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In this paper, Patrick J. Coles et al., aim to explain the principles of quantum programming straight-forward algebra that makes understanding the underlying quantum mechanics optional (but still fascinating). The authors give an introduction to quantum computing algorithms and their implementation on real quantum hardware and survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. They show how these algorithms can be implemented on an actual quantum-processor (in this case an IBM QPU) and in each case discuss the results of the implementation with respect to differences of the results on a simulator (QVM) or the actual processor (QPU).

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Efficient quantum simulations of classically intractable instances of the associated electronic structure problem promise breakthroughs in our understanding of basic chemistry and could revolutionize research into new materials, pharmaceuticals, and industrial catalysts. In Quantum Computational Chemistry solutions, the Variational Quantum Eigensolver (VQE) algorithm offers a hybrid classical-quantum, and thus low quantum circuit depth, alternative to the Phase Estimation algorithm used to measure the ground-state energy of a molecular Hamiltonian. In this paper, Hempel et al. use a digital quantum simulator based on trapped ions to experimentally investigate the VQE algorithm for the calculation of molecular ground state energies of two simple molecules  (H2 and LiH) and experimentally demonstrate and compare different encoding methods using up to four qubits. 

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In this paper Flamini et al. provide a comprehensive overview of the current (March 2018) state of the art in the field of photonic quantum information processing including quantum communication and photonic quantum simulation.

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Clustering is a form of unsupervised machine learning, where instances are organized into groups whose members share similarities. The assignments are, in contrast to classification, not known a priori, but generated by the algorithm. In this paper, Neukart et al.  present an algorithm for quantum-assisted cluster analysis (QACA) that makes use of the topological properties of a D-Wave 2000Q quantum processing unit (QPU). They explain how the problem can be expressed as a quadratic unconstrained binary optimization (QUBO) problem, and show that the introduced quantum-assisted clustering algorithm is, regarding accuracy, equivalent to commonly used classical clustering algorithms.

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Quantum machine learning (QML) algorithms based on the Harrow-Hassidim- Lloyd (HHL) algorithm rely on quantum phase estimation which requires high circuit-depth. To allow QML on current noisy intermediate scale quantum (NISQ) devices classical-quantum hybrid algorithms have been suggested applying low-depth circuits like quantum variational eigensolvers and quantum approximate optimization. Such hybrid algorithms typically divide the ML problem into two parts, each part to be performed either classically or on a quantum-computer. In this paper, Mitarai et al. present a new hybrid framework, called quantum circuit learning (QCL), which is easily realizable on current NISQ devices. Under QCL a circuit learns by providing input data, while iteratively tuning the circuit parameters to give the desired output. They show that QCL is able to learn nonlinear functions and perform simple classification tasks. They also show that a 6-qubit circuit is capable of learning dynamics of a 10-spin system with a fully connected Ising Hamiltonian, implying that QCL could be well suited for learning complex many-body systems.

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In this paper, Matthew Hastings presents a quantum algorithm to exactly solve certain problems in combinatorial optimization, including weighted MAX-2-SAT.  While the time required is still exponential, the algorithm provably outperforms Grover's algorithm assuming a mild condition on the number of low energy states of the target Hamiltonian.

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The perceptron algorithm dates back to the late 1950s and is an algorithm for supervised learning of binary classifiers. In a 2016 paper, Wiebe et al. proposed a quantum algorithm (based on Grover’s quantum-search approach), which can quadratically speed-up the training of a perceptron. In this paper, Zheng et al. describe their design for a quantum-circuit to implement the training-algorithm of Wiebe et al. They also analyze the resource requirements (qubits and gates) and demonstrate the feasibility of their quantum-circuit by testing it on the ibmqx5 (a 16 qubit universal gate quantum processor developed by IBM)

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Atomic ions can be trapped by electric fields in ultra-high vacuum and then laser-cooled to extremely low temperatures. The internal states of such a trapped ion can be used to encode a qubit. Such qubit systems have very long coherence times and their internal states can be precisely manipulated using lasers, and measured efficiently. Current, room temperature, systems are limited to 50 ions to to collisions with background gas. At cryogenic temperatures (4K) , most of the residual background gas is trapped enabling further scale-up of ion-trap systems. In this paper, Pagano et al. present experimental results from a trapped ion system with such cryogenic-pumping, which enables them to trap over 100 ions in a linear configuration for hours, paving the way for future quantum simulation of spin models that are intractable with classical computer modelling.

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Usually quantum information is encoded into a single, well-controlled degree of freedom, such as a spin. In some cases, however, establishing so called hyper-entanglement among several degrees-of-freedom (e.g. photon path, polarization and angular momentum), can be beneficial, e.g. improve the capacity of dense coding in linear optics.  In this paper, Li et al. propose a scheme that allows to combine both (single degree-of-freedom) entanglement and hyper-entanglement. Specifically, they show how two identical, initially separated particles can become spin-entangled, momenta-entangled and spin-and-momenta-hyper-entangled.

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Coupling between superconducting qubits is typically controlled not by changing the qubit-qubit coupling constant, but by suppressing the coupling by detuning their transition frequency. This approach becomes much more difficult with a high number of qubits, due to the ever-more crowded transition-frequency spectrum. In this paper, Casparis et al. demonstrate an alternative coupling scheme, in the form of a voltage controlled quantum-bus with the ability to change the effective qubit-qubit coupling by a factor of 8 between the on- and off-states without causing significant qubit decoherence.

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Change point detection is a vast branch of statistical analysis developing techniques for uncovering abrupt changes in the underlying probability distribution of streaming data. This can be done off-line (using time-series data) or online (processing data sequentially). The latter enables real-time decision making, require less memory and is most relevant in machine learning. In this paper, Sentis et al. discuss online detection strategies for identifying a change point in a stream of quantum particles allegedly prepared in identical states. They show that the identification of the change point can be done without error via sequential local measurements, requiring only one classical bit of memory between subsequent measurements.

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Transition metal dichalcogenide monolayers (TMDC) are atomic-thin two-dimensional materials in which electrostatic quantum dots (QD) can be created. The electrons or holes confined in these QD have not only a spin degree of freedom, but also a valley degree of freedom. This additional degree of freedom can be used to encode a qubit creating a new field of electronics called valleytronics. In this paper Pawlowski et al. show how to create a QD in a MoS2 monolayer material and how to perform the NOT operation on its valley degree of freedom.

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