Flux Qubits and Readout Device with Two Independent Flux Lines

We report measurements on two superconducting flux qubits coupled to a readout Superconducting QUantum Interference Device (SQUID). Two on-chip flux bias lines allow independent flux control of any two of the three elements, as illustrated by a two-dimensional qubit flux map. The application of microwaves yields a frequency-flux dispersion curve for 1- and 2-photon driving of the single-qubit excited state, and coherent manipulation of the single-qubit state results in Rabi oscillations and Ramsey fringes. This architecture should be scalable to many qubits and SQUIDs on a single chip.Comment: 5 pages, 4 figures, higher quality figures available upon request. Submitted to PR

A Simple, Quick, and Precise Procedure for the Determination of Water in Organic Solvents

A procedure for the UV/VIS-spectroscopic determination of water by the use of a solvatochromic pyridiniumphenolate betaine is given. The water content of organic solvents is calculated by a two parameter equation from λmax of the dye. A typical, detection limit is of the order of 1 mg in 1 ml solvent for routine spectrometers. The parameters for the determination of water are given for a number of commonly used solvents

Keeping a Quantum Bit Alive by Optimized π\pi-Pulse Sequences

A general strategy to maintain the coherence of a quantum bit is proposed. The analytical result is derived rigorously including all memory and back-action effects. It is based on an optimized $\pi$-pulse sequence for dynamic decoupling extending the Carr-Purcell-Meiboom-Gill (CPMG) cycle. The optimized sequence is very efficient, in particular for strong couplings to the environment.Comment: 4 pages, 2 figures; revised version with additional references for better context, more stringent discussio

Lattice dynamics and electron-phonon coupling in Sr2RuO4

The lattice dynamics in Sr$_2$RuO$_4$ has been studied by inelastic neutron scattering combined with shell-model calculations. The in-plane bond-stretching modes in Sr$_2$RuO$_4$ exhibit a normal dispersion in contrast to all electronically doped perovskites studied so far. Evidence for strong electron phonon coupling is found for c-polarized phonons suggesting a close connection with the anomalous c-axis charge transport in Sr$_2$RuO$_4$.Comment: 11 pages, 8 figures 2 table

Quantum error correction benchmarks for continuous weak parity measurements

We present an experimental procedure to determine the usefulness of a measurement scheme for quantum error correction (QEC). A QEC scheme typically requires the ability to prepare entangled states, to carry out multi-qubit measurements, and to perform certain recovery operations conditioned on measurement outcomes. As a consequence, the experimental benchmark of a QEC scheme is a tall order because it requires the conjuncture of many elementary components. Our scheme opens the path to experimental benchmarks of individual components of QEC. Our numerical simulations show that certain parity measurements realized in circuit quantum electrodynamics are on the verge of being useful for QEC

Improved magic states distillation for quantum universality

Given stabilizer operations and the ability to repeatedly prepare a single-qubit mixed state rho, can we do universal quantum computation? As motivation for this question, "magic state" distillation procedures can reduce the general fault-tolerance problem to that of performing fault-tolerant stabilizer circuits. We improve the procedures of Bravyi and Kitaev in the Hadamard "magic" direction of the Bloch sphere to achieve a sharp threshold between those rho allowing universal quantum computation, and those for which any calculation can be efficiently classically simulated. As a corollary, the ability to repeatedly prepare any pure state which is not a stabilizer state (e.g., any single-qubit pure state which is not a Pauli eigenstate), together with stabilizer operations, gives quantum universality. It remains open whether there is also a tight separation in the so-called T direction.Comment: 6 pages, 5 figure

Quantum interference effects in resonant Raman spectroscopy of single- and triple-layer MoTe2_2 from first principles

We present a combined experimental and theoretical study of resonant Raman spectroscopy in single- and triple-layer MoTe$_2$. Raman intensities are computed entirely from first principles by calculating finite differences of the dielectric susceptibility. In our analysis, we investigate the role of quantum interference effects and the electron-phonon coupling. With this method, we explain the experimentally observed intensity inversion of the $A^\prime_1$ vibrational modes in triple-layer MoTe2 with increasing laser photon energy. Finally, we show that a quantitative comparison with experimental data requires the proper inclusion of excitonic effects.Comment: Main Text (5 Figures, 1 Tables) + Supporting Information (6 Figures

Electron-phonon interaction in the three-band model

We study the half-breathing phonon in the three-band model of a high temperature superconductor, allowing for vibrations of atoms and resulting changes of hopping parameters. Two different approaches are compared. From the three-band model a t-J model with phonons can be derived, and phonon properties can be calculated. To make contact to density functional calculations, we also study the three-band model in the Hartree-Fock (HF) approximation. The paramagnetic HF solution, appropriate for the doped cuprates, has similarities to the local-density approximation (LDA). However, in contrast to the LDA, the existence of an antiferromagnetic insulating solution for the undoped system makes it possible to study the softening of the half-breathing phonon under doping. We find that although the HF approximation and the t-J model give similar softenings, these softenings happen in quite different ways. We also find that the HF approximation gives an incorrect doping and q dependence for the softening and too small a width for the (half-)breathing phonon.Comment: 7 pages, RevTeX, 4 eps figure

Community Structure in Time-Dependent, Multiscale, and Multiplex Networks

Network science is an interdisciplinary endeavor, with methods and applications drawn from across the natural, social, and information sciences. A prominent problem in network science is the algorithmic detection of tightly-connected groups of nodes known as communities. We developed a generalized framework of network quality functions that allowed us to study the community structure of arbitrary multislice networks, which are combinations of individual networks coupled through links that connect each node in one network slice to itself in other slices. This framework allows one to study community structure in a very general setting encompassing networks that evolve over time, have multiple types of links (multiplexity), and have multiple scales.Comment: 31 pages, 3 figures, 1 table. Includes main text and supporting material. This is the accepted version of the manuscript (the definitive version appeared in Science), with typographical corrections included her

Statistical Mechanics of Community Detection

Starting from a general \textit{ansatz}, we show how community detection can be interpreted as finding the ground state of an infinite range spin glass. Our approach applies to weighted and directed networks alike. It contains the \textit{at hoc} introduced quality function from \cite{ReichardtPRL} and the modularity $Q$ as defined by Newman and Girvan \cite{Girvan03} as special cases. The community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices. We elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study. Further we show, how hierarchies and overlap in the community structure can be detected. Computationally effective local update rules for optimization procedures to find the ground state are given. We show how the \textit{ansatz} may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension. Finally, we give expectation values for the modularity of random graphs, which can be used in the assessment of statistical significance of community structure