arXiv subjects

Remy Mosseri

Publications and source records attributed to Remy Mosseri.

4 recordsLinked to original sources

arXiv2008

Geometrical approach to SU(2) navigation with Fibonacci anyons

Topological quantum computation with Fibonacci anyons relies on the possibility of efficiently generating unitary transformations upon pseudoparticles braiding. The crucial fact that such set of braids has a dense image in the unitary operations space is well known; in addition, the Solovay-Kitaev algorithm allows to approach a given unitary operation to any desired accuracy. In this paper, the latter task is fulfilled with an alternative method, in the SU(2) case, based on a generalization of the geodesic dome construction to higher dimension.

quant-ph↗

arXiv2004

Geometric Approach to Digital Quantum Information

We present geometric methods for uniformly discretizing the continuous N-qubit Hilbert space. When considered as the vertices of a geometrical figure, the resulting states form the equivalent of a Platonic solid. The discretization technique inherently describes a class of pi/2 rotations that connect neighboring states in the set, i.e. that leave the geometrical figures invariant. These rotations are shown to generate the Clifford group, a general group of discrete transformations on N qubits. Discretizing the N-qubit Hilbert space allows us to define its digital quantum information content, and we show that this information content grows as N^2. While we believe the discrete sets are interesting because they allow extra-classical behavior--such as quantum entanglement and quantum parallelism--to be explored while circumventing the continuity of Hilbert space, we also show how they may be a useful tool for problems in traditional quantum computation. We describe in detail the discrete sets for one and two qubits.

quant-ph↗

arXiv2004

Aperiodic Quantum Random Walks

We generalize the quantum random walk protocol for a particle in a one-dimensional chain, by using several types of biased quantum coins, arranged in aperiodic sequences, in a manner that leads to a rich variety of possible wave function evolutions. Quasiperiodic sequences, following the Fibonacci prescription, are of particular interest, leading to a sub-ballistic wavefunction spreading. In contrast, random sequences leads to diffusive spreading, similar to the classical random walk behaviour. We also describe how to experimentally implement these aperiodic sequences.

quant-ph↗

arXiv2003

Two and Three Qubits Geometry and Hopf Fibrations

This paper reviews recent attempts to describe the two- and three-qubit Hilbert space geometries with the help of Hopf fibrations. In both cases, it is shown that the associated Hopf map is strongly sensitive to states entanglement content. In the two-qubit case, a generalization of the one-qubit celebrated Bloch sphere representation is described.

quant-ph↗