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 $XXZ$ Heisenberg model, the Quantum Phase Model, and the Bose Hubbard Model is established as the contractions of the algebra $u(2)$ underlying the dynamics of the $XXZ$ 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.