Efficient quantum algorithms for simulating sparse Hamiltonians

We present an efficient quantum algorithm for simulating the evolution of a sparse Hamiltonian H for a given time t in terms of a procedure for computing the matrix entries of H. In particular, when H acts on n qubits, has at most a constant number of nonzero entries in each row/column, and |H| is bounded by a constant, we may select any positive integer $k$ such that the simulation requires O((\log^*n)t^{1+1/2k}) accesses to matrix entries of H. We show that the temporal scaling cannot be significantly improved beyond this, because sublinear time scaling is not possible.Comment: 9 pages, 2 figures, substantial revision

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

Quantum central limit theorem for continuous-time quantum walks on odd graphs in quantum probability theory

The method of the quantum probability theory only requires simple structural data of graph and allows us to avoid a heavy combinational argument often necessary to obtain full description of spectrum of the adjacency matrix. In the present paper, by using the idea of calculation of the probability amplitudes for continuous-time quantum walk in terms of the quantum probability theory, we investigate quantum central limit theorem for continuous-time quantum walks on odd graphs.Comment: 19 page, 1 figure

Hitting Time of Quantum Walks with Perturbation

The hitting time is the required minimum time for a Markov chain-based walk (classical or quantum) to reach a target state in the state space. We investigate the effect of the perturbation on the hitting time of a quantum walk. We obtain an upper bound for the perturbed quantum walk hitting time by applying Szegedy's work and the perturbation bounds with Weyl's perturbation theorem on classical matrix. Based on the definition of quantum hitting time given in MNRS algorithm, we further compute the delayed perturbed hitting time (DPHT) and delayed perturbed quantum hitting time (DPQHT). We show that the upper bound for DPQHT is actually greater than the difference between the square root of the upper bound for a perturbed random walk and the square root of the lower bound for a random walk.Comment: 9 page

Realization of quantum process tomography in NMR

Quantum process tomography is a procedure by which the unknown dynamical evolution of an open quantum system can be fully experimentally characterized. We demonstrate explicitly how this procedure can be implemented with a nuclear magnetic resonance quantum computer. This allows us to measure the fidelity of a controlled-not logic gate and to experimentally investigate the error model for our computer. Based on the latter analysis, we test an important assumption underlying nearly all models of quantum error correction, the independence of errors on different qubits.Comment: 8 pages, 7 EPS figures, REVTe

Rotational kinetics of absorbing dust grains in neutral gas

We study the rotational and translational kinetics of massive particulates (dust grains) absorbing the ambient gas. Equations for microscopic phase densities are deduced resulting in the Fokker-Planck equation for the dust component. It is shown that although there is no stationary distribution, the translational and rotational temperatures of dust tend to certain values, which differ from the temperature of the ambient gas. The influence of the inner structure of grains on rotational kinetics is also discussed.Comment: REVTEX4, 20 pages, 2 figure

Entanglement capability of self-inverse Hamiltonian evolution

We determine the entanglement capability of self-inverse Hamiltonian evolution, which reduces to the known result for Ising Hamiltonian, and identify optimal input states for yielding the maximal entanglement rate. We introduce the concept of the operator entanglement rate, and find that the maximal operator entanglement rate gives a lower bound on the entanglement capability of a general Hamiltonian.Comment: 4 pages, no figures. Version 3: small change

O-band excited state quantum dot bilayer lasers

Bilayer InAs/GaAs quantum dot(QD) lasers operating in the excited state at wavelengths that span the O-band are demonstrated. The higher saturated gain and lower scattering time of the excited states of the ensemble of QDs offers the opportunity for fast direct-modulation lasers. We predict an increase in K-factor limited modulation bandwidth from QD lasers operating in the excited state due to a reduction in carrier transport and scattering times whilst maintaining high peak modal gain

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa