A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem

A quantum system will stay near its instantaneous ground state if the Hamiltonian that governs its evolution varies slowly enough. This quantum adiabatic behavior is the basis of a new class of algorithms for quantum computing. We test one such algorithm by applying it to randomly generated, hard, instances of an NP-complete problem. For the small examples that we can simulate, the quantum adiabatic algorithm works well, and provides evidence that quantum computers (if large ones can be built) may be able to outperform ordinary computers on hard sets of instances of NP-complete problems.Comment: 15 pages, 6 figures, email correspondence to [email protected] ; a shorter version of this article appeared in the April 20, 2001 issue of Science; see http://www.sciencemag.org/cgi/content/full/292/5516/47

Using Classical Probability To Guarantee Properties of Infinite Quantum Sequences

We consider the product of infinitely many copies of a spin-$1\over 2$ system. We construct projection operators on the corresponding nonseparable Hilbert space which measure whether the outcome of an infinite sequence of $\sigma^x$ measurements has any specified property. In many cases, product states are eigenstates of the projections, and therefore the result of measuring the property is determined. Thus we obtain a nonprobabilistic quantum analogue to the law of large numbers, the randomness property, and all other familiar almost-sure theorems of classical probability.Comment: 7 pages in LaTe

Derivation of the Quantum Probability Rule without the Frequency Operator

We present an alternative frequencists' proof of the quantum probability rule which does not make use of the frequency operator, with expectation that this can circumvent the recent criticism against the previous proofs which use it. We also argue that avoiding the frequency operator is not only for technical merits for doing so but is closely related to what quantum mechanics is all about from the viewpoint of many-world interpretation.Comment: 12 page

The new mythologies and premature aging in the youth culture

Comparative studies of aging men in a variety of preliterate traditional societies suggest that older men, across cultures, are relatively mild and uncompetitive, as compared to younger men from the same communities. Older men are more interested in receiving than in producing, more interested in communion than in agency; their sense of pleasure and security is based on food, religion, and the assurance of love. The counterculture gives priority to the same themes, and thereby seems to sponsor a premature senescence, in the psychological sense. Various contemporary myths stemming from affluence and consumerism that have led to the new geriatrics are examined, particularly the myth of the all-including, omnipotential self, which is seen as a translation of socialist, collectivist ideals into the domain of personality. The effects of the new psychic collectivism on ego development in the adolescent and postadolescent periods are also considered.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45279/1/10964_2005_Article_BF02214091.pd

Improved Error-Scaling for Adiabatic Quantum State Transfer

We present a technique that dramatically improves the accuracy of adiabatic state transfer for a broad class of realistic Hamiltonians. For some systems, the total error scaling can be quadratically reduced at a fixed maximum transfer rate. These improvements rely only on the judicious choice of the total evolution time. Our technique is error-robust, and hence applicable to existing experiments utilizing adiabatic passage. We give two examples as proofs-of-principle, showing quadratic error reductions for an adiabatic search algorithm and a tunable two-qubit quantum logic gate.Comment: 10 Pages, 4 figures. Comments are welcome. Version substantially revised to generalize results to cases where several derivatives of the Hamiltonian are zero on the boundar

Fortran coarray implementation of semi-lagrangian convected air particles within an atmospheric model

This work added semi-Lagrangian convected air particles to the Intermediate Complexity Atmospheric Research (ICAR) model. The ICAR model is a simplified atmospheric model using quasi-dynamical downscaling to gain performance over more traditional atmospheric models. The ICAR model uses Fortran coarrays to split the domain amongst images and handle the halo region communication of the image’s boundary regions. The newly implemented convected air particles use trilinear interpolation to compute initial properties from the Eulerian domain and calculate humidity and buoyancy forces as the model runs. This paper investigated the performance cost and scaling attributes of executing unsaturated and saturated air particles versus the original particle-less model. An in-depth analysis was done on the communication patterns and performance of the semi-Lagrangian air particles, as well as the performance cost of a variety of initial conditions such as wind speed and saturation mixing ratios. This study found that given a linear increase in the number of particles communicated, there is an initial decrease in performance, but that it then levels out, indicating that over the runtime of the model, there is an initial cost of particle communication, but that the computational benefits quickly offset it. The study provided insight into the number of processors required to amortize the additional computational cost of the air particles

Grover's algorithm on a Feynman computer

We present an implementation of Grover's algorithm in the framework of Feynman's cursor model of a quantum computer. The cursor degrees of freedom act as a quantum clocking mechanism, and allow Grover's algorithm to be performed using a single, time-independent Hamiltonian. We examine issues of locality and resource usage in implementing such a Hamiltonian. In the familiar language of Heisenberg spin-spin coupling, the clocking mechanism appears as an excitation of a basically linear chain of spins, with occasional controlled jumps that allow for motion on a planar graph: in this sense our model implements the idea of "timing" a quantum algorithm using a continuous-time random walk. In this context we examine some consequences of the entanglement between the states of the input/output register and the states of the quantum clock

Convergence theorems for quantum annealing

We prove several theorems to give sufficient conditions for convergence of quantum annealing, which is a protocol to solve generic optimization problems by quantum dynamics. In particular the property of strong ergodicity is proved for the path-integral Monte Carlo implementation of quantum annealing for the transverse Ising model under a power decay of the transverse field. This result is to be compared with the much slower inverse-log decay of temperature in the conventional simulated annealing. Similar results are proved for the Green's function Monte Carlo approach. Optimization problems in continuous space of particle configurations are also discussed.Comment: 19 page

Pain symptomology, functional impact, and treatment of people with Neurofibromatosis type 1

Introduction: Neurofibromatosis type 1 (NF1) is a neurogenetic disorder affecting 1 in 3000 people worldwide, where individuals are prone to develop benign and malignant tumors. In addition, many people with NF1 complain of pain that limits their daily functioning. Due to the complexity of the disorder, there are few options for treating pain symptoms besides surgery and medications. Moreover, the spectrum of pain symptomatology and treatment, as well as the mechanisms underlying NF1-associated pain, has been understudied. Methodology: To address this knowledge gap, we conducted a survey of 255 adults with NF1, leveraging the Washington University NF1 Patient Registry Initiative (NPRI) database. Demographic and pain data were collected using a Qualtrics survey. Results: All participants had at least one surgical procedure, with 55% reporting having at least one surgery within the last year and 17% being currently prescribed opioid medication. A positive relationship was shown ( Conclusion: The current study demonstrates that individuals with NF1 report a higher incidence of pain severity and interference than observed in NF1 previous studies, with pain symptoms not localized to any specific region of the body. The consideration for alternative treatments and careful monitoring of current treatments that are more conservative or have less potential adverse side effects may improve pain management and reduce the risk of developing medication dependence

Shared developmental gait disruptions across two mouse models of neurodevelopmental disorders

BACKGROUND: Motor deficits such as abnormal gait are an underappreciated yet characteristic phenotype of many neurodevelopmental disorders (NDDs), including Williams Syndrome (WS) and Neurofibromatosis Type 1 (NF1). Compared to cognitive phenotypes, gait phenotypes are readily and comparably assessed in both humans and model organisms and are controlled by well-defined CNS circuits. Discovery of a common gait phenotype between NDDs might suggest shared cellular and molecular deficits and highlight simple outcome variables to potentially quantify longitudinal treatment efficacy in NDDs. METHODS: We characterized gait using the DigiGait assay in two different murine NDD models: the complete deletion (CD) mouse, which models hemizygous loss of the complete WS locus, and the Nf1 RESULTS: Compared to wildtype littermate controls, both models displayed markedly similar spatial, temporal, and postural gait abnormalities during development. Developing CD mice also displayed significant decreases in variability metrics. Multiple gait abnormalities observed across development in the Nf1 CONCLUSIONS: These findings suggest that the subcomponents of gait affected in NDDs show overlap between disorders as well as some disorder-specific features, which may change over the course of development. Our incorporation of spatial, temporal, and postural gait measures also provides a template for gait characterization in other NDD models and a platform to examining circuits or longitudinal therapeutics