On the stability of quantum holonomic gates

We provide a unified geometrical description for analyzing the stability of holonomic quantum gates in the presence of imprecise driving controls (parametric noise). We consider the situation in which these fluctuations do not affect the adiabatic evolution but can reduce the logical gate performance. Using the intrinsic geometric properties of the holonomic gates, we show under which conditions on noise's correlation time and strength, the fluctuations in the driving field cancel out. In this way, we provide theoretical support to previous numerical simulations. We also briefly comment on the error due to the mismatch between real and nominal time of the period of the driving fields and show that it can be reduced by suitably increasing the adiabatic time.Comment: 7 page

Multi-Domain Walls in Massive Supersymmetric Sigma-Models

Massive maximally-supersymmetric sigma models are shown to exhibit multiple static kink-domain wall solutions that preserve 1/2 of the supersymmetry. The kink moduli space admits a natural Kahler metric. We examine in some detail the case when the target of the sigma model is given by the co-tangent bundle of CP^n equipped with the Calabi metric, and we show that there exist BPS solutions corresponding to n kinks at arbitrary separation. We also describe how 1/4-BPS charged and intersecting domain walls are described in the low-energy dynamics on the kink moduli space. We comment on the similarity of these results to monopole dynamics.Comment: 15 pages, 3 figures, Latex. Introduction extended with discussion of complex central charge

Kraus representation for density operator of arbitrary open qubit system

We show that the time evolution of density operator of open qubit system can always be described in terms of the Kraus representation. A general scheme on how to construct the Kraus operators for an open qubit system is proposed, which can be generalized to open higher dimensional quantum systems.Comment: 5 pages, no figures. Some words are rephrase

Inelastic Collapse of Three Particles

A system of three particles undergoing inelastic collisions in arbitrary spatial dimensions is studied with the aim of establishing the domain of ``inelastic collapse''---an infinite number of collisions which take place in a finite time. Analytic and simulation results show that for a sufficiently small restitution coefficient, $0\leq r<7-4\sqrt{3}\approx 0.072$, collapse can occur. In one dimension, such a collapse is stable against small perturbations within this entire range. In higher dimensions, the collapse can be stable against small variations of initial conditions, within a smaller $r$ range, $0\leq r<9-4\sqrt{5}\approx 0.056$.Comment: 6 pages, figures on request, accepted by PR

Rank 3 permutation characters and maximal subgroups

In this paper we classify all maximal subgroups M of a nearly simple primitive rank 3 group G of type L=Omega_{2m+1}(3), m > 3; acting on an L-orbit E of non-singular points of the natural module for L such that 1_P^G <=1_M^G where P is a stabilizer of a point in E. This result has an application to the study of minimal genera of algebraic curves which admit group actions.Comment: 41 pages, to appear in Forum Mathematicu

Twist-3 Contributions in Semi-Inclusive DIS in the Target Fragmentation Region

We present the complete results up to twist-3 for hadron production in the target fragmentation region of semi-inclusive deep inelastic scattering with a polarized lepton beam and polarized nucleon target. The non-perturbative effects are factorized into fracture functions. The calculation up to twist-3 is non-trivial since one has to keep gauge invariance. By applying collinear expansion, we show that the hadronic tensor can be expressed by gauge-invariant fracture functions. We also present the results for the structure functions and azimuthal asymmetries.Comment: 11 pages, 2 figure

Topological engineering of interfacial optical Tamm states for highly-sensitive near-singular-phase optical detection

We developed planar multilayered photonic-plasmonic structures, which support topologically protected optical states on the interface between metal and dielectric materials, known as optical Tamm states. Coupling of incident light to the Tamm states can result in perfect absorption within one of several narrow frequency bands, which is accompanied by a singular behavior of the phase of electromagnetic field. In the case of near-perfect absorptance, very fast local variation of the phase can still be engineered. In this work, we theoretically and experimentally demonstrate how these drastic phase changes can improve sensitivity of optical sensors. A planar Tamm absorber was fabricated and used to demonstrate remote near-singular-phase temperature sensing with an over an order of magnitude improvement in sensor sensitivity and over two orders of magnitude improvement in the figure of merit over the standard approach of measuring shifts of resonant features in the reflectance spectra of the same absorber. Our experimentally demonstrated phase-to-amplitude detection sensitivity improvement nearly doubles that of state-of-the-art nano-patterned plasmonic singular-phase detectors, with further improvements possible via more precise fabrication. Tamm perfect absorbers form the basis for robust planar sensing platforms with tunable spectral characteristics, which do not rely on low-throughput nano-patterning techniques.Comment: 31 pages; 6 main text figures and 10 supplementary figure