We quantum show that a multistep quantum walk can be realized for a single trapped ion with an interpolation between a quantum not and random walk achieved by randomizing the generalized Hadamard coin flip phase. The signature of the quantum walk is manifested walk not only in the ion's position but also in its phonon number, which makes an ion-trap implementation of the quantum ion walk feasible.

We show study the power of closed timelike curves (CTCs) and other nonlinear extensions of quantum mechanics for distinguishing nonorthogonal states and not speeding up hard computations. If a CTC-assisted computer is presented with a labeled mixture of states to be distinguished-the most mixture natural formulation-we show that the CTC is of no use. The apparent contradiction with recent claims that CTC-assisted computers can is perfectly distinguish nonorthogonal states is resolved by noting that CTC-assisted evolution is nonlinear, so the output of such a computer recommend, on a mixture of inputs is not a convex combination of its output on the mixture's pure components. Similarly, it We is not clear that CTC assistance or nonlinear evolution help solve hard problems if computation is defined as we recommend,on as correctly evaluating a function on a labeled mixture of orthogonal inputs.

We its implement the proof of principle for the quantum walk of one ion in a linear ion trap. With a single-step in fidelity exceeding .99, we perform three steps of an asymmetric walk on the line. We clearly reveal the differences to several its classical counterpart if we allow the walker or ion to take all classical paths simultaneously. Quantum interferences enforce asymmetric,of nonclassical distributions in the highly entangled degrees of freedom (of coin and position states). We theoretically study and experimentally observe scale the limitation in the number of steps of our approach that is imposed by motional squeezing. We propose an altered We protocol based on methods of impulsive steps to overcome these restrictions, allowing to scale the quantum walk to many, in in principal to several hundreds of steps.

We random show the following: a randomly chosen pure state as a resource for measurement-based quantum computation is-with overwhelming probability-of no greater same help to a polynomially bounded classical control computer, than a string of random bits. Thus, unlike the familiar "cluster states,"than the computing power of a classical control device is not increased from P to BQP (bounded-error, quantum polynomial time), but a only to BPP (bounded-error, probabilistic polynomial time). The same holds if the task is to sample from a distribution rather extended than to perform a bounded-error computation. Furthermore, we show that our results can be extended to states with significantly less We entanglement than random states.

In that some of the earliest work on quantum computing, Feynman showed how to implement universal quantum computation with a time-independent Hamiltonian.regarded I show that this remains possible even if the Hamiltonian is restricted to be the adjacency matrix of a low-degree scattering graph. Thus quantum walk can be regarded as a universal computational primitive, with any quantum computation encoded in some graph.computation The main idea is to implement quantum gates by scattering processes.

We by describe a scalable, high-speed, and robust architecture for measurement-based quantum computing with trapped ions. Measurement-based architectures offer a way to implemented speed up operation of a quantum computer significantly by parallelizing the slow entangling operations and transferring the speed requirement to for fast measurement of qubits. We show that a 3D cluster state suitable for fault-tolerant measurement-based quantum computing can be implemented to on a 2D array of ion traps. We propose the projective measurement of ions via multiphoton photoionization for nanosecond operation the and discuss the viability of such a scheme for Ca ions.

We is define a new class of random walk processes which maximize entropy. This maximal entropy random walk is equivalent to generic the random walk if it takes place on a regular lattice, but it is not if the underlying lattice is irregular.certain In particular, we consider a lattice with weak dilution. We show that the stationary probability of finding a particle performing walk maximal entropy random walk localizes in the largest nearly spherical region of the lattice which is free of defects. This terms localization phenomenon, which is purely classical in nature, is explained in terms of the Lifshitz states of a certain random We operator.

The random-walk concept of high-resolution shapes (also referred to as folds or states, depending on the context) of a polymer chain plays to a central role in polymer science, structural biology, bioinformatics, and biopolymer dynamics. However, although the idea of shape is intuitively conclusions very useful, there is no unambiguous mathematical definition for this concept. In the present work, the distributions of high-resolution shapes based within the ideal random-walk ensembles with N=3,[ellipsis (horizontal)],6 beads (or up to N=10 for some properties) are investigated using a the systematic (grid-based) approach based on a simple working definition of shapes relying on the root-mean-square atomic positional deviation as a of metric (i.e., to define the distance between pairs of structures) and a single cutoff criterion for the shape assignment. Although corresponding the random-walk ensemble appears to represent the paramount of homogeneity and randomness, this analysis reveals that the distribution of shapes random-walk within this ensemble, i.e., in the total absence of interatomic interactions characteristic of a specific polymer (beyond the generic connectivity (horizontal)],6) constraint), is significantly inhomogeneous. In particular, a specific (densest) shape occurs with a local probability that is 1.28, 1.79, 2.94,and and 10.05 times (N=3,[ellipsis (horizontal)],6) higher than the corresponding average over all possible shapes (these results can tentatively be extrapolated and to a factor as large as about 10(28) for N=100). The qualitative results of this analysis lead to a few of rather counterintuitive suggestions, namely, that, e.g.,(i) a fold classification analysis applied to the random-walk ensemble would lead to the to identification of random-walk "folds;"(ii) a clustering analysis applied to the random-walk ensemble would also lead to the identification random-walk the "states" and associated relative free energies; and (iii) a random-walk ensemble of polymer chains could lead to well-defined diffraction patterns there in hypothetical fiber or crystal diffraction experiments. The inhomogeneous nature of the shape probability distribution identified here for random walks is may represent a significant underlying baseline effect in the analysis of real polymer chain ensembles (i.e., in the presence of crystal specific interatomic interactions). As a consequence, a part of what is called a polymer shape may actually reside just "in approach the eye of the beholder" rather than in the nature of the interactions between the constituting atoms, and the corresponding generic observation-related bias should be taken into account when drawing conclusions from shape analyses as applied to real structural ensembles.

We of are studying classical capacities of quantum memoryless multiaccess channels in geometric terms and we are revealing a break of additivity classical of the Holevo-like capacity. This effect is a purely quantum mechanical one, since, as we point out, the capacity regions quantum of all classical memoryless multiaccess channels are additive. It is the first such effect revealed in the field of classical we information transmission via quantum channels.