Iterative Quantum Algorithms for Maximum Independent Set: A Tale of Low-Depth Quantum Algorithms

Quantum algorithms have been widely studied in the context of combinatorial optimization problems. While this endeavor can often analytically and practically achieve quadratic speedups, theoretical and numeric studies remain limited, especially compared to the study of classical algorithms. We propose and study a new class of hybrid approaches to quantum optimization, termed Iterative Quantum Algorithms, which in particular generalizes the Recursive Quantum Approximate Optimization Algorithm. This paradigm can incorporate hard problem constraints, which we demonstrate by considering the Maximum Independent Set (MIS) problem. We show that, for QAOA with depth $p=1$, this algorithm performs exactly the same operations and selections as the classical greedy algorithm for MIS. We then turn to deeper $p>1$ circuits and other ways to modify the quantum algorithm that can no longer be easily mimicked by classical algorithms, and empirically confirm improved performance. Our work demonstrates the practical importance of incorporating proven classical techniques into more effective hybrid quantum-classical algorithms.Comment: 15 pages, 3 figure

Quantum Adversarial Learning in Emulation of Monte-Carlo Methods for Max-cut Approximation: QAOA is not optimal

One of the leading candidates for near-term quantum advantage is the class of Variational Quantum Algorithms, but these algorithms suffer from classical difficulty in optimizing the variational parameters as the number of parameters increases. Therefore, it is important to understand the expressibility and power of various ans\"atze to produce target states and distributions. To this end, we apply notions of emulation to Variational Quantum Annealing and the Quantum Approximate Optimization Algorithm (QAOA) to show that QAOA is outperformed by variational annealing schedules with equivalent numbers of parameters. Our Variational Quantum Annealing schedule is based on a novel polynomial parameterization that can be optimized in a similar gradient-free way as QAOA, using the same physical ingredients. In order to compare the performance of ans\"atze types, we have developed statistical notions of Monte-Carlo methods. Monte-Carlo methods are computer programs that generate random variables that approximate a target number that is computationally hard to calculate exactly. While the most well-known Monte-Carlo method is Monte-Carlo integration (e.g. Diffusion Monte-Carlo or path-integral quantum Monte-Carlo), QAOA is itself a Monte-Carlo method that finds good solutions to NP-complete problems such as Max-cut. We apply these statistical Monte-Carlo notions to further elucidate the theoretical framework around these quantum algorithms

Lower Bounds on Quantum Annealing Times

The adiabatic theorem provides sufficient conditions for the time needed to prepare a target ground state. While it is possible to prepare a target state much faster with more general quantum annealing protocols, rigorous results beyond the adiabatic regime are rare. Here, we provide such a result, deriving lower bounds on the time needed to successfully perform quantum annealing. The bounds are asymptotically saturated by three toy models where fast annealing schedules are known: the Roland and Cerf unstructured search model, the Hamming spike problem, and the ferromagnetic p-spin model. Our bounds demonstrate that these schedules have optimal scaling. Our results also show that rapid annealing requires coherent superpositions of energy eigenstates, singling out quantum coherence as a computational resource.Comment: accepted to PR

Background-free detection of trapped ions

We demonstrate a Doppler cooling and detection scheme for ions with low-lying D levels which almost entirely suppresses scattered laser light background, while retaining a high fluorescence signal and efficient cooling. We cool a single ion with a laser on the 2S1/2 to 2P1/2 transition as usual, but repump via the 2P3/2 level. By filtering out light on the cooling transition and detecting only the fluorescence from the 2P_3/2 to 2S1/2 decays, we suppress the scattered laser light background count rate to 1 per second while maintaining a signal of 29000 per second with moderate saturation of the cooling transition. This scheme will be particularly useful for experiments where ions are trapped in close proximity to surfaces, such as the trap electrodes in microfabricated ion traps, which leads to high background scatter from the cooling beam

Heating rate and electrode charging measurements in a scalable, microfabricated, surface-electrode ion trap

We characterise the performance of a surface-electrode ion "chip" trap fabricated using established semiconductor integrated circuit and micro-electro-mechanical-system (MEMS) microfabrication processes which are in principle scalable to much larger ion trap arrays, as proposed for implementing ion trap quantum information processing. We measure rf ion micromotion parallel and perpendicular to the plane of the trap electrodes, and find that on-package capacitors reduce this to <~ 10 nm in amplitude. We also measure ion trapping lifetime, charging effects due to laser light incident on the trap electrodes, and the heating rate for a single trapped ion. The performance of this trap is found to be comparable with others of the same size scale.Comment: 6 pages, 10 figure

A Systematic Review of Mosquito Coils and Passive Emanators: Defining Recommendations for Spatial Repellency Testing Methodologies.

Mosquito coils, vaporizer mats and emanators confer protection against mosquito bites through the spatial action of emanated vapor or airborne pyrethroid particles. These products dominate the pest control market; therefore, it is vital to characterize mosquito responses elicited by the chemical actives and their potential for disease prevention. The aim of this review was to determine effects of mosquito coils and emanators on mosquito responses that reduce human-vector contact and to propose scientific consensus on terminologies and methodologies used for evaluation of product formats that could contain spatial chemical actives, including indoor residual spraying (IRS), long lasting insecticide treated nets (LLINs) and insecticide treated materials (ITMs). PubMed, (National Centre for Biotechnology Information (NCBI), U.S. National Library of Medicine, NIH), MEDLINE, LILAC, Cochrane library, IBECS and Armed Forces Pest Management Board Literature Retrieval System search engines were used to identify studies of pyrethroid based coils and emanators with key-words "Mosquito coils" "Mosquito emanators" and "Spatial repellents". It was concluded that there is need to improve statistical reporting of studies, and reach consensus in the methodologies and terminologies used through standardized testing guidelines. Despite differing evaluation methodologies, data showed that coils and emanators induce mortality, deterrence, repellency as well as reduce the ability of mosquitoes to feed on humans. Available data on efficacy outdoors, dose-response relationships and effective distance of coils and emanators is inadequate for developing a target product profile (TPP), which will be required for such chemicals before optimized implementation can occur for maximum benefits in disease control

Past and future spread of the arbovirus vectors Aedes aegypti and Aedes albopictus

The global population at risk from mosquito-borne diseases—including dengue, yellow fever, chikungunya and Zika—is expanding in concert with changes in the distribution of two key vectors: Aedes aegypti and Aedes albopictus. The distribution of these species is largely driven by both human movement and the presence of suitable climate. Using statistical mapping techniques, we show that human movement patterns explain the spread of both species in Europe and the United States following their introduction. We find that the spread of Ae. aegypti is characterized by long distance importations, while Ae. albopictus has expanded more along the fringes of its distribution. We describe these processes and predict the future distributions of both species in response to accelerating urbanization, connectivity and climate change. Global surveillance and control efforts that aim to mitigate the spread of chikungunya, dengue, yellow fever and Zika viruses must consider the so far unabated spread of these mosquitos. Our maps and predictions offer an opportunity to strategically target surveillance and control programmes and thereby augment efforts to reduce arbovirus burden in human populations globally

Malignant melanoma arising from a perianal fistula and harbouring a BRAF gene mutation: a case report

<p>Abstract</p> <p>Background</p> <p>Melanoma of the anal region is a very uncommon disease, accounting for only 0.2-0.3% of all melanoma cases. Mutations of the <it>BRAF </it>gene are usually absent in melanomas occurring in this region as well as in other sun-protected regions. The development of a tumour in a longstanding perianal fistula is also extremely rare. More frequent is the case of a tumour presenting as a fistula, that is, the fistula being a consequence of the cancerous process, although we have found only two cases of fistula-generating melanomas reported in the literature.</p> <p>Case Presentation</p> <p>Here we report the case of a 38-year-old male who presented with a perianal fistula of four years of evolution. Histopathological examination of the fistulous tract confirmed the presence of malignant melanoma. Due to the small size and the central location of the melanoma inside the fistulous tract, we believe the melanoma reported here developed in the epithelium of the fistula once the latter was already formed. Resected sentinel lymph nodes were negative and the patient, after going through a wide local excision, remains disease-free nine years after diagnosis. DNA obtained from melanoma tissue was analysed by automated direct sequencing and the <it>V600E </it>(<it>T1799A</it>) mutation was detected in exon 15 of the <it>BRAF </it>gene.</p> <p>Conclusion</p> <p>Since fistulae experience persistent inflammation, the fact that this melanoma harbours a <it>BRAF </it>mutation strengthens the view that oxidative stress caused by inflammatory processes plays an important role in the genesis of <it>BRAF </it>gene mutations.</p