Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance

Quantum ground-state problems are computationally hard problems; for general many-body Hamiltonians, there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many problems in physics and chemistry, a quantum computer could employ this trial wavefunction to project the ground state by means of the phase estimation algorithm (PEA). We performed an experimental realization of this idea by implementing a variational-wavefunction approach to solve the ground-state problem of the Heisenberg spin model with an NMR quantum simulator. Our iterative phase estimation procedure yields a high accuracy for the eigenenergies (to the 10^-5 decimal digit). The ground-state fidelity was distilled to be more than 80%, and the singlet-to-triplet switching near the critical field is reliably captured. This result shows that quantum simulators can better leverage classical trial wavefunctions than classical computers.Comment: 11 pages, 13 figure

Simulating quantum statistics with entangled photons: a continuous transition from bosons to fermions

In contrast to classical physics, quantum mechanics divides particles into two classes-bosons and fermions-whose exchange statistics dictate the dynamics of systems at a fundamental level. In two dimensions quasi-particles known as 'anyons' exhibit fractional exchange statistics intermediate between these two classes. The ability to simulate and observe behaviour associated to fundamentally different quantum particles is important for simulating complex quantum systems. Here we use the symmetry and quantum correlations of entangled photons subjected to multiple copies of a quantum process to directly simulate quantum interference of fermions, bosons and a continuum of fractional behaviour exhibited by anyons. We observe an average similarity of 93.6\pm0.2% between an ideal model and experimental observation. The approach generalises to an arbitrary number of particles and is independent of the statistics of the particles used, indicating application with other quantum systems and large scale application.Comment: 10 pages, 5 figure

Calculating Unknown Eigenvalues with a Quantum Algorithm

Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct the algorithm. We have implemented the complete quantum phase estimation algorithm for a single qubit unitary in which the answer is calculated by the algorithm. We use a new approach to implementing the controlled-unitary operations that lie at the heart of the majority of quantum algorithms that is more efficient and does not require the eigenvalues of the unitary to be known. These results point the way to efficient quantum simulations and quantum metrology applications in the near term, and to factoring large numbers in the longer term. This approach is architecture independent and thus can be used in other physical implementations

Optical parametric oscillation with distributed feedback in cold atoms

There is currently a strong interest in mirrorless lasing systems, in which the electromagnetic feedback is provided either by disorder (multiple scattering in the gain medium) or by order (multiple Bragg reflection). These mechanisms correspond, respectively, to random lasers and photonic crystal lasers. The crossover regime between order and disorder, or correlated disorder, has also been investigated with some success. Here, we report one-dimensional photonic-crystal lasing (that is, distributed feedback lasing) with a cold atom cloud that simultaneously provides both gain and feedback. The atoms are trapped in a one-dimensional lattice, producing a density modulation that creates a strong Bragg reflection with a small angle of incidence. Pumping the atoms with auxiliary beams induces four-wave mixing, which provides parametric gain. The combination of both ingredients generates a mirrorless parametric oscillation with a conical output emission, the apex angle of which is tunable with the lattice periodicity

How Gaussian competition leads to lumpy or uniform species distributions

A central model in theoretical ecology considers the competition of a range of species for a broad spectrum of resources. Recent studies have shown that essentially two different outcomes are possible. Either the species surviving competition are more or less uniformly distributed over the resource spectrum, or their distribution is 'lumped' (or 'clumped'), consisting of clusters of species with similar resource use that are separated by gaps in resource space. Which of these outcomes will occur crucially depends on the competition kernel, which reflects the shape of the resource utilization pattern of the competing species. Most models considered in the literature assume a Gaussian competition kernel. This is unfortunate, since predictions based on such a Gaussian assumption are not robust. In fact, Gaussian kernels are a border case scenario, and slight deviations from this function can lead to either uniform or lumped species distributions. Here we illustrate the non-robustness of the Gaussian assumption by simulating different implementations of the standard competition model with constant carrying capacity. In this scenario, lumped species distributions can come about by secondary ecological or evolutionary mechanisms or by details of the numerical implementation of the model. We analyze the origin of this sensitivity and discuss it in the context of recent applications of the model.Comment: 11 pages, 3 figures, revised versio

A randomised control trial of low glycaemic index carbohydrate diet versus no dietary intervention in the prevention of recurrence of macrosomia

<p>Abstract</p> <p>Background</p> <p>Maternal weight and maternal weight gain during pregnancy exert a significant influence on infant birth weight and the incidence of macrosomia. Fetal macrosomia is associated with an increase in both adverse obstetric and neonatal outcome, and also confers a future risk of childhood obesity. Studies have shown that a low glycaemic diet is associated with lower birth weights, however these studies have been small and not randomised <abbrgrp><abbr bid="B1">1</abbr><abbr bid="B2">2</abbr></abbrgrp>. Fetal macrosomia recurs in a second pregnancy in one third of women, and maternal weight influences this recurrence risk <abbrgrp><abbr bid="B3">3</abbr></abbrgrp>.</p> <p>Methods/Design</p> <p>We propose a randomised control trial of low glycaemic index carbohydrate diet vs. no dietary intervention in the prevention of recurrence of fetal macrosomia.</p> <p>Secundigravid women whose first baby was macrosomic, defined as a birth weight greater than 4000 g will be recruited at their first antenatal visit.</p> <p>Patients will be randomised into two arms, a control arm which will receive no dietary intervention and a diet arm which will be commenced on a low glycaemic index diet.</p> <p>The primary outcome measure will be the mean birth weight centiles and ponderal indices in each group.</p> <p>Discussion</p> <p>Altering the source of maternal dietary carbohydrate may prove to be valuable in the management of pregnancies where there has been a history of fetal macrosomia. Fetal macrosomia recurs in a second pregnancy in one third of women. This randomised control trial will investigate whether or not a low glycaemic index diet can affect this recurrence risk.</p> <p>Current Controlled Trials Registration Number</p> <p>ISRCTN54392969</p

Quantum Simulation of Tunneling in Small Systems

A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because of the number of gates and qubits necessary, however, digital quantum particle simulations remain untested. A contributing factor to the system size required is the number of ancillary qubits needed to implement matrix exponentials of the potential operator. Here, we show that a set of tunneling problems may be investigated with no ancillary qubits and a cost of one single-qubit operator per time step for the potential evolution. We show that physically interesting simulations of tunneling using 2 qubits (i.e. on 4 lattice point grids) may be performed with 40 single and two-qubit gates. Approximately 70 to 140 gates are needed to see interesting tunneling dynamics in three-qubit (8 lattice point) simulations.Comment: 4 pages, 2 figure

Testing foundations of quantum mechanics with photons

The foundational ideas of quantum mechanics continue to give rise to counterintuitive theories and physical effects that are in conflict with a classical description of Nature. Experiments with light at the single photon level have historically been at the forefront of tests of fundamental quantum theory and new developments in photonics engineering continue to enable new experiments. Here we review recent photonic experiments to test two foundational themes in quantum mechanics: wave-particle duality, central to recent complementarity and delayed-choice experiments; and Bell nonlocality where recent theoretical and technological advances have allowed all controversial loopholes to be separately addressed in different photonics experiments.Comment: 10 pages, 5 figures, published as a Nature Physics Insight review articl

Multi-level selection and the issue of environmental homogeneity

In this paper, I identify two general positions with respect to the relationship between environment and natural selection. These positions consist in claiming that selective claims need and, respectively, need not be relativized to homogenous environments. I then show that adopting one or the other position makes a difference with respect to the way in which the effects of selection are to be measured in certain cases in which the focal population is distributed over heterogeneous environments. Moreover, I show that these two positions lead to two different interpretations – the Pricean and contextualist ones – of a type of selection scenarios in which multiple groups varying in properties affect the change in the metapopulation mean of individual-level traits. Showing that these two interpretations stem from different attitudes towards environmental homogeneity allows me to argue: a) that, unlike the Pricean interpretation, the contextualist interpretation can only claim that drift or selection is responsible for the change in frequency of the focal trait in a given metapopulation if details about whether or not group formation is random are specified; b) that the traditional main objection against the Pricean interpretation – consisting in arguing that the latter takes certain side-effects of individual selection to be effects of group selection – is unconvincing. This leads me to suggest that the ongoing debate about which of the two interpretations is preferable should concentrate on different issues than previously thought