Efficient Algorithms for Universal Quantum Simulation

A universal quantum simulator would enable efficient simulation of quantum dynamics by implementing quantum-simulation algorithms on a quantum computer. Specifically the quantum simulator would efficiently generate qubit-string states that closely approximate physical states obtained from a broad class of dynamical evolutions. I provide an overview of theoretical research into universal quantum simulators and the strategies for minimizing computational space and time costs. Applications to simulating many-body quantum simulation and solving linear equations are discussed

Universal simulation of Hamiltonian dynamics for qudits

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd et al. (quant-ph/0106064) provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries.Comment: 13 pages, an error in the "Pauli-Euclid-Gottesman Lemma" fixed, main results unchange

Aerial Survey Estimates of Abundance of the Eastern Chukchi Sea Stock of Beluga Whales (Delphinapterus leucas) in 2012

The eastern Chukchi Sea (ECS) stock of beluga whales is one of three stocks in western Alaska that are co-managed by the National Marine Fisheries Service and the Alaska Beluga Whale Committee. Abundance of this stock was estimated as 3710 in 1991 from incomplete data. Analysis of data from satellite-linked time-depth recorders (SDRs) attached to belugas in summer concentration areas of the ECS and Beaufort Sea (BS) stocks provided an overview of beluga distribution and movements and allowed the identification of an area (140˚ W to 157˚ W in the BS) and a time period (19 July – 20 August) in which the distributions of the two stocks do not overlap. Aerial survey data were collected by the Aerial Surveys of Arctic Marine Mammals (ASAMM) project in that region and time period in 2012. We used those data in a line transect analysis that estimated there were 5547 (CV = 0.22) surface-visible belugas in the study area. Data from SDRs were used to develop correction factors to account for animals that were missed because they were either outside of the study area or diving too deep to be seen, resulting in a total abundance estimate of 20 752 (CV = 0.70). The average annual Alaska Native subsistence harvest from the ECS stock (57) is about 0.3% of the population estimate. Without data collected by the ASAMM project and from satellite-linked tags, this analysis would not have been possible. Additional surveys and tagging of ECS belugas are warranted.Le stock de bélugas de l’est de la mer des Tchouktches (EMT) figure parmi les trois stocks de l’ouest de l’Alaska à être gérés conjointement par le National Marine Fisheries Service et l’Alaska Beluga Whale Committee. À partir de données incomplètes, l’abondance de ce stock a été estimée à 3 710 en 1991. L’analyse des données recueillies à l’aide d’enregistreurs de profondeur temporelle satellitaires (SDR) fixés aux bélugas dans les zones de concentration estivales de l’EMT et de la mer de Beaufort (MB) a permis d’obtenir un aperçu de la répartition et du déplacement des bélugas ainsi que de cerner une zone (de 140˚ O à 157˚ O dans la MB) et une période (du 19 juillet au 20 août) pour lesquelles la répartition des deux stocks ne se chevauchent pas. Le projet Aerial Surveys of Arctic Marine Mammals (ASAMM) a permis de recueillir des données à partir de levés aériens pour la région et la période concernées en 2012. Grâce à une analyse de lignes interceptées, ces données ont permis d’estimer qu’il y avait 5 547 (CV = 0,22) bélugas visibles à la surface dans la zone à l’étude. Les données en provenance de SDR ont servi à mettre au point des facteurs de correction pour tenir compte des bélugas qui n’ont pas été captés, soit parce qu’ils se trouvaient en dehors de la zone visée par l’étude, soit parce qu’ils plongeaient trop loin pour être vus, ce qui s’est traduit par une estimation totale d’abondance de 20 752 (CV = 0,70) bélugas. La prise de subsistance annuelle moyenne de stock (57) par les Autochtones de l’Alaska dans l’EMT correspond à environ à 0,3 % de l’estimation de la population. Cette analyse n’aurait pu être possible sans les données prélevées par le projet ASAMM et les SDR. D’autres levés et l’étiquetage des bélugas de l’EMT s’imposent

Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? We provide an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling n-qubit Hamiltonian and local unitaries. It follows that universal quantum computation can be performed using any entangling interaction and local unitary operations.Comment: Added references to NMR refocusing and to earlier work by Leung et al and Jones and Knil

Protecting Quantum Information with Entanglement and Noisy Optical Modes

We incorporate active and passive quantum error-correcting techniques to protect a set of optical information modes of a continuous-variable quantum information system. Our method uses ancilla modes, entangled modes, and gauge modes (modes in a mixed state) to help correct errors on a set of information modes. A linear-optical encoding circuit consisting of offline squeezers, passive optical devices, feedforward control, conditional modulation, and homodyne measurements performs the encoding. The result is that we extend the entanglement-assisted operator stabilizer formalism for discrete variables to continuous-variable quantum information processing.Comment: 7 pages, 1 figur

Mechanistic investigation of Rh(i)-catalysed asymmetric Suzuki–Miyaura coupling with racemic allyl halides

Understanding how catalytic asymmetric reactions with racemic starting materials can operate would enable new enantioselective cross-coupling reactions that give chiral products. Here we propose a catalytic cycle for the highly enantioselective Rh(I)-catalysed Suzuki–Miyaura coupling of boronic acids and racemic allyl halides. Natural abundance 13C kinetic isotope effects provide quantitative information about the transition-state structures of two key elementary steps in the catalytic cycle, transmetallation and oxidative addition. Experiments with configurationally stable, deuterium-labelled substrates revealed that oxidative addition can happen via syn- or anti-pathways, which control diastereoselectivity. Density functional theory calculations attribute the extremely high enantioselectivity to reductive elimination from a common Rh complex formed from both allyl halide enantiomers. Our conclusions are supported by analysis of the reaction kinetics. These insights into the sequence of bond-forming steps and their transition-state structures will contribute to our understanding of asymmetric Rh–allyl chemistry and enable the discovery and application of asymmetric reactions with racemic substrates

NMR quantum computation with indirectly coupled gates

An NMR realization of a two-qubit quantum gate which processes quantum information indirectly via couplings to a spectator qubit is presented in the context of the Deutsch-Jozsa algorithm. This enables a successful comprehensive NMR implementation of the Deutsch-Jozsa algorithm for functions with three argument bits and demonstrates a technique essential for multi-qubit quantum computation.Comment: 9 pages, 2 figures. 10 additional figures illustrating output spectr

Predicting knee osteoarthritis

Treatment options for osteoarthritis (OA) beyond pain relief or total knee replacement are very limited. Because of this, attention has shifted to identifying which factors increase the risk of OA in vulnerable populations in order to be able to give recommendations to delay disease onset or to slow disease progression. The gold standard is then to use principles of risk management, first to provide subject-specific estimates of risk and then to find ways of reducing that risk. Population studies of OA risk based on statistical associations do not provide such individually tailored information. Here we argue that mechanistic models of cartilage tissue maintenance and damage coupled to statistical models incorporating model uncertainty, united within the framework of structural reliability analysis, provide an avenue for bridging the disciplines of epidemiology, cell biology, genetics and biomechanics. Such models promise subject-specific OA risk assessment and personalized strategies for mitigating or even avoiding OA. We illustrate the proposed approach with a simple model of cartilage extracellular matrix synthesis and loss regulated by daily physical activity

On the relationship between continuous- and discrete-time quantum walk

Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or discrete time. But whereas a continuous-time random walk can be obtained as the limit of a sequence of discrete-time random walks, the two types of quantum walk appear fundamentally different, owing to the need for extra degrees of freedom in the discrete-time case. In this article, I describe a precise correspondence between continuous- and discrete-time quantum walks on arbitrary graphs. Using this correspondence, I show that continuous-time quantum walk can be obtained as an appropriate limit of discrete-time quantum walks. The correspondence also leads to a new technique for simulating Hamiltonian dynamics, giving efficient simulations even in cases where the Hamiltonian is not sparse. The complexity of the simulation is linear in the total evolution time, an improvement over simulations based on high-order approximations of the Lie product formula. As applications, I describe a continuous-time quantum walk algorithm for element distinctness and show how to optimally simulate continuous-time query algorithms of a certain form in the conventional quantum query model. Finally, I discuss limitations of the method for simulating Hamiltonians with negative matrix elements, and present two problems that motivate attempting to circumvent these limitations.Comment: 22 pages. v2: improved presentation, new section on Hamiltonian oracles; v3: published version, with improved analysis of phase estimatio

On Quantum Control via Encoded Dynamical Decoupling

I revisit the ideas underlying dynamical decoupling methods within the framework of quantum information processing, and examine their potential for direct implementations in terms of encoded rather than physical degrees of freedom. The usefulness of encoded decoupling schemes as a tool for engineering both closed- and open-system encoded evolutions is investigated based on simple examples.Comment: 12 pages, no figures; REVTeX style. This note collects various theoretical considerations complementing/motivated by the experimental demonstration of encoded control by Fortunato et a