Quantum matchgate computations and linear threshold gates

The theory of matchgates is of interest in various areas in physics and computer science. Matchgates occur in e.g. the study of fermions and spin chains, in the theory of holographic algorithms and in several recent works in quantum computation. In this paper we completely characterize the class of boolean functions computable by unitary two-qubit matchgate circuits with some probability of success. We show that this class precisely coincides with that of the linear threshold gates. The latter is a fundamental family which appears in several fields, such as the study of neural networks. Using the above characterization, we further show that the power of matchgate circuits is surprisingly trivial in those cases where the computation is to succeed with high probability. In particular, the only functions that are matchgate-computable with success probability greater than 3/4 are functions depending on only a single bit of the input

Quadratic Scaling Bosonic Path Integral Molecular Dynamics

We present an algorithm for bosonic path integral molecular dynamics simulations, which reduces the computational complexity with the number of particles from cubic to quadratic. Path integral molecular dynamics simulations of large bosonic systems are challenging, since a straightforward implementation scales exponentially with the number of particles. We recently developed a recursive algorithm that reduced the computational complexity from exponential to cubic. It allowed performing the first path integral molecular dynamics simulations of ~100 bosons, but the cubic scaling hindered applications to much larger systems. Here, we report an improved algorithm that scales only quadratically with system size. Simulations with our new method are orders of magnitude faster, with a speedup that scales as $PN$, where $P$ and $N$ are the number of beads (imaginary time slices) and particles, respectively. In practice, this eliminates most of the cost of including bosonic exchange effects in path integral molecular dynamics simulations. We use the algorithm to simulate thousands of interacting bosons using path integral molecular dynamics for the first time, spending days of computation on simulations that would have otherwise taken decades to complete

Interplay between structure and magnetism in Mo12S9I9Mo_{12} S_9 I_9 nanowires

We investigate the equilibrium geometry and electronic structure of Mo$_{12}$S$_{9}$I$_{9}$ nanowires using ab initio Density Functional calculations. The skeleton of these unusually stable nanowires consists of rigid, functionalized Mo octahedra, connected by flexible, bi-stable sulphur bridges. This structural flexibility translates into a capability to stretch up to approximate 20% at almost no energy cost. The nanowires change from conductors to narrow-gap magnetic semiconductors in one of their structural isomers.Comment: 4 pages with PRL standards and 3 figure

Electrical Manipulation of Nanomagnets

We demonstrate a possibility to manipulate the magnetic coupling between two nanomagnets with a help of ac electric field. In the scheme suggested the magnetic coupling in question is mediated by a magnetic particle contacting with both of the nanomagnets through the tunnel barriers. The electric field providing a successive suppression of the barriers leads to pumping of magnetization through the mediating particle. Time dependent dynamics of the particle magnetization allows to to switch between ferro- and antiferromagnetic couplings.Comment: 4 pages, 2 figure

Computing Stable Coalitions: Approximation Algorithms for Reward Sharing

Consider a setting where selfish agents are to be assigned to coalitions or projects from a fixed set P. Each project k is characterized by a valuation function; v_k(S) is the value generated by a set S of agents working on project k. We study the following classic problem in this setting: "how should the agents divide the value that they collectively create?". One traditional approach in cooperative game theory is to study core stability with the implicit assumption that there are infinite copies of one project, and agents can partition themselves into any number of coalitions. In contrast, we consider a model with a finite number of non-identical projects; this makes computing both high-welfare solutions and core payments highly non-trivial. The main contribution of this paper is a black-box mechanism that reduces the problem of computing a near-optimal core stable solution to the purely algorithmic problem of welfare maximization; we apply this to compute an approximately core stable solution that extracts one-fourth of the optimal social welfare for the class of subadditive valuations. We also show much stronger results for several popular sub-classes: anonymous, fractionally subadditive, and submodular valuations, as well as provide new approximation algorithms for welfare maximization with anonymous functions. Finally, we establish a connection between our setting and the well-studied simultaneous auctions with item bidding; we adapt our results to compute approximate pure Nash equilibria for these auctions.Comment: Under Revie

R-parity Conservation via the Stueckelberg Mechanism: LHC and Dark Matter Signals

We investigate the connection between the conservation of R-parity in supersymmetry and the Stueckelberg mechanism for the mass generation of the B-L vector gauge boson. It is shown that with universal boundary conditions for soft terms of sfermions in each family at the high scale and with the Stueckelberg mechanism for generating mass for the B-L gauge boson present in the theory, electric charge conservation guarantees the conservation of R-parity in the minimal B-L extended supersymmetric standard model. We also discuss non-minimal extensions. This includes extensions where the gauge symmetries arise with an additional U(1)_{B-L} x U(1)_X, where U(1)_X is a hidden sector gauge group. In this case the presence of the additional U(1)_X allows for a Z' gauge boson mass with B-L interactions to lie in the sub-TeV region overcoming the multi-TeV LEP constraints. The possible tests of the models at colliders and in dark matter experiments are analyzed including signals of a low mass Z' resonance and the production of spin zero bosons and their decays into two photons. In this model two types of dark matter candidates emerge which are Majorana and Dirac particles. Predictions are made for a possible simultaneous observation of new physics events in dark matter experiments and at the LHC.Comment: 38 pages, 7 fig

Optimal Principal Component Analysis in Distributed and Streaming Models

We study the Principal Component Analysis (PCA) problem in the distributed and streaming models of computation. Given a matrix $A \in R^{m \times n},$ a rank parameter $k < rank(A)$, and an accuracy parameter $0 < \epsilon < 1$, we want to output an $m \times k$ orthonormal matrix $U$ for which $$|| A - U U^T A ||_F^2 \le \left(1 + \epsilon \right) \cdot || A - A_k||_F^2,$$ where $A_k \in R^{m \times n}$ is the best rank-$k$ approximation to $A$. This paper provides improved algorithms for distributed PCA and streaming PCA.Comment: STOC2016 full versio