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The first quantum computers are expected to perform well at quadratic optimisation problems. In this paper a quadratic problem in finance is taken, the Portfolio Optimisation problem. Here, a set of assets is chosen for investment, such that the total risk is minimised, a minimum return is realised and a budget constraint is met. This problem is solved for several instances in two main indices, the Nikkei225 and the S&P500 index, using the state-of-the-art implementation of D-Wave's quantum annealer and its hybrid solvers. The results are benchmarked against conventional, stateof-the-art, commercially available tooling. Results show that for problems of the size of the used instances, the D-Wave solution, in its current, still limited size, comes already close to the performance of commercial solvers.

This study investigates how qubits of modern quantum annealers (QA) such as D-Wave can be applied for generating truly random numbers. We show how a QA can be initialised and how the annealing schedule can be set so that after the annealing, thousands of truly random binary numbers are measured in parallel. Those can then be converted to uniformly distributed natural or real numbers in desired ranges, either biased or unbiased. We discuss the observed qubits' properties and their influence on the random number generation and consider various physical factors that influence the performance of our generator, i.e., digital-to-analogue quantisation errors, flux errors, temperature errors and spin bath polarisation. The numbers generated by the proposed algorithm successfully pass various tests on randomness from the NIST test suite. Our source code and large sets of truly random numbers are publicly available on our project web page https://4dqv.mpi-inf.mpg.de/QRNG/.

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Jointly matching multiple, non-rigidly deformed 3D shapes is a challenging, N P-hard problem. A perfect matching is necessarily cycle-consistent: Following the pairwise point correspondences along several shapes must end up at the starting vertex of the original shape. Unfortunately, existing quantum shape-matching methods do not support multiple shapes and even less cycle consistency. This paper addresses the open challenges and introduces the first quantum-hybrid approach for 3D shape multimatching; in addition, it is also cycle-consistent. Its iterative formulation is admissible to modern adiabatic quantum hardware and scales linearly with the total number of input shapes. Both these characteristics are achieved by reducing the N -shape case to a sequence of three-shape matchings, the derivation of which is our main technical contribution. Thanks to quantum annealing, high-quality solutions with low energy are retrieved for the intermediate N Phard objectives. On benchmark datasets, the proposed approach significantly outperforms extensions to multi-shape matching of a previous quantum-hybrid two-shape matching method and is on-par with classical multi-matching methods. Our source code is available at 4dqv.mpiinf.mpg.de/CCuantuMM/.