On the Role of Hadamard Gates in Quantum Circuits

We study a reduced quantum circuit computation paradigm in which the only allowable gates either permute the computational basis states or else apply a "global Hadamard operation", i.e. apply a Hadamard operation to every qubit simultaneously. In this model, we discuss complexity bounds (lower-bounding the number of global Hadamard operations) for common quantum algorithms : we illustrate upper bounds for Shor's Algorithm, and prove lower bounds for Grover's Algorithm. We also use our formalism to display a gate that is neither quantum-universal nor classically simulable, on the assumption that Integer Factoring is not in BPP.Comment: 16 pages, last section clarified, typos corrected, references added, minor rewordin

Binary Matroids and Quantum Probability Distributions

We characterise the probability distributions that arise from quantum circuits all of whose gates commute, and show when these distributions can be classically simulated efficiently. We consider also marginal distributions and the computation of correlation coefficients, and draw connections between the simulation of stabiliser circuits and the combinatorics of representable matroids, as developed in the 1990s.Comment: 24 pages (inc appendix & refs

The 1999 Center for Simulation of Dynamic Response in Materials Annual Technical Report

Introduction: This annual report describes research accomplishments for FY 99 of the Center for Simulation of Dynamic Response of Materials. The Center is constructing a virtual shock physics facility in which the full three dimensional response of a variety of target materials can be computed for a wide range of compressive, ten- sional, and shear loadings, including those produced by detonation of energetic materials. The goals are to facilitate computation of a variety of experiments in which strong shock and detonation waves are made to impinge on targets consisting of various combinations of materials, compute the subsequent dy- namic response of the target materials, and validate these computations against experimental data

Non-adaptive Measurement-based Quantum Computation and Multi-party Bell Inequalities

Quantum correlations exhibit behaviour that cannot be resolved with a local hidden variable picture of the world. In quantum information, they are also used as resources for information processing tasks, such as Measurement-based Quantum Computation (MQC). In MQC, universal quantum computation can be achieved via adaptive measurements on a suitable entangled resource state. In this paper, we look at a version of MQC in which we remove the adaptivity of measurements and aim to understand what computational abilities still remain in the resource. We show that there are explicit connections between this model of computation and the question of non-classicality in quantum correlations. We demonstrate this by focussing on deterministic computation of Boolean functions, in which natural generalisations of the Greenberger-Horne-Zeilinger (GHZ) paradox emerge; we then explore probabilistic computation, via which multipartite Bell Inequalities can be defined. We use this correspondence to define families of multi-party Bell inequalities, which we show to have a number of interesting contrasting properties.Comment: 13 pages, 4 figures, final version accepted for publicatio

A virtual test facility for simulating the dynamic response of materials

The goal of the Caltech Center is to construct a virtual test facility (VTF): a problem solving environment for full 3D parallel simulation of the dynamic response of materials undergoing compression due to shock waves. The objective is to design a software environment that will: facilitate computation in a variety of experiments in which strong shock waves impinge on targets comprising various combinations of materials; compute the target materials' subsequent dynamic response; and validate these computations against experimental data. Successfully constructing such a facility requires modeling of the highest accuracy. We must model at atomistic scales to correctly describe the material properties of the target materials and high explosives; at intermediate (meso) scales to understand the micromechanical response of the target materials; and at continuum scales to capture properly the evolution of macroscopic effects. The article outlines such a test facility. Although it is a very simplified version of the facilities found in a shock-compression laboratory, our VTF includes all the basic features, offering a problem solving environment for validating experiments and facilitating further development of simulation capabilities

Dark Matter in the Coming Decade: Complementary Paths to Discovery and Beyond

In this report we summarize the many dark matter searches currently being pursued through four complementary approaches: direct detection, indirect detection, collider experiments, and astrophysical probes. The essential features of broad classes of experiments are described, each with their own strengths and weaknesses. The complementarity of the different dark matter searches is discussed qualitatively and illustrated quantitatively in two simple theoretical frameworks. Our primary conclusion is that the diversity of possible dark matter candidates requires a balanced program drawing from all four approaches.Comment: Report prepared for the Community Summer Study (Snowmass) 2013, on behalf of Cosmic Frontier Working Groups 1-4 (CF1: WIMP Dark Matter Direct Detection, CF2: WIMP Dark Matter Indirect Detection, CF3: Non-WIMP Dark Matter, and CF4: Dark Matter Complementarity); published versio

GRADUATE STUDENTS’ EVALUATION OF THE CHARACTER AND CARING OF THEIR INSTRUCTORS

Recent research concludes that student-teacher relationships are foundational for greater instructional effectiveness and its concomitant increase in overall student achievement or learning. Similarly, research seems to demonstrate conclusively that trust is a vital component in the development of strong relationships. Recently, 488 current participants and recent graduates of an online and blended Master of Education program were surveyed about their perceptions of their instructors’ character and concern for them as individuals. Survey respondents were public school teachers. Based on the survey’s results, the personal qualities and characteristics that graduate students most seem to prefer in their instructors when determining their own evaluation of that professor’s character and integrity include the following: interacting with students as individuals, remembering individual student needs, and acting consistently in a compassionate manner. The data indicate that students are much less “impressed” by what a professor may claim about integrity or compassion. Conversely, the qualities and characteristics that most damage a graduate instructor’s character in the eyes of his or her students include the following: acting in a manner that communicates a lack of concern for individual student needs; being disrespectful, rude, critical, uncaring, harsh toward the class; presenting biased attitudes; and declining to help students in obvious need

Recommendations of the LHC Dark Matter Working Group: Comparing LHC searches for heavy mediators of dark matter production in visible and invisible decay channels

Weakly-coupled TeV-scale particles may mediate the interactions between normal matter and dark matter. If so, the LHC would produce dark matter through these mediators, leading to the familiar "mono-X" search signatures, but the mediators would also produce signals without missing momentum via the same vertices involved in their production. This document from the LHC Dark Matter Working Group suggests how to compare searches for these two types of signals in case of vector and axial-vector mediators, based on a workshop that took place on September 19/20, 2016 and subsequent discussions. These suggestions include how to extend the spin-1 mediated simplified models already in widespread use to include lepton couplings. This document also provides analytic calculations of the relic density in the simplified models and reports an issue that arose when ATLAS and CMS first began to use preliminary numerical calculations of the dark matter relic density in these models.Comment: 19 pages, 4 figures; v2: author list and LaTeX problem fixe