2,502 research outputs found
Algebraic equivalence between certain models for superfluid--insulator transition
Algebraic contraction is proposed to realize mappings between models
Hamiltonians. This transformation contracts the algebra of the degrees of
freedom underlying the Hamiltonian. The rigorous mapping between the
anisotropic Heisenberg model, the Quantum Phase Model, and the Bose
Hubbard Model is established as the contractions of the algebra
underlying the dynamics of the Heisenberg model.Comment: 5 pages, revte
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
Simple Phase Bias for Superconducting Circuits
A phase-bias tool, based on a trapped fluxoid in a ring, is proposed and
demonstrated. It can provide arbitrary phase values and is simple to fabricate.
The phase bias has been realized in two superconducting quantum interference
devices, where the critical current versus magnetic flux is shown to be shifted
by a \pi/2 and \pi.Comment: 5 pages, including 4 figures. Submitted to AP
A single-electron inverter
A single-electron inverter was fabricated that switches from a high output to
a low output when a fraction of an electron is added to the input. For the
proper operation of the inverter, the two single-electron transistors that make
up the inverter must exhibit voltage gain. Voltage gain was achieved by
fabricating a combination of parallel-plate gate capacitors and small tunnel
junctions in a two-layer circuit. Voltage gain of 2.6 was attained at 25 mK and
remained larger than one for temperatures up to 140 mK. The temperature
dependence of the gain agrees with the orthodox theory of single-electron
tunneling.Comment: 3 pages, 4 figures (1 color), to be published in Appl. Phys. Let
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.
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