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Quantum sensing and metrology may benefit from a spatially distributed network architecture employing entangled states and measurements to enhance precision. Given the challenges faced in the creation and manipulation of entangled states, a complete understanding of when entanglement is (and is not) critical to optimizing estimation precision is importance. In this paper, Proctor et al. introduce a general model for a network of quantum sensors, and use this model to determine whether precision enhancement can be achieved in a range of practical applications.

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Several physical platforms are aiming to realize a fully programmable, coherent and scalable quantum annealing device. In this paper, Glaetzle et al. show that combining a quantum simulation toolbox for Rydberg atoms with the Lechner-Hauke-Zoller (LHZ) architecture allows one to build a prototype for a coherent adiabatic quantum computer with all-to-all Ising interactions. 

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Networks of coupled optical parametric oscillators (OPOs) are an alternative physical system for solving Ising type problems. Theoretical/numerical investigations have shown that in principle quantum effects (like entanglement between delay-coupled pulses) can play meaningful roles in such systems. In this paper, McMahon et al. (and an earlier paper of Inagaki et al.), show that this type of architecture is relatively scalable and can be used to solve max cut problems accurately, although in the current prototype devices the quantum features are 'washed out' by high round-trip losses (typically 10 dB), to the point that a purely semi-classical description of the system is sufficient to explain all the observed experimental results. The next step would be to realize this architecture in a system where the quantum nature is not lost.

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In this paper, Venturelli et al. present a quantum annealing solver for the renowned job-shop scheduling problem (JSP). They formulate the problem as a time-indexed quadratic unconstrained binary optimization problem, several pre-processing and graph embedding strategies are employed to compile optimally parametrized families of the JSP for scheduling instances of up to six jobs and six machines on the D-Wave Systems Vesuvius (DW2) processor. Problem simplifications and partitioning algorithms are discussed and the results from the processor are compared against state-of-the-art global-optimum solvers.

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In this paper, Puri et al. propose an alternative to the typical quantum annealing architecture with a scalable network of all-to-all connected, two-photon driven Kerr-nonlinear resonators. Each of these resonators encode an Ising spin in a robust degenerate subspace formed by two coherent states of opposite phases. A fully-connected optimization problem is mapped onto local fields driving the resonators, which are themselves connected by local four-body interactions. They describe an adiabatic annealing protocol in this system and analyze its performance in the presence of photon loss. Numerical simulations indicate substantial resilience to this noise channel, making it a promising platform for implementing a large scale quantum Ising machine.

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A recommendation engine uses the past purchases or ratings to construct a (partial) preference matrix, which is used to provide personalized recommendations to individual users. In this paper, Kerenidis et al. present a quantum recommendation system which updates the partial preference matrix each time data comes in and can, based on such matrix, provides a recommendation in time polylog to the matrix-dimension, exponentially faster than classical recommendation systems.

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Mean-variance portfolio optimization problems are traditionally solved as continuous-variable problems. However, for assets that can only be traded in large lots, or for asset managers who are constrained to trading large blocks of assets, solving the continuous problem yields an approximation. The discrete problem, is expected to provide better results, but is non-convex due to the fragmented nature of the domain, and is therefore much harder to solve. In this paper, Rosenberg et al. attempt to solve a discrete multi-period portfolio optimisation problem using D-Wave Systems' quantum annealer. They derive a formulation of the problem, discuss several possible integer encoding schemes, and present numerical examples that show high success rates. They also present insight into how results may be improved using suitable software enhancements, and why current quantum annealing technology limits the size of problem that can be successfully solved today. The formulation presented is specifically designed to be scalable, with the expectation that as quantum annealing technology improves, larger problems will be solvable using the same techniques. 

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In this paper, Ashley Montanaro, gives a broad overview of quantum algorithms, focusing on algorithms with clear applications and rigorous performance bounds, and including recent progress in the field. The paper does not a detailed discussion of how the quantum algorithms mentioned work, but aims to provide structure to the different classes of quantum-algorithms, which were known in November 2015

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In this paper, Andrew Lucas provides Ising formulations for many NP-complete and NP-hard problems, including all of Karp's 21 NP-complete problems. In each case, the required number of spins is at most cubic in the size of the problem. This work may be useful in designing adiabatic quantum optimization algorithms.

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