Quantum Walks, Quantum Gates and Quantum Computers

The physics of quantum walks on graphs is formulated in Hamiltonian language, both for simple quantum walks and for composite walks, where extra discrete degrees of freedom live at each node of the graph. It is shown how to map between quantum walk Hamiltonians and Hamiltonians for qubit systems and quantum circuits; this is done for both a single- and multi-excitation coding, and for more general mappings. Specific examples of spin chains, as well as static and dynamic systems of qubits, are mapped to quantum walks, and walks on hyperlattices and hypercubes are mapped to various gate systems. We also show how to map a quantum circuit performing the quantum Fourier transform, the key element of Shor's algorithm, to a quantum walk system doing the same. The results herein are an essential preliminary to a Hamiltonian formulation of quantum walks in which coupling to a dynamic quantum environment is included.Comment: 17 pages, 10 figure

Origin of strange metallic phase in cuprate superconductors

The origin of strange metallic phase is shown to exist due to these two conditions---(i) the electrons are strongly interacting such that there are no band and Mott-Hubbard gaps, and (ii) the electronic energy levels are crossed in such a way that there is an electronic energy gap between two energy levels associated to two different wave functions. The theory is also exploited to explain (i) the upward- and downward-shifts in the $T$-linear resistivity curves, and (ii) the spectral weight transfer observed in the soft X-ray absorption spectroscopic measurements of the La-Sr-Cu-O Mott insulator.Comment: To be published in J. Supercond. Nov. Mag

Normal Accidents of Expertise

Charles Perrow used the term “normal accidents” to characterize a type of catastrophic failure that resulted when complex, tightly coupled production systems encountered a certain kind of anomalous event. These were events in which systems failures interacted with one another in a way that could not be anticipated, and could not be easily understood and corrected. Systems of the production of expert knowledge are increasingly becoming tightly coupled. Unlike classical science, which operated with a long time horizon, many current forms of expert knowledge are directed at immediate solutions to complex problems. These are prone to breakdowns like the kind discussed by Perrow. The example of the Homestake mine experiment shows that even in modern physics complex systems can produce knowledge failures that last for decades. The concept of knowledge risk is introduced, and used to characterize the risk of failure in such systems of knowledge production

Mice Null for Calsequestrin 1 Exhibit Deficits in Functional Performance and Sarcoplasmic Reticulum Calcium Handling

In skeletal muscle, the release of calcium (Ca2+) by ryanodine sensitive sarcoplasmic reticulum (SR) Ca2+ release channels (i.e., ryanodine receptors; RyR1s) is the primary determinant of contractile filament activation. Much attention has been focused on calsequestrin (CASQ1) and its role in SR Ca2+ buffering as well as its potential for modulating RyR1, the L-type Ca2+ channel (dihydropyridine receptor, DHPR) and other sarcolemmal channels through sensing luminal [Ca2+]. The genetic ablation of CASQ1 expression results in significant alterations in SR Ca2+ content and SR Ca2+ release especially during prolonged activation. While these findings predict a significant loss-of-function phenotype in vivo, little information on functional status of CASQ1 null mice is available. We examined fast muscle in vivo and in vitro and identified significant deficits in functional performance that indicate an inability to sustain contractile activation. In single CASQ1 null skeletal myofibers we demonstrate a decrease in voltage dependent RyR Ca2+ release with single action potentials and a collapse of the Ca2+ release with repetitive trains. Under voltage clamp, SR Ca2+ release flux and total SR Ca2+ release are significantly reduced in CASQ1 null myofibers. The decrease in peak Ca2+ release flux appears to be solely due to elimination of the slowly decaying component of SR Ca2+ release, whereas the rapidly decaying component of SR Ca2+ release is not altered in either amplitude or time course in CASQ1 null fibers. Finally, intra-SR [Ca2+] during ligand and voltage activation of RyR1 revealed a significant decrease in the SR[Ca2+]free in intact CASQ1 null fibers and a increase in the release and uptake kinetics consistent with a depletion of intra-SR Ca2+ buffering capacity. Taken together we have revealed that the genetic ablation of CASQ1 expression results in significant functional deficits consistent with a decrease in the slowly decaying component of SR Ca2+ release

Fluo-4 fluorescence transients are altered in CASQ1 null FDB myofibers.

<p>Free [Ca²⁺] and Ca²⁺ release flux from WT (left) and CASQ1 null fibers (right). Average (n = 4) time course of fluo-4 F/F₀ records expanded in time elicited at different voltages are displayed for WT fibers (<b>A</b>) and for CASQ1 null fibers (<b>B</b>). (<b>C</b>) and (<b>D</b>) are free [Ca²⁺] waveforms derived from <i>A</i> and <i>B</i> while (<b>E</b>) and (<b>F</b>) are Ca²⁺ release flux calculated from <i>C</i> and <i>D</i>. Comparison of the two sets of data show significant suppression of the amplitude of F/F₀, free Ca²⁺ and peak and maintained Ca²⁺ release flux in the CASQ1 null fibers.</p

CASQ1 null myofibers have a reduction in relative SR [Ca²⁺]_free.

<p><b>A.</b> Representative SR Fluo5N fluorescence profile of a WT and CASQ1 null myofibers challenged with 1 mM 4-CmC. This profile was normalized to the maximum 4-CmC depletion (ΔF/F_4-CmC). <b>B.</b> The evaluation of F_initial as a surrogate to SR [Ca²⁺]_free (see results) revealed that CASQ1 null myofibers had a ∼24% reduction in relative SR [Ca²⁺]_free compared to WT myofibers (Mann-Whitney rank-sum test, P<0.05).</p

The kinetics of the Ca²⁺ release time courses differ between CASQ1 null and WT myofibers.

<p>Superimposed average Ca²⁺ release time courses at −40 mV (<b>A</b>), −20 mV (<b>B</b>), 0 mV (<b>C</b>) and +20 mV (<b>D</b>) voltage steps from WT (black traces) and CASQ1 null fibers (red traces). (<b>E</b>–<b>H</b>) Time course of the normalized Ca²⁺ release flux in the WT and CASQ1 null fibers derived from panels <i>A–D</i> to show effects of CASQ1 elimination on the kinetics of Ca²⁺ release. <i>Insets</i> show zoom-in versions of the raising phase of the rate of Ca²⁺ release. The kinetics of the peak formation appear unchanged from the WT fibers to the CASQ1 null fibers however the slow component is virtually eliminated, suggesting a rapid decline of the SR Ca²⁺ content in the absence of CASQ1.</p