Franklin L. Marquezino

Spatial search on a honeycomb network

The spatial search problem consists of minimising the number of steps required to find a given site in a network under the restriction that only oracle queries or translations to neighbouring sites are allowed. We propose a quantum algorithm for the spatial search problem on a honeycomb lattice with N sites and torus-like boundary conditions. The search algorithm is based on a modified quantum walk on an hexagonal lattice and the general framework proposed by Ambainis, Kempe and Rivosh (Ambainis et al. 2005) is employed to show that the time complexity of this quantum search algorithm is

Mixing times in quantum walks on the hypercube

O(\sqrt{N \log N})

The QWalk simulator of quantum walks

.

Spatial search algorithms on Hanoi networks

The mixing time of a discrete-time quantum walk on the hypercube is considered. The mean probability distribution of a Markov chain on a hypercube is known to mix to a uniform distribution in time

Thermodynamics ofN-dimensional quantum walks

O(n\text{ }\text{log}\text{ }n)

Quantum search algorithms on hierarchical networks

. We show that the mean probability distribution of a discrete-time quantum walk on a hypercube mixes to a (generally nonuniform) distribution

Preserving privacy in a smart grid scenario using quantum mechanics

\ensuremath{\pi}(x)

Quantum Query as a State Decomposition

in time

A new reversible circuit synthesis algorithm based on cycle representations of permutations

O(n)

Obtaining the Quantum Fourier Transform from the classical FFT with QR decomposition

, and the stationary distribution is determined by the initial state of the walk. An explicit expression for