Complexity classification of two-qubit commuting hamiltonians

We classify two-qubit commuting Hamiltonians in terms of their computational complexity. Suppose one has a two-qubit commuting Hamiltonian H which one can apply to any pair of qubits, starting in a computational basis state. We prove a dichotomy theorem: either this model is efficiently classically simulable or it allows one to sample from probability distributions which cannot be sampled from classically unless the polynomial hierarchy collapses. Furthermore, the only simulable Hamiltonians are those which fail to generate entanglement. This shows that generic two-qubit commuting Hamiltonians can be used to perform computational tasks which are intractable for classical computers under plausible assumptions. Our proof makes use of new postselection gadgets and Lie theory.Comment: 34 page

A nomogram to determine required seed air kerma strength in planar 131 Cesium permanent seed implant brachytherapy

Purpose: Intraoperatively implanted Cesium-131 ( 131 Cs) permanent seed brachytherapy is used to deliver highly localized re-irradiation in recurrent head and neck cancers. A single planar implant of uniform air kerma strength (AKS) seeds and 10 mm seed-to-seed spacing is used to deliver the prescribed dose to a point 5 mm or 10 mm perpendicular to the center of the implant plane. Nomogram tables to quickly determine the required AKS for rectangular and irregularly shaped implants were created and dosimetrically verified. By eliminating the need for a full treatment planning system plan, nomogram tables allow for fast dose calculation for intraoperative re-planning and for a second check method. Material and methods: TG-43U1 recommended parameters were used to create a point-source model in MATLAB. The dose delivered to the prescription point from a single 1 U seed at each possible location in the implant plane was calculated. Implant tables were verified using an independent seed model in MIM Symphony LDR™. Implant tables were used to retrospectively determine seed AKS for previous cases: three rectangular and three irregular. Results: For rectangular implants, the percent difference between required seed AKS calculated using MATLAB and MIM was at most 0.6%. For irregular implants, the percent difference between MATLAB and MIM calculations for individual seed locations was within 1.5% with outliers of less than 3.1% at two distal locations (10.6 cm and 8.8 cm), which have minimal dose contribution to the prescription point. The retrospectively determined AKS for patient implants using nomogram tables agreed with previous calculations within 5% for all six cases. Conclusions: Nomogram tables were created to determine required AKS per seed for planar uniform AKS 131 Cs implants. Comparison with the treatment planning system confirms dosimetric accuracy that is acceptable for use as a second check or for dose calculation in cases of intraoperative re-planning

Applying Computer Vision Techniques to Topographic Objects

Automatic structuring (feature coding and object recognition) of topographic data, such as that derived from air survey or raster scanning large-scale paper maps, requires the classification of objects such as buildings, roads, rivers, fields and railways. The recognition of objects is largely based on the matching of descriptions of shapes. Fourier descriptors, moment invariants, boundary chain coding and scalar descriptors are widely used in image processing and computer vision to describe and classify shapes. They have been developed to describe shape irrespective of position, orientation and scale. The applicability of the above four methods to topographic shapes is described and their usefulness evaluated.

A compact variant of the QCR method for quadratically constrained quadratic 0-1 programs

Quadratic Convex Reformulation (QCR) is a technique that was originally proposed for quadratic 0-1 programs, and then extended to various other problems. It is used to convert non-convex instances into convex ones, in such a way that the bound obtained by solving the continuous relaxation of the reformulated instance is as strong as possible. In this paper, we focus on the case of quadratically constrained quadratic 0-1 programs. The variant of QCR previously proposed for this case involves the addition of a quadratic number of auxiliary continuous variables. We show that, in fact, at most one additional variable is needed. Some computational results are also presented