Diffusive spin transport

Information to be stored and transported requires physical carriers. The quantum bit of information (qubit) can for instance be realised as the spin 1/2 degree of freedom of a massive particle like an electron or as the spin 1 polarisation of a massless photon. In this lecture, I first use irreducible representations of the rotation group to characterise the spin dynamics in a least redundant manner. Specifically, I describe the decoherence dynamics of an arbitrary spin S coupled to a randomly fluctuating magnetic field in the Liouville space formalism. Secondly, I discuss the diffusive dynamics of the particle's position in space due to the presence of randomly placed impurities. Combining these two dynamics yields a coherent, unified picture of diffusive spin transport, as applicable to mesoscopic electronic devices or photons propagating in cold atomic clouds.Comment: Lecture notes, published in A. Buchleitner, C. Viviescas, and M. Tiersch (Eds.), "Entanglement and Decoherence. Foundations and Modern Trends", Lecture Notes in Physics 768, Springer, Berlin (2009

The Bravyi-Kitaev transformation for quantum computation of electronic structure

Quantum simulation is an important application of future quantum computers with applications in quantum chemistry, condensed matter, and beyond. Quantum simulation of fermionic systems presents a specific challenge. The Jordan-Wigner transformation allows for representation of a fermionic operator by O(n) qubit operations. Here we develop an alternative method of simulating fermions with qubits, first proposed by Bravyi and Kitaev [S. B. Bravyi, A.Yu. Kitaev, Annals of Physics 298, 210-226 (2002)], that reduces the simulation cost to O(log n) qubit operations for one fermionic operation. We apply this new Bravyi-Kitaev transformation to the task of simulating quantum chemical Hamiltonians, and give a detailed example for the simplest possible case of molecular hydrogen in a minimal basis. We show that the quantum circuit for simulating a single Trotter time-step of the Bravyi-Kitaev derived Hamiltonian for H2 requires fewer gate applications than the equivalent circuit derived from the Jordan-Wigner transformation. Since the scaling of the Bravyi-Kitaev method is asymptotically better than the Jordan-Wigner method, this result for molecular hydrogen in a minimal basis demonstrates the superior efficiency of the Bravyi-Kitaev method for all quantum computations of electronic structure

Flip Distance Between Triangulations of a Planar Point Set is APX-Hard

In this work we consider triangulations of point sets in the Euclidean plane, i.e., maximal straight-line crossing-free graphs on a finite set of points. Given a triangulation of a point set, an edge flip is the operation of removing one edge and adding another one, such that the resulting graph is again a triangulation. Flips are a major way of locally transforming triangular meshes. We show that, given a point set $S$ in the Euclidean plane and two triangulations $T_1$ and $T_2$ of $S$, it is an APX-hard problem to minimize the number of edge flips to transform $T_1$ to $T_2$.Comment: A previous version only showed NP-completeness of the corresponding decision problem. The current version is the one of the accepted manuscrip

Q2Q^2 Independence of QF2/F1QF_2/F_1, Poincare Invariance and the Non-Conservation of Helicity

A relativistic constituent quark model is found to reproduce the recent data regarding the ratio of proton form factors, $F_2(Q^2)/F_1(Q^2)$. We show that imposing Poincare invariance leads to substantial violation of the helicity conservation rule, as well as an analytic result that the ratio $F_2(Q^2)/F_1(Q^2)\sim 1/Q$ for intermediate values of $Q^2$.Comment: 13 pages, 7 figures, to be submitted to Phys. Rev. C typos corrected, references added, 1 new figure to show very high Q^2 behavio