https://biblio.ugent.be/publication/685594/file/1130605.pdf

Review of Particle Physics

http://risa.stanford.edu/teaching/362/particledarkmatter.pdf

Particle dark matter: Evidence, candidates and constraints

Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations that are necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states. The fault tolerance of a topological quantum computer arises from the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the $\ensuremath{\nu}=5∕2$ state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thin-film superconductors. In this review article, current research in this field is described, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. Both the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the $\ensuremath{\nu}=5∕2$ fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.

Non-Abelian Anyons and Topological Quantum Computation

Anyons in an exactly solved model and beyond

Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as {it Non-Abelian anyons}, meaning that they obey {it non-Abelian braiding statistics}. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations which are necessary for quantum computation are carried out by braiding quasiparticles, and then measuring the multi-quasiparticle states. The fault-tolerance of a topological quantum computer arises from the non-local encoding of the states of the quasiparticles, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the nu=5/2 state, although several other prospective candidates have been proposed in systems as disparate as ultra-cold atoms in optical lattices and thin film superconductors. In this review article, we describe current research in this field, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. We address both the mathematical underpinnings of topological quantum computation and the physics of the subject using the nu=5/2 fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.

A complete analysis of FCNC and CP constraints in general SUSY extensions of the standard model

Neurons that fire high-frequency bursts of spikes are found in various sensory systems. Although the functional implications of burst firing might differ from system to system, bursts are often thought to represent a distinct mode of neuronal signalling. The firing of bursts in response to sensory input relies on intrinsic cellular mechanisms that work with feedback from higher centres to control the discharge properties of these cells. Recent work sheds light on the information that is conveyed by bursts about sensory stimuli, on the cellular mechanisms that underlie bursting, and on how feedback can control the firing mode of burst-capable neurons, depending on the behavioural context. These results provide strong evidence that bursts have a distinct function in sensory information transmission.

Burst firing in sensory systems

Multiplicative operations are important in sensory processing, but their biophysical implementation remains largely unknown. We investigated an identified neuron (the lobula giant movement detector, LGMD, of locusts) whose output firing rate in response to looming visual stimuli has been described by two models, one of which involves a multiplication. In this model, the LGMD multiplies postsynaptically two inputs (one excitatory, one inhibitory) that converge onto its dendritic tree; in the other model, inhibition is presynaptic to the LGMD. By using selective activation and inactivation of pre- and postsynaptic inhibition, we show that postsynaptic inhibition has a predominant role, suggesting that multiplication is implemented within the neuron itself. Our pharmacological experiments and measurements of firing rate versus membrane potential also reveal that sodium channels act both to advance the response of the LGMD in time and to map membrane potential to firing rate in a nearly exponential manner. These results are consistent with an implementation of multiplication based on dendritic subtraction of two converging inputs encoded logarithmically, followed by exponentiation through active membrane conductances.

Multiplicative computation in a visual neuron sensitive to looming

The lobula giant motion detector (LGMD) in the locust visual system is a wide-field, motion-sensitive neuron that responds vigorously to objects approaching the animal on a collision course. We investigated the computation performed by LGMD when it responds to approaching objects by recording the activity of its postsynaptic target, the descending contralateral motion detector (DCMD). In each animal, peak DCMD activity occurred a fixed delay delta (15 </= delta </= 35 msec) after the approaching object had reached a specific angular threshold thetathres on the retina (15 degrees </= thetathres </= 40 degrees). thetathres was independent of the size or velocity of the approaching object. This angular threshold computation was quite accurate: the error of LGMD and DCMD in estimating thetathres (3.1-11.9 degrees) corresponds to the angular separation between two and six ommatidia at each edge of the expanding object on the locust retina. It was also resistant to large amplitude changes in background luminosity, contrast, and body temperature. Using several experimentally derived assumptions, the firing rate of LGMD and DCMD could be shown to depend on the product psi(t - delta). e-alphatheta(t-delta), where theta(t) is the angular size subtended by the object during approach, psi(t) is the angular edge velocity of the object and the constant, and alpha is related to the angular threshold size [alpha = 1/tan(thetathres/2)]. Because LGMD appears to receive distinct input projections, respectively motion- and size-sensitive, this result suggests that a multiplication operation is implemented by LGMD. Thus, LGMD might be an ideal model to investigate the biophysical implementation of a multiplication operation by single neurons.

/pdf/computation-of-object-approach-by-a-wide-field-motion-2pd1d09had.pdf

Computation of Object Approach by a Wide-Field, Motion-Sensitive Neuron

An essential function of the brain is to detect threats, such as those posed by objects or predators on a collision course. A wide-field, movement-sensitive visual neuron in the brain of the locust was studied by presenting simulated approaching, receding, and translating objects. The neuron's responses could be described simply by multiplying the velocity of the image edge (dθ/dt) with an exponential function of the size of the object's image on the retina (e−αθ). Because this product peaks before the image reaches its maximum size during approach, this neuron can anticipate collision. The neuron's activity peaks approximately when the approaching object reaches a certain angular size. Because this neuron receives distinct inputs about image size and velocity, the dendritic tree of a single neuron may function as a biophysical device that can carry out a multiplication of two independent input signals.

https://science.sciencemag.org/content/sci/270/5238/1000.full.pdf

Fabrizio Gabbiani

Papers

A complete analysis of FCNC and CP constraints in general SUSY extensions of the standard model

Burst firing in sensory systems

Multiplicative computation in a visual neuron sensitive to looming

Computation of Object Approach by a Wide-Field, Motion-Sensitive Neuron

Elementary computation of object approach by a wide-field visual neuron