On the Complexity of Random Quantum Computations and the Jones Polynomial

There is a natural relationship between Jones polynomials and quantum computation. We use this relationship to show that the complexity of evaluating relative-error approximations of Jones polynomials can be used to bound the classical complexity of approximately simulating random quantum computations. We prove that random quantum computations cannot be classically simulated up to a constant total variation distance, under the assumption that (1) the Polynomial Hierarchy does not collapse and (2) the average-case complexity of relative-error approximations of the Jones polynomial matches the worst-case complexity over a constant fraction of random links. Our results provide a straightforward relationship between the approximation of Jones polynomials and the complexity of random quantum computations.Comment: 8 pages, 4 figure

Multisensory perception of looming and receding objects in human newborns

When newborns leave the enclosed spatial environment of the uterus and arrive in the outside world, they are faced with a new audiovisual environment of dynamic objects, actions and events both close to themselves and further away. One particular challenge concerns matching and making sense of the visual and auditory cues specifying object motion [1-5]. Previous research shows that adults prioritise the integration of auditory and visual information indicating looming (for example [2]) and that rhesus monkeys can integrate multisensory looming, but not receding, audiovisual stimuli [4]. Despite the clear adaptive value of correctly perceiving motion towards or away from the self - for defence against and physical interaction with moving objects - such a perceptual ability would clearly be undermined if newborns were unable to correctly match the auditory and visual cues to such motion. This multisensory perceptual skill has scarcely been studied in human ontogeny. Here we report that newborns only a few hours old are sensitive to matches between changes in visual size and in auditory intensity. This early multisensory competence demonstrates that, rather than being entirely na\uefve to their new audiovisual environment, newborns can make sense of the multisensory cue combinations specifying motion with respect to themselves

Patient safety indicators for England from hospital administrative data: case-control analysis and comparison with US data

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.The Healthcare Commission received a small grant from the Health and Social Care Information Centre to support the initial recoding work

Simulating Hamiltonian dynamics using many-qudit Hamiltonians and local unitary control

When can a quantum system of finite dimension be used to simulate another quantum system of finite dimension? What restricts the capacity of one system to simulate another? In this paper we complete the program of studying what simulations can be done with entangling many-qudit Hamiltonians and local unitary control. By entangling we mean that every qudit is coupled to every other qudit, at least indirectly. We demonstrate that the only class of finite-dimensional entangling Hamiltonians that aren't universal for simulation is the class of entangling Hamiltonians on qubits whose Pauli operator expansion contains only terms coupling an odd number of systems, as identified by Bremner et. al. [Phys. Rev. A, 69, 012313 (2004)]. We show that in all other cases entangling many-qudit Hamiltonians are universal for simulation

The partially alternating ternary sum in an associative dialgebra

The alternating ternary sum in an associative algebra, $abc - acb - bac + bca + cab - cba$, gives rise to the partially alternating ternary sum in an associative dialgebra with products $\dashv$ and $\vdash$ by making the argument $a$ the center of each term: $a \dashv b \dashv c - a \dashv c \dashv b - b \vdash a \dashv c + c \vdash a \dashv b + b \vdash c \vdash a - c \vdash b \vdash a$. We use computer algebra to determine the polynomial identities in degree $\le 9$ satisfied by this new trilinear operation. In degrees 3 and 5 we obtain $[a,b,c] + [a,c,b] \equiv 0$ and $[a,[b,c,d],e] + [a,[c,b,d],e] \equiv 0$; these identities define a new variety of partially alternating ternary algebras. We show that there is a 49-dimensional space of multilinear identities in degree 7, and we find equivalent nonlinear identities. We use the representation theory of the symmetric group to show that there are no new identities in degree 9.Comment: 14 page

Quantum Sampling Problems, BosonSampling and Quantum Supremacy

There is a large body of evidence for the potential of greater computational power using information carriers that are quantum mechanical over those governed by the laws of classical mechanics. But the question of the exact nature of the power contributed by quantum mechanics remains only partially answered. Furthermore, there exists doubt over the practicality of achieving a large enough quantum computation that definitively demonstrates quantum supremacy. Recently the study of computational problems that produce samples from probability distributions has added to both our understanding of the power of quantum algorithms and lowered the requirements for demonstration of fast quantum algorithms. The proposed quantum sampling problems do not require a quantum computer capable of universal operations and also permit physically realistic errors in their operation. This is an encouraging step towards an experimental demonstration of quantum algorithmic supremacy. In this paper, we will review sampling problems and the arguments that have been used to deduce when sampling problems are hard for classical computers to simulate. Two classes of quantum sampling problems that demonstrate the supremacy of quantum algorithms are BosonSampling and IQP Sampling. We will present the details of these classes and recent experimental progress towards demonstrating quantum supremacy in BosonSampling.Comment: Survey paper first submitted for publication in October 2016. 10 pages, 4 figures, 1 tabl

Contraception for Men: A Breakthrough New Approach

There has not been a new reversible contraceptive for men since the development of the condom, centuries ago. Matzuk et al. describe a new molecular approach using administration of a small molecule to directly and reversibly inhibit spermatogenesis in mice by blocking the function of a testicular bromodomain without apparent adverse effect on the organism or offspring

Object categorisation, object naming, and viewpoint-independence in visual remembering: Evidence from young children's drawings of a novel object

A simple object-drawing task confirms a three-way association between object categorisation, viewpoint independence, and longer-term visual remembering. Young children (5- to 7-year-olds) drew a familiar object or a novel object, immediately after it had been hidden from view or on the following day. Both objects were shown from a full range of viewpoints or from just two viewpoints, from neither of which would either object normally be drawn after unrestricted viewing. When drawing from short-term memory after restricted viewing, both objects were most likely to be depicted from a seen viewpoint. When drawing from longer-term memory after restricted viewing, the novel object continued to be drawn from a seen viewpoint, but the mug was now most likely to be drawn from a preferred viewpoint from which it had not been seen. Naming the novel object with a novel count noun ("Look at this. This is a dax"), to signal that it belonged to an object category, resulted in it being drawn in the same way as the familiar object. The results concur with other evidence indicating that short-term and longer-term visual remembering are differentially associated with viewpoint-dependent representations of individual objects and viewpoint independent representations of object categories, respectively

Influence of PWM on the proximity loss in permanent magnet brushless AC machines

The winding copper loss can be significantly increased due to skin and proximity eddy current effects. The skin and proximity losses due to fundamental frequency current has been investigated in literature, but the influence of PWM on the skin and proximity losses has not been reported. In this paper, 2-D finite element method is employed to analyze the skin and proximity losses in a permanent magnet brushless AC machine, in which significant proximity loss exists due to high frequency current ripples induced by the PWM, as confirmed by both theoretical calculation and experiment. The analyses should be generally applicable to other machines