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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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In this paper, Dunjko et al. provide a comprehensive review of the current (Sept 2017) state of quantum machine learning, including quantum providing speed-ups or enhancing classical ML and classical classical ML being used for quantum-control or to design quantum-circuits

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Topological codes, and the surface code in particular, are popular choices for many quantum computing architectures, because of high error thresholds and local stabilizers. In this paper, Tuckett et al. show that a simple modification of the surface code can exhibit a fourfold  gain in the error correction threshold for a noise model in which Pauli Z errors (dephasing) occur more frequently than X or Y errors (which is common in many quantum architectures, including superconducting qubits). For pure dephasing an improved threshold of 43,7% is found (versus 10.9% for the optimal surface code), while 28,2% applies with a noise-bias-ratio of 10 (more realistic regime).

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In recent years many academics and corporates have focus on solving combinatorial optimization problems on quantum-annealing devices like those offered by D-Wave. Now that noisy intermediate scale (NISQ) gate-based quantum-processers (like those of Google, IBM, Rigetti and Intel) are nearing the moment of quantum-supremacy, it is interesting to learn what gate-based quantum-computers can bring to combinatorial optimization problems. In this work, In this paper, Zahedinejad et al. provide a survey of the approaches to solving different types of combinatorial optimization problems, in particular quadratic unconstrained binary optimization (QUBO) problems on a gate model quantum computer. They focus on four different approaches including digitizing the adiabatic quantum computing, global quantum optimization algorithms, the quantum algorithms that approximate the ground state of a general QUBO problem, and quantum sampling. 

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Quantum dot based spin qubits may offer significant advantages due to their potential for high densities, all-electrical operation, and integration onto an industrial platform. However, in quantum-dots, charge and nuclear spin noise are dominant sources of decoherence and gate errors. Silicon naturally has few nuclear spin isotopes, which can be removed through purification. As a host material, Silicon, enables single-qubit gate fidelities above 99%. In this paper, Watson et al. demonstrate a programmable two-qubit quantum processor in silicon by performing both the Deutsch-Josza and the Grover search algorithms.

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Superpositions of bit strings (many-body spin configurations) have been recently proposed as a key to quantum machine learning applications. Adiabatic protocols may serve as an effective method to prepare such states. If the ground state of the final Hamiltonian in an adiabatic protocol is energetically degenerate, the final state of the protocol is a superposition of the configurations in the degenerate manifold. The challenge is to be able to control the dynamics of the protocol such that the amplitudes of the final state can be deterministically programmed. In this paper, Sieberer et al. present a framework to do precisely that. They apply an adiabatic protocol with controlled diabatic transitions to dynamically prepare programmable superpositions, where the control parameters can, even for large systems, be determined efficiently.

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This report by Olson et al. summarizes the resuts of an NSF Workshop on Quantum Computational Chemistry held in November 2016. The workshop was attended by a wide range of experts from directly quantum-oriented fields such as algorithms, chemistry, machine learning, optics, simulation, and metrology, as well as experts in related fields such as condensed matter physics, biochemistry, physical chemistry, inorganic and organic chemistry, and spectroscopy. The goal of the workshop was to summarize recent progress in research at the interface of quantum information science and chemistry as well as to discuss the promising research challenges and opportunities in the field.

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Shor's algorithm  for breaking both RSA and discrete-log public-key cryptography depend on the availability of a relatively large-scale quantum computer (e.g. Kutin et al. showed in 2006 that factoring a 1024-bit number requires 3132 qubits and 5.7x10^9 T gates). However, in quantum hardware developments are progressing while at the same time quantum algorithms are getting more efficient. So the timing when quantum computers will be able to break e.g. RSA is shifting. In this paper, Berstein et al. present a factoring algorithm that, assuming standard heuristics, uses a sublinear number of qubits. The time complexity of their new algorithm is asymptotically worse than Shor's algorithm, but the qubit requirements are asymptotically better, so it may be possible to physically implement the new algorithm sooner than Shor's algorithm.

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At its core, the detailed understanding and prediction of complex chemical reaction mechanisms, requires highly accurate electronic structure methods. For molecules with many energetically close-lying orbitals, much less than a hundred strongly correlated electrons are already out of reach for classical calculation methods that could achieve the required accuracy. In this paper, Reiher et al. using as an example the open problem of biological nitrogen fixation in nitrogenase, to show how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. They demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources (in this case as little as 111 qubits and 1.0x10^14 T gates)

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In this article, Matthias Möller and Cornelis Vuik of the Institute of Applied Mathematics at Delft University of Technology describe their vision of future developments in scientific computing that would be enabled by the advent of software-programmable quantum computers. In their analysis they assume that quantum computers will form part of a hybrid accelerated computing platform like GPUs and co-processor cards do today. In particular, they address the potential of quantum algorithms to bring major breakthroughs in applied mathematics and its applications. Finally, the authors give several examples that demonstrate the possible impact of quantum-accelerated scientific computing on society.

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