Quantum games via search algorithms

We build new quantum games, similar to the spin flip game, where as a novelty the players perform measurements on a quantum system associated to a continuous time search algorithm. The measurements collapse the wave function into one of the two possible states. These games are characterized by a continuous space of strategies and the selection of a particular strategy is determined by the moments when the players measure.Comment: 4 pages, 3 figure

Hilbert Space Average Method and adiabatic quantum search

We discuss some aspects related to the so-called Hilbert space Average Method, as an alternative to describe the dynamics of open quantum systems. First we present a derivation of the method which does not make use of the algebra satisfied by the operators involved in the dynamics, and extend the method to systems subject to a Hamiltonian that changes with time. Next we examine the performance of the adiabatic quantum search algorithm with a particular model for the environment. We relate our results to the criteria discussed in the literature for the validity of the above-mentioned method for similar environments.Comment: 6 pages, 1 figur

Simulation of the elementary evolution operator with the motional states of an ion in an anharmonic trap

Following a recent proposal of L. Wang and D. Babikov, J. Chem. Phys. 137, 064301 (2012), we theoretically illustrate the possibility of using the motional states of a $Cd^+$ ion trapped in a slightly anharmonic potential to simulate the single-particle time-dependent Schr\"odinger equation. The simulated wave packet is discretized on a spatial grid and the grid points are mapped on the ion motional states which define the qubit network. The localization probability at each grid point is obtained from the population in the corresponding motional state. The quantum gate is the elementary evolution operator corresponding to the time-dependent Schr\"odinger equation of the simulated system. The corresponding matrix can be estimated by any numerical algorithm. The radio-frequency field able to drive this unitary transformation among the qubit states of the ion is obtained by multi-target optimal control theory. The ion is assumed to be cooled in the ground motional state and the preliminary step consists in initializing the qubits with the amplitudes of the initial simulated wave packet. The time evolution of the localization probability at the grids points is then obtained by successive applications of the gate and reading out the motional state population. The gate field is always identical for a given simulated potential, only the field preparing the initial wave packet has to be optimized for different simulations. We check the stability of the simulation against decoherence due to fluctuating electric fields in the trap electrodes by applying dissipative Lindblad dynamics.Comment: 31 pages, 8 figures. Revised version. New title, new figure and new reference

Sub-ballistic behavior in quantum systems with L\'evy noise

We investigate the quantum walk and the quantum kicked rotor in resonance subjected to noise with a L\'evy waiting time distribution. We find that both systems have a sub-ballistic wave function spreading as shown by a power-law tail of the standard deviation.Comment: 4 pages, 4 figure

Topological Insulators with Inversion Symmetry

Topological insulators are materials with a bulk excitation gap generated by the spin orbit interaction, and which are different from conventional insulators. This distinction is characterized by Z_2 topological invariants, which characterize the groundstate. In two dimensions there is a single Z_2 invariant which distinguishes the ordinary insulator from the quantum spin Hall phase. In three dimensions there are four Z_2 invariants, which distinguish the ordinary insulator from "weak" and "strong" topological insulators. These phases are characterized by the presence of gapless surface (or edge) states. In the 2D quantum spin Hall phase and the 3D strong topological insulator these states are robust and are insensitive to weak disorder and interactions. In this paper we show that the presence of inversion symmetry greatly simplifies the problem of evaluating the Z_2 invariants. We show that the invariants can be determined from the knowledge of the parity of the occupied Bloch wavefunctions at the time reversal invariant points in the Brillouin zone. Using this approach, we predict a number of specific materials are strong topological insulators, including the semiconducting alloy Bi_{1-x} Sb_x as well as \alpha-Sn and HgTe under uniaxial strain. This paper also includes an expanded discussion of our formulation of the topological insulators in both two and three dimensions, as well as implications for experiments.Comment: 16 pages, 7 figures; published versio

Quantum random walk on the line as a markovian process

We analyze in detail the discrete--time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic increase in the variance of the quantum walker's position with time is a direct consequence of the coherence of the quantum evolution. If the evolution is decoherent, as in the classical case, the variance is shown to increase linearly with time, as expected. Furthermore we show that this system has an evolution operator analogous to that of a resonant quantum kicked rotor. As this rotator may be described through a quantum computational algorithm, one may employ this algorithm to describe the time evolution of the quantum walker.Comment: few typos corrected, 13 pages, 2 figures, to appear in Physica

Impact of chronic health conditions and injury on school performance and health outcomes in New South Wales, Australia : a retrospective record linkage study protocol

Introduction: Children who have sustained a serious injury or who have a chronic health condition, such as diabetes or epilepsy, may have their school performance adversely impacted by the condition, treatment of the condition and/or time away from school. Examining the potential adverse impact requires the identification of children most likely to be affected and the use of objective measures of education performance. This may highlight educational disparities that could be addressed with learning support. This study aims to examine education performance, school completion and health outcomes of children in New South Wales (NSW), Australia, who were hospitalised with an injury or a chronic health condition compared with children who have not been hospitalised for these conditions. Method and analysis This research will be a retrospective population-level case-comparison study of hospitalised injured or chronically ill children (ie, diabetes, epilepsy, asthma or mental health conditions) aged ≤18 years in NSW, Australia, using linked health and education administrative data collections. It will examine the education performance, school completion and health outcomes of children who have been hospitalised in NSW with an injury or a chronic health condition compared with children randomly drawn from the NSW population (matched on gender, age and residential postcode) who have not been hospitalised for these conditions. Ethics and dissemination The study received ethics approval from the NSW Population Health Services Research Ethics Committee (2018HRE0904). Findings from the research will be published in peer-reviewed journals and presented at scientific conferences