
nondestructive determination of the quantum state of the qubit, as needed for
readout of multiple qubits in a quantum computer. We performed spectroscopy of
a flux qubit and we measured relaxation times of the order of 80 .Comment: 4 pages, 4 figures; modified content, figures and references;
accepted for publication in Phys. Rev. Let
Phase-slip flux qubits
In thin superconducting wires, phase-slip by thermal activation near the
critical temperature is a well-known effect. It has recently become clear that
phase-slip by quantum tunnelling through the energy barrier can also have a
significant rate at low temperatures. In this paper it is suggested that
quantum phase-slip can be used to realize a superconducting quantum bit without
Josephson junctions. A loop containing a nanofabricated very thin wire is
biased with an externally applied magnetic flux of half a flux quantum,
resulting in two states with opposite circulating current and equal energy.
Quantum phase-slip should provide coherent coupling between these two
macroscopic states. Numbers are given for a wire of amorphous niobium-silicon
that can be fabricated with advanced electron beam lithography.Comment: Submitted to New Journal of Physics, special issue solid state
quantum informatio
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