Displaying items by tag: Quantum annealing

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At Qu&Co we always restrained ourselves from reacting to exaggerated claims about the short-term potential of quantum-computing. Rather we focused on our scientifically rigorous work to advance the field of quantum as we strongly believe in its long-term potential. However, we draw the line at quantum being pushed as a short-term solution for researchers working on COVID, like this WSJ article in which a quantum hardware manufacturer offers free hardware access to researchers studying COVID, stating ‘we have a fairly unique system that could add value’. Although this offer could be a misplaced April-fools joke, we want to stress that, although quantum has strong long-term potential, there is zero chance it will provide any short-term value for COVID research. Therefore, no serious researchers working on the current pandemic should be distracted by this offer. If you are determined to use novel methods to solve today’s combinatorial optimisation problems, perhaps try simulated annealing on a purpose-built classical processor. And of course, if your time horizon is >2 years and you want to work on collaborative quantum-algorithm R&D, without distracting scarce COVID R&D staff, we are here to help. Stay safe and focused!

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Many financial services players are experimenting with quantum-computing so that they can be the first to start exploiting its benefits in speed-up and tractability. Algorithms have been developed for a wide range of finance related topics e.g. Monte Carlo simulation, portfolio optimization, anomaly (fraud) detection, market forecasting and reduction of slippage. In this paper Orus et al. provide a nice overview of most of these applications. Although the paper puts much emphasis on what has been done with quantum-annealers, applying the Quantum Approximate Optimization Algorithm (QAOA) lets us map all of them to universal-gate devices, which ensures that these applications stay relevant even when annealers become obsolete.

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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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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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Quantum annealers such as the D-Wave 2X allow solving NP-hard optimization problems that can be expressed as quadratic unconstrained binary (QUBO) programs. However, the relatively small number of available qubits poses a severe limitation to the range of problems that can be solved. In this paper, Hahn et al. explore the suitability of preprocessing methods for reducing the sizes of the input programs and thereby the number of qubits required for their solution on quantum computers. Specifically preprocessing reductions are discussed for max. clique and max. cut problems.

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In this paper, Djidjev et al. evaluate the performance of the D-Wave 2X quantum annealer on two NP-hard graph problems: clique finding and graph partitioning. Overall, they conclude that general problems which allow to be mapped onto the D-Wave architecture are typically still too small to show a quantum speedup (although the D-wave does provide similar quality solutions as the classical solvers). For simple simulated annealing algorithms, D-Wave is considerably faster and selected instances especially designed to fit D-Wave's particular chimera architecture can be solved orders of magnitude faster than with classical techniques.

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In the 2016 US presidential elections, many of the professional polling groups had overestimated the probability of a Clinton victory. Multiple post-election analyses concluded that a leading cause of error in their forecast models was a lack of correlation between predictions for individual states. Uncorrelated models, though much simpler to build and train, cannot capture the more complex behavior of a fully-connected system. Accurate, reliable sampling from fully-connected graphs with arbitrary correlations quickly becomes classically intractable as the graph size grows. In this paper, Henderson et al. show an initial implementation of quantum-trained Boltzmann machine used for sampling from correlated systems. They show that such a quantum-trained machine is able to generate election forecasts with similar structural properties and outcomes as a best in class modeling group.

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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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Thus far, quantum chemistry quantum algorithms have been experimentally demonstrated only on gate-based quantum computers. Efforts have been made to also map the chemistry problem Fermionic Hamiltonian to an Ising Hamiltonian in order to solve it on a quantum annealer.  However, the number of qubits required still scales exponentially with the problem size (the number of orbitals considered in the electronic structure problem). As an alternative, this paper presents a different approach exploiting the efficiency at which quantum annealers can solve discrete optimization problems, and mapping a qubit coupled cluster method to this form. They simulate their method on an ideal Ising machine and on a D-Wave 2000Q system, and find promising success rates for smaller molecules. However, further investigation would be necessary to investigate the usability for larger or more complex systems, as the scaling of their folding technique with the number of local minima is unknown. In addition, it is unclear from the experimental data whether the limitations of the D-Wave system  as compared to a perfect Ising machine could hinder expected performance gains for more complex systems.

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In this paper, Gardas et al. propose the use of the quantum fluctuation theorem to benchmark the performance of quantum annealers in respect to computational errors caused by thermal noise. They experimentally test their proposal on 2 quantum annealing devices to illustrate the sensitivity of the fluctuation theorem to the smallest aberrations from ideal annealing.

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