Metal alloy resistivity measurements at very low temperatures

High speed, automated system accurately measures to approximately one percent in three minutes. System identifies materials having constant thermal or electric conductivity, predicts new material properties, develops alloys in accordance with desired specifications, and develops nondestructive devices for measuring precipitation hardening

The Viscosity and Thermal Conductivity Coefficients of Dilute Neon, Krypton, and Xenon

Viscosity and thermoconductivity coefficients of dilute neon, krypton, and xeno

Distinguishing n Hamiltonians on C^n by a single measurement

If an experimentalist wants to decide which one of n possible Hamiltonians acting on an n dimensional Hilbert space is present, he can conjugate the time evolution by an appropriate sequence of known unitary transformations in such a way that the different Hamiltonians result in mutual orthogonal final states. We present a general scheme providing such a sequence.Comment: 4 pages, Revte

Effects of Noise, Correlations and errors in the preparation of initial states in Quantum Simulations

In principle a quantum system could be used to simulate another quantum system. The purpose of such a simulation would be to obtain information about problems which cannot be simulated with a classical computer due to the exponential increase of the Hilbert space with the size of the system and which cannot be measured or controlled in an actual experiment. The system will interact with the surrounding environment, with the other particles in the system and be implemented using imperfect controls making it subject to noise. It has been suggested that noise does not need to be controlled to the same extent as it must be for general quantum computing. However the effects of noise in quantum simulations and how to treat them are not completely understood. In this paper we study an existing quantum algorithm for the one-dimensional Fano-Anderson model to be simulated using a liquid-state NMR device. We calculate the evolution of different initial states in the original model, and then we add interacting spins to simulate a more realistic situation. We find that states which are entangled with their environment, and sometimes correlated but not necessarily entangled have an evolution which is described by maps which are not completely positive. We discuss the conditions for this to occur and also the implications.Comment: Revtex 4-1, 14 pages, 21 figures, version 2 has typos corrected and acknowledgement adde

Limit Theorem for Continuous-Time Quantum Walk on the Line

Concerning a discrete-time quantum walk X^{(d)}_t with a symmetric distribution on the line, whose evolution is described by the Hadamard transformation, it was proved by the author that the following weak limit theorem holds: X^{(d)}_t /t \to dx / \pi (1-x^2) \sqrt{1 - 2 x^2} as t \to \infty. The present paper shows that a similar type of weak limit theorems is satisfied for a {\it continuous-time} quantum walk X^{(c)}_t on the line as follows: X^{(c)}_t /t \to dx / \pi \sqrt{1 - x^2} as t \to \infty. These results for quantum walks form a striking contrast to the central limit theorem for symmetric discrete- and continuous-time classical random walks: Y_{t}/ \sqrt{t} \to e^{-x^2/2} dx / \sqrt{2 \pi} as t \to \infty. The work deals also with issue of the relationship between discrete and continuous-time quantum walks. This topic, subject of a long debate in the previous literature, is treated within the formalism of matrix representation and the limit distributions are exhaustively compared in the two cases.Comment: 15 pages, title correcte

Exploring the Cosmic Evolution of Habitability with Galaxy Merger Trees

We combine inferred galaxy properties from a semi-analytic galaxy evolution model incorporating dark matter halo merger trees with new estimates of supernova and gamma ray burst rates as a function of metallicity from stellar population synthesis models incorporating binary interactions. We use these to explore the stellar mass fraction of galaxies irradiated by energetic astrophysical transients and its evolution over cosmic time, and thus the fraction which is potentially habitable by life like our own. We find that 18 per cent of the stellar mass in the Universe is likely to have been irradiated within the last 260 Myr, with GRBs dominating that fraction. We do not see a strong dependence of irradiated stellar mass fraction on stellar mass or richness of the galaxy environment. We consider a representative merger tree as a Local Group analogue, and find that there are galaxies at all masses which have retained a high habitable fraction (>40 per cent) over the last 6 Gyr, but also that there are galaxies at all masses where the merger history and associated star formation have rendered galaxies effectively uninhabitable. This illustrates the need to consider detailed merger trees when evaluating the cosmic evolution of habitability.Comment: 11 page, 10 figures. MNRAS accepted 13th Dec 2017. Updated to match accepted version, with additional discussion of metallicity effect

Measuring Energy, Estimating Hamiltonians, and the Time-Energy Uncertainty Relation

Suppose that the Hamiltonian acting on a quantum system is unknown and one wants to determine what is the Hamiltonian. We show that in general this requires a time $\Delta t$ which obeys the uncertainty relation $\Delta t \Delta H \gtrsim 1$ where $\Delta H$ is a measure of how accurately the unknown Hamiltonian must be estimated. We then apply this result to the problem of measuring the energy of an unknown quantum state. It has been previously shown that if the Hamiltonian is known, then the energy can in principle be measured in an arbitrarily short time. On the other hand we show that if the Hamiltonian is not known then an energy measurement necessarily takes a minimum time $\Delta t$ which obeys the uncertainty relation $\Delta t \Delta E \gtrsim 1$ where $\Delta E$ is the precision of the energy measurement. Several examples are studied to address the question of whether it is possible to saturate these uncertainty relations. Their interpretation is discussed in detail.Comment: 12pages, revised version with small correction

Quantum algorithm for the Boolean hidden shift problem

The hidden shift problem is a natural place to look for new separations between classical and quantum models of computation. One advantage of this problem is its flexibility, since it can be defined for a whole range of functions and a whole range of underlying groups. In a way, this distinguishes it from the hidden subgroup problem where more stringent requirements about the existence of a periodic subgroup have to be made. And yet, the hidden shift problem proves to be rich enough to capture interesting features of problems of algebraic, geometric, and combinatorial flavor. We present a quantum algorithm to identify the hidden shift for any Boolean function. Using Fourier analysis for Boolean functions we relate the time and query complexity of the algorithm to an intrinsic property of the function, namely its minimum influence. We show that for randomly chosen functions the time complexity of the algorithm is polynomial. Based on this we show an average case exponential separation between classical and quantum time complexity. A perhaps interesting aspect of this work is that, while the extremal case of the Boolean hidden shift problem over so-called bent functions can be reduced to a hidden subgroup problem over an abelian group, the more general case studied here does not seem to allow such a reduction.Comment: 10 pages, 1 figur

Optimal estimation of quantum dynamics

We construct the optimal strategy for the estimation of an unknown unitary transformation $U\in SU(d)$. This includes, in addition to a convenient measurement on a probe system, finding which is the best initial state on which $U$ is to act. When $U\in SU(2)$, such an optimal strategy can be applied to estimate simultaneously both the direction and the strength of a magnetic field, and shows how to use a spin 1/2 particle to transmit information about a whole coordinate system instead of only a direction in space.Comment: 4 pages, REVTE

One- and two-dimensional quantum walks in arrays of optical traps

We propose a novel implementation of discrete time quantum walks for a neutral atom in an array of optical microtraps or an optical lattice. We analyze a one-dimensional walk in position space, with the coin, the additional qubit degree of freedom that controls the displacement of the quantum walker, implemented as a spatially delocalized qubit, i.e., the coin is also encoded in position space. We analyze the dependence of the quantum walk on temperature and experimental imperfections as shaking in the trap positions. Finally, combining a spatially delocalized qubit and a hyperfine qubit, we also give a scheme to realize a quantum walk on a two-dimensional square lattice with the possibility of implementing different coin operators.Comment: 10 pages, 8 figures; v2: some comments added and other minor change