Polynomial-Time Solution to the Hidden Subgroup Problem for a Class of non-abelian Groups

We present a family of non-abelian groups for which the hidden subgroup problem can be solved efficiently on a quantum computer.Comment: 16 pages, LaTeX2e, 3 figure

An analytic model for redshift-space distortions

Understanding the formation and evolution of large-scale structure is a central problem in cosmology and enables precise tests of General Relativity on cosmological scales and constraints on dark energy. An essential ingredient is an accurate description of the pairwise velocities of biased tracers of the matter field. In this paper we compute the first and second moments of the pairwise velocity distribution by extending the Convolution Lagrangian Perturbation theory (CLPT) formalism of Carlson et al. (2012). Our predictions outperform standard perturbation theory calculations in many cases when compared to statistics measured in N-body simulations. We combine the CLPT predictions of real-space clustering and velocity statistics in the Gaussian streaming model of Reid & White (2011) to obtain predictions for the monopole and quadrupole correlation functions accurate to 2 and 4 per cent respectively down to <25Mpc/h for halos hosting the massive galaxies observed by SDSS-III BOSS. We also discuss contours of the 2D correlation function and clustering "wedges". We generalize the scheme to cross-correlation functions.Comment: 12 pages, 12 figures. Minor modifications to match version accepted by MNRA

Fast Quantum Fourier Transforms for a Class of Non-abelian Groups

An algorithm is presented allowing the construction of fast Fourier transforms for any solvable group on a classical computer. The special structure of the recursion formula being the core of this algorithm makes it a good starting point to obtain systematically fast Fourier transforms for solvable groups on a quantum computer. The inherent structure of the Hilbert space imposed by the qubit architecture suggests to consider groups of order 2^n first (where n is the number of qubits). As an example, fast quantum Fourier transforms for all 4 classes of non-abelian 2-groups with cyclic normal subgroup of index 2 are explicitly constructed in terms of quantum circuits. The (quantum) complexity of the Fourier transform for these groups of size 2^n is O(n^2) in all cases.Comment: 16 pages, LaTeX2

Universal Simulation of Hamiltonians Using a Finite Set of Control Operations

Any quantum system with a non-trivial Hamiltonian is able to simulate any other Hamiltonian evolution provided that a sufficiently large group of unitary control operations is available. We show that there exist finite groups with this property and present a sufficient condition in terms of group characters. We give examples of such groups in dimension 2 and 3. Furthermore, we show that it is possible to simulate an arbitrary bipartite interaction by a given one using such groups acting locally on the subsystems.Comment: 18 pages, LaTeX2

A Decentralized Parallelization-in-Time Approach with Parareal

With steadily increasing parallelism for high-performance architectures, simulations requiring a good strong scalability are prone to be limited in scalability with standard spatial-decomposition strategies at a certain amount of parallel processors. This can be a show-stopper if the simulation results have to be computed with wallclock time restrictions (e.g.\,for weather forecasts) or as fast as possible (e.g. for urgent computing). Here, the time-dimension is the only one left for parallelization and we focus on Parareal as one particular parallelization-in-time method. We discuss a software approach for making Parareal parallelization transparent for application developers, hence allowing fast prototyping for Parareal. Further, we introduce a decentralized Parareal which results in autonomous simulation instances which only require communicating with the previous and next simulation instances, hence with strong locality for communication. This concept is evaluated by a prototypical solver for the rotational shallow-water equations which we use as a representative black-box solver

Multidimensional Recovery Among an Opioid Use Disorder Outpatient Treatment Population

Background: Given the current opioid crisis, recovery from opioid use disorder (OUD) warrants attention. SAMHSA’s working definition of recovery highlights dimensions that support recovery including health, home, community, and purpose. Recovery capital captures factors that support recovery within these dimensions and has been associated with recovery outcomes. Prior research highlights possible gender differences in recovery outcomes. Objective: 1) Describe and compare recovery capital among an OUD outpatient treatment population by gender; 2) Identify the relationship between recovery capital and length of time in treatment within this population. Methods: Patients (n=126) taking medication for OUD at a single outpatient substance use treatment clinic completed an electronic, cross-sectional survey (July-September 2019). The Brief Assessment of Recovery Capital (BARC-10) assessed recovery components. Length of current treatment episode was abstracted from Virginia’s Prescription Monitoring Program. Descriptive statistics were calculated. Chi square and Mann Whitney-U were used to test differences by gender. Multivariate linear regression was conducted. Results: Participants (n=126) were 45.3% men and 54.7% women. Most identified as Black (67.7%) and were single (69.0%). Compared to men, women were younger (38.8711.31 vs. 47.0712.12; p\u3c.001) and more likely to be unemployed (60.9% vs. 42.1%; p=.037). Mean BARC-10 score was 45.08 (9.73) and did not vary by gender. Several BARC-10 individual items within the purpose recovery dimension differed by gender (p\u3c.05). More social support was associated with higher BARC-10 score (p\u3c.001); length of treatment was not (p=.599). Conclusions: Recovery capital was high and gender differences minimal. Individuals receiving medication for OUD can initiate and sustain recovery.https://scholarscompass.vcu.edu/gradposters/1061/thumbnail.jp

On optimal quantum codes

We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary prime power. It is shown that codes with parameters [[n,n-2d+2,d]]_q exist for all 3 <= n <= q and 1 <= d <= n/2+1. We also present quantum MDS codes with parameters [[q^2,q^2-2d+2,d]]_q for 1 <= d <= q which additionally give rise to shortened codes [[q^2-s,q^2-2d+2-s,d]]_q for some s.Comment: Accepted for publication in the International Journal of Quantum Informatio