Negative Quasi-Probability as a Resource for Quantum Computation

A central problem in quantum information is to determine the minimal physical resources that are required for quantum computational speedup and, in particular, for fault-tolerant quantum computation. We establish a remarkable connection between the potential for quantum speed-up and the onset of negative values in a distinguished quasi-probability representation, a discrete analog of the Wigner function for quantum systems of odd dimension. This connection allows us to resolve an open question on the existence of bound states for magic-state distillation: we prove that there exist mixed states outside the convex hull of stabilizer states that cannot be distilled to non-stabilizer target states using stabilizer operations. We also provide an efficient simulation protocol for Clifford circuits that extends to a large class of mixed states, including bound universal states.Comment: 15 pages v4: This is a major revision. In particular, we have added a new section detailing an explicit extension of the Gottesman-Knill simulation protocol to deal with positively represented states and measurement (even when these are non-stabilizer). This paper also includes significant elaboration on the two main results of the previous versio

Quasi-probability representations of quantum theory with applications to quantum information science

This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional quantum theory. We focus on both the characteristics and applications of these representations with an emphasis toward quantum information theory. We discuss the recently proposed unification of the set of possible quasi-probability representations via frame theory and then discuss the practical relevance of negativity in such representations as a criteria for quantumness.Comment: v3: typos fixed, references adde

Quantum Fourier transform, Heisenberg groups and quasiprobability distributions

This paper aims to explore the inherent connection among Heisenberg groups, quantum Fourier transform and (quasiprobability) distribution functions. Distribution functions for continuous and finite quantum systems are examined first as a semiclassical approach to quantum probability distribution. This leads to studying certain functionals of a pair of "conjugate" observables, connected via the quantum Fourier transform. The Heisenberg groups emerge naturally from this study and we take a rapid look at their representations. The quantum Fourier transform appears as the intertwining operator of two equivalent representation arising out of an automorphism of the group. Distribution functions correspond to certain distinguished sets in the group algebra. The marginal properties of a particular class of distribution functions (Wigner distributions) arise from a class of automorphisms of the group algebra of the Heisenberg group. We then study the reconstruction of Wigner function from the marginal distributions via inverse Radon transform giving explicit formulas. We consider applications of our approach to quantum information processing and quantum process tomography.Comment: 39 page

Structural and functional aspects of social support as predictors of mental and physical health trajectories: Whitehall II cohort study

BACKGROUND: Social support is associated with better health. However, only a limited number of studies have examined the association of social support with health from the adult life course perspective and whether this association is bidirectional. METHODS: Participants (n=6797; 30% women; age range from 40 to 77 years) who were followed from 1989 (phase 2) to 2006 (phase 8) were selected from the ongoing Whitehall II Study. Structural and functional social support was measured at follow-up phases 2, 5 and 7. Mental and physical health was measured at five consecutive follow-up phases (3–8). RESULTS: Social support predicted better mental health, and certain functional aspects of social support, such as higher practical support and higher levels of negative aspects in social relationships, predicted poorer physical health. The association between negative aspects of close relationships and physical health was found to strengthen over the adult life course. In women, the association between marital status and mental health weakened until the age of approximately 60 years. Better mental and physical health was associated with higher future social support. CONCLUSIONS: The strength of the association between social support and health may vary over the adult life course. The association with health seems to be bidirectional

Robust Online Hamiltonian Learning

In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer-Rao lower bound, certifying its own performance.Comment: 24 pages, 12 figures; to appear in New Journal of Physic

Work factors and psychological distress in nurses' aides: a prospective cohort study

<p>Abstract</p> <p>Background</p> <p>Nurses' aides (assistant nurses), the main providers of practical patient care in many countries, are doing both emotional and heavy physical work, and are exposed to frequent social encounters in their job. There is scarce knowledge, though, of how working conditions are related to psychological distress in this occupational group. The aim of this study was to identify work factors that predict the level of psychological distress in nurses' aides.</p> <p>Methods</p> <p>The sample of this prospective study comprised 5076 Norwegian nurses' aides, not on leave when they completed a mailed questionnaire in 1999. Of these, 4076 (80.3 %) completed a second questionnaire 15 months later. A wide spectrum of physical, psychological, social, and organisational work factors were measured at baseline. Psychological distress (anxiety and depression) was assessed at baseline and follow-up by the SCL-5, a short version of Hopkins Symptom Checklist-25.</p> <p>Results</p> <p>In a linear regression model of the level of psychological distress at follow-up, with baseline level of psychological distress, work factors, and background factors as independent variables, work factors explained 2 % and baseline psychological distress explained 34 % of the variance. Exposures to role conflicts, exposures to threats and violence, working in apartment units for the aged, and changes in the work situation between baseline and follow-up that were reported to result in less support and encouragement were positively associated with the level of psychological distress. Working in psychiatric departments, and changes in the work situation between baseline and follow-up that gave lower work pace were negatively associated with psychological distress.</p> <p>Conclusion</p> <p>The study suggests that work factors explain only a modest part of the psychological distress in nurses' aides. Exposures to role conflicts and threats and violence at work may contribute to psychological distress in nurses' aides. It is important that protective measures against violent patients are implemented, and that occupational health officers offer victims of violence appropriate support or therapy. It is also important that health service organisations focus on reducing role conflicts, and that leaders listen to and consider the views of the staff.</p

Smallest disentangling state spaces for general entangled bipartite quantum states

PACS numbers: 03.67.-a, 03.65.-w, 03.65.Ta, 03.65.Ud.Entangled quantum states can be given a separable decomposition if we relax the restriction that the local operators be quantum states. Motivated by the construction of classical simulations and local hidden variable models, we construct `smallest' local sets of operators that achieve this. In other words, given an arbitrary bipartite quantum state we construct convex sets of local operators that allow for a separable decomposition, but that cannot be made smaller while continuing to do so. We then consider two further variants of the problem where the local state spaces are required to contain the local quantum states, and obtain solutions for a variety of cases including a region of pure states around the maximally entangled state. The methods involve calculating certain forms of cross norm. Two of the variants of the problem have a strong relationship to theorems on ensemble decompositions of positive operators, and our results thereby give those theorems an added interpretation. The results generalise those obtained in our previous work on this topic [New J. Phys. 17, 093047 (2015)].EP/K022512/1/Engineering and Physical Sciences Research Counci

Wigner formalism for a particle on an infinite lattice: dynamics and spin

The recently proposed Wigner function for a particle in an infinite lattice (Hinarejos M, Banuls MC and Perez A 2012 New J. Phys. 14 103009) is extended here to include an internal degree of freedom as spin. This extension is made by introducing a Wigner matrix. The formalism is developed to account for dynamical processes, with or without decoherence. We show explicit solutions for the case of Hamiltonian evolution under a position-dependent potential, and for evolution governed by a master equation under some simple models of decoherence, for which the Wigner matrix formalism is well suited. Discrete processes are also discussed. Finally, we discuss the possibility of introducing a negativity concept for the Wigner function in the case where the spin degree of freedom is included

Experimental Quantum Hamiltonian Learning

Efficiently characterising quantum systems, verifying operations of quantum devices and validating underpinning physical models, are central challenges for the development of quantum technologies and for our continued understanding of foundational physics. Machine-learning enhanced by quantum simulators has been proposed as a route to improve the computational cost of performing these studies. Here we interface two different quantum systems through a classical channel - a silicon-photonics quantum simulator and an electron spin in a diamond nitrogen-vacancy centre - and use the former to learn the latter's Hamiltonian via Bayesian inference. We learn the salient Hamiltonian parameter with an uncertainty of approximately $10^{-5}$. Furthermore, an observed saturation in the learning algorithm suggests deficiencies in the underlying Hamiltonian model, which we exploit to further improve the model itself. We go on to implement an interactive version of the protocol and experimentally show its ability to characterise the operation of the quantum photonic device. This work demonstrates powerful new quantum-enhanced techniques for investigating foundational physical models and characterising quantum technologies

Dependence of cancer cell adhesion kinetics on integrin ligand surface density measured by a high-throughput label-free resonant waveguide grating biosensor

A novel high-throughput label-free resonant waveguide grating (RWG) imager biosensor, the Epic® BenchTop (BT), was utilized to determine the dependence of cell spreading kinetics on the average surface density (vRGD) of integrin ligand RGD-motifs. vRGD was tuned over four orders of magnitude by co-adsorbing the biologically inactive PLL-g-PEG and the RGD-functionalized PLL-g-PEG-RGD synthetic copolymers from their mixed solutions onto the sensor surface. Using highly adherent human cervical tumor (HeLa) cells as a model system, cell adhesion kinetic data of unprecedented quality were obtained. Spreading kinetics were fitted with the logistic equation to obtain the spreading rate constant (r) and the maximum biosensor response (Δλmax), which is assumed to be directly proportional to the maximum spread contact area (Amax). r was found to be independent of the surface density of integrin ligands. In contrast, Δλmax increased with increasing RGD surface density until saturation at high densities. Interpreting the latter behavior with a simple kinetic mass action model, a 2D dissociation constant of 1753 ± 243 μm−2 (corresponding to a 3D dissociation constant of ~30 μM) was obtained for the binding between RGD-specific integrins embedded in the cell membrane and PLL-g-PEG-RGD. All of these results were obtained completely noninvasively without using any labels