arXiv subjects

Simon C. Benjamin

Publications and source records attributed to Simon C. Benjamin.

100 records · Page 6Linked to original sources

arXiv2001

Simple Pulses for Universal Quantum Computation with a Heisenberg ABAB Chain

Recently Levy has shown that quantum computation can be performed using an ABAB.. chain of spin-1/2 systems with nearest-neighbor Heisenberg interactions. Levy notes that all necessary elementary computational `gates' can be achieved by using spin-resonance techniques involving modulating the spin-spin interaction strength at high frequency. Here we note that, as an alternative to that approach, it is possible to perform the elementary gates with simple, non-oscillatory pulses.

quant-ph↗

arXiv2001

Multi-Player Quantum Games

Recently the concept of quantum information has been introduced into game theory. Here we present the first study of quantum games with more than two players. We discover that such games can possess a new form of equilibrium strategy, one which has no analogue either in traditional games or even in two-player quantum games. In these `pure' coherent equilibria, entanglement shared among multiple players enables new kinds of cooperative behavior: indeed it can act as a contract, in the sense that it prevents players from successfully betraying one-another.

quant-ph↗

arXiv2001

Evolutionary quantum game

We present the first study of a dynamical quantum game. Each agent has a `memory' of her performance over the previous m timesteps, and her strategy can evolve in time. The game exhibits distinct regimes of optimality. For small m the classical game performs better, while for intermediate m the relative performance depends on whether the source of qubits is `corrupt'. For large m, the quantum players dramatically outperform the classical players by `freezing' the game into high-performing attractors in which evolution ceases.

quant-ph↗

arXiv2000

Comment on `Quantum Games and Quantum Strategies'

In a recent paper, Eisert et al. presented a quantum mechanical generalization of Prisoner's Dilemma. They asserted that the maximally entangled game exhibits a unique Nash equilibrium which yields a pay-off equivalent to cooperative behaviour. In this comment we show that their observation is incorrect: there is no Nash equilibrium in the space of deterministic quantum strategies.

quant-ph↗

arXiv1998

Structures for Data Processing in the Quantum Regime

We present a novel scheme for data processing which is well-suited for implementation at the nanometer scale. The logic circuits comprise two-state cellular units which are driven by externally applied updates, in contrast to earlier proposals which relied on ground-state relaxation. The present structures can simultaneously process many inputs and are suitable for conventional, dissipative computing in addition to classical reversible computing and quantum computing.

cond-mat.mes-hall↗

arXiv1997

A Possible Nanometer-scale Computing Device Based on an Adding Cellular Automaton

We present a simple one-dimensional Cellular Automaton (CA) which has the property that an initial state composed of two binary numbers evolves quickly into a final state which is their sum. We call this CA the Adding Cellular Automaton (ACA). The ACA requires only 2N two-state cells in order to add any two N-1 bit binary numbers. The ACA could be directly realized as a wireless nanometer-scale computing device - a possible implementation using coupled quantum dots is outlined.

cond-mat.mes-hall↗

arXiv1996

Exact dynamical response of an N-electron quantum dot subject to a time-dependent potential

We calculate analytically the exact dynamical response of a droplet of N interacting electrons in a quantum dot with an arbitrarily time-dependent parabolic confinement potential ω(t) and a perpendicular magnetic field. We find that, for certain frequency ranges, a sinusoidal perturbation acts like an attractive effective interaction between electrons. In the absence of a time-averaged confinement potential, the N electrons can bind together to form a stable, free-standing droplet.

cond-mat↗

arXiv1996

Some exact analytic results for the linear and non-linear response of atoms in a trap with a model interaction

We present an exact expression for the evolution of the wavefunction of $N$ interacting atoms in an arbitrarily time-dependent, $d$-dimensional parabolic trap potential $ω(t)$. The interaction potential between atoms is taken to be of the form $ξ/r^2$ with $ξ>0$. For a constant trap potential $ω(t)=ω_0$, we find an exact, infinite set of relative mode excitations. These excitations are relevant to the linear response of the system; they are universal in that their frequencies are independent of the initial state of the system (e.g. Bose-Einstein condensate), the strength $ξ$ of the atom-atom interaction, the dimensionality $d$ of the trap and the number of atoms $N$. The time evolution of the system for general $ω(t)$ derives entirely from the solution to the corresponding classical 1D single-particle problem. An analytic expression for the frequency response of the $N$-atom cluster is given in terms of $ω(t)$. We consider the important example of a sinusoidally-varying trap perturbation. Our treatment, being exact, spans the `linear' and `non-linear' regimes. Certain features of the response spectrum are found to be insensitive to interaction strength and atom number.

cond-mat↗

arXiv1996

Cellular automata models of traffic flow along a highway containing a junction

We examine various realistic generalizations of the basic cellular automaton model describing traffic flow along a highway. In particular, we introduce a {\em slow-to-start} rule which simulates a possible delay before a car pulls away from being stationary. Having discussed the case of a bare highway, we then consider the presence of a junction. We study the effects of acceleration, disorderness, and slow-to-start behavior on the queue length at the entrance to the highway. Interestingly, the junction's efficiency is {\it improved} by introducing disorderness along the highway, and by imposing a speed limit.

cond-mat↗

arXiv1995

Entangled Electronic States in Multiple Quantum-Dot Systems

We present an analytically solvable model of $P$ colinear, two-dimensional quantum dots, each containing two electrons. Inter-dot coupling via the electron-electron interaction gives rise to sets of entangled ground states. These ground states have crystal-like inter-plane correlations and arise discontinously with increasing magnetic field. Their ranges and stabilities are found to depend on dot size ratios, and to increase with $P$.

cond-mat↗