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In this paper, Wang et al. present experimental results showing genuine multipartite entanglement of up to 16 qubits on the ibmqx5 device, a 16 transmon-qubit universal quantum computing device developed by IBM. Prior to these results entanglement had been reported up to 10 superconducting qubits.

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Quantum computers promise to reduce the computational complexity of simulating quantum many-body systems from exponential to polynomial. Much effort is being put in reducing the complexity of the necessary algorithms, to allow them to be run on noisy intermediate scale quantum computers. In this paper, Dumitrescu et al. report a quantum simulation of the deuteron binding energy on 2 such small-scale noisy cloud accessible quantum processors (the IBM QX5 and Rigetti 19Q).

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Understanding and modeling the behavior of large numbers of interacting fermions is key to understanding the macroscopic properties of matter. However, the memory required to represent such a many-body state scales exponentially with the number of fermions, which makes simulation of many interesting cases intractable on classical computers. Algorithms leveraging the advantages of quantum computers for quantum simulations have steadily been developed in the past two decades. Variational quantum eigensolvers (VQE) have recently appeared as a promising class of quantum algorithms designed to prepare states for such quantum simulations. Low-depth circuits for such state preparation and quantum simulation are needed for practical quantum chemistry applications on near-term quantum devices with limited coherence. In this paper, Dallaire-Demers et al. present a new type of low-depth VQE ansatz, which should be in reach of near-term quantum devices and which can accurately prepare the ground state of correlated fermionic systems.

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In this article, John Preskill provides his view on the near-term (5-10 years ahead) societal and commercial impact of quantum-computers. Specifically, the author focuses on what he calls Noisy Intermediate-Scale Quantum (NISQ) technology: quantum computers with 50-100 qubits for which noise in quantum gates will limit the size of quantum circuits that can be executed reliably. Such NISQ devices may be able to perform tasks which surpass the capabilities of today’s classical digital computers and will be useful tools for exploring e.g. many-body quantum physics, and may have other useful applications, but, the author states, the 100-qubit quantum computer will not change the world right away and we should regard them as a significant step toward the more powerful quantum technologies of the future.

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Quantum annealers can be used to solve optimization and sampling problems. However,  they can also solve certain combinational logic problems on the basis of an Ising-model implementation of Boolean logic. In this paper, Maezawa et al. propose a prime factoring machine operated in a frame work of quantum annealing (QA). The idea is inverse operation of a quantum-mechanically reversible multiplier implemented with QA-based Boolean logic circuits. They discuss their plan toward a practical-scale factoring machine from concept to technology.

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Practical applications for current noise and small quantum-computing hardware, has focused mostly on short-depth parameterized quantum circuits used as a subroutine embedded in a larger classical optimization loop. In this paper, Otterbach et al. describe experiments with unsupervised machine learning (specifically clustering), which they translate into a combinatorial optimization problem solved by the quantum approximate optimization algorithm (QAOA) running on the Rigetti 19Q (a 19 qubit gate-based processor). They show that their implementation finds optimal solution for this task even with relatively noisy gates.

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For (un-)supervised learning, with applications in data-mining, prediction and classification, already quite a few quantum algorithms have been developed showing potential for (super-) polynomial speed-ups. Less is known about the benefits quantum can bring to reinforcement learning (RL), which has applications in a.o. AI and autonomous driving. In RL  a learning-agent perceives (aspects of) the states of a task environment, and influences subsequent states by performing actions. Certain state-action-state transitions are rewarding, and successful learning agents learn optimal behavior. In this paper, Dunjko et al. construct quantum-enhanced reinforcement-learners, which learn super-polynomially, and even exponentially faster than any classical reinforcement learning model.

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So-called holonomic quantum gates based on geometric phases are robust against control-errors. Zanardi and Rasetti, first proposed the adiabatic holonomic quantum computation (AHQC), which has the unavoidable challenge of long run-time needed for adiabatic evolution increasing the vulnerability to decoherence. Therefore non-adiabatic HQC schemes, with much shorter gate-times, were proposed and realized in platforms based on trapped ions, NMR, superconducting circuits and nitrogen-vacancy centers in diamond. In this paper, Zhao et al. propose a non-adiabatic HQC scheme based on Rydberg atoms, which combines robustness to control-errors, short gate times and long coherence times.

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Majorana bound states are quasi-particles, which obey non-Abelian braiding statistics (meaning they are neither bosons nor fermions). Topological quantum computation uses multiple such quasiparticles to store quantum information, where the non-local encoding provides high fault-tolerance (immunity to local perturbations). Unitary gates can be created by braiding. A semiconductor nanowire coupled to a superconductor can be tuned into a topological superconductor with two Majorana zero-modes localized at the wire ends. Tunneling into a Majorana mode will show a robustly quantized zero-bias peak (ZBP) in the differential conductance. In this paper, Zhang et al. are the first to experimentally show the exact theoretically predicted ZBP quantization, which strongly supports the existence of non-Abelian Majorana zero-modes in their system, paving the way for their next challenge: braiding experiments.

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Quantum Computational Chemistry is one of the most promising applications for both near-term and large scale fault-tolerant quantum-computers. In this paper, McClean et al. present Open Fermion (www.openfermion.org), an open-source software library written largely in Python, aimed at enabling the simulation of fermionic models and quantum chemistry problems on quantum hardware. Without such a library, developing and studying algorithms for these problems is be difficult due to the prohibitive amount of domain knowledge required in both the area of chemistry and quantum algorithms. Beginning with an interface to common electronic structure packages, it simplifies the translation between a molecular specification and a quantum circuit for solving or studying the electronic structure problem on a quantum computer, minimizing the amount of domain expertise required to enter the field.

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Reinforcement learning6 differs from supervised and unsupervised learning in that it takes into account a scalar parameter (reward) to evaluate the input-output relation in a trial and error way. In this paper, Cardenas-Lopez et al. propose a protocol to perform generalized quantum reinforcement learning. They consider diverse possible scenarios for an agent, an environment, and a register that connects them, involving multi-qubit and multi-level systems, as well as open-system dynamics and they propose possible implementations of this protocol in trapped ions and superconducting circuits. 

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In this paper, Neill et al. (Google/UCSB), present experimental results for their 9 transmon (gmon) qubit device and illustrate that these experiments form a blueprint for demonstrating quantum supremacy on their next-generation (50 qubit) system. By individually tuning the qubit parameters, they are able to generate thousands of unique Hamiltonian evolutions and probe the output probabilities. The measured probabilities obey a universal distribution, consistent with uniformly sampling the full Hilbert-space. As the number of qubits in the algorithm is varied, the system continues to explore the exponentially growing number of states. They also compare the measurement results with the expected behavior and show that the algorithm can be implemented with high fidelity.

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