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Quantum-computing related developments

On this page we post about interesting quantum-computing related research and news which we are following.

Quantum recommendation systems

Quantum recommendation systems

A recommendation engine uses the past purchases or ratings to construct a (partial) preference matrix, which is used to provide personalized recommendations to individual users. In this paper, Kerenidis et al. present a quantum recommendation system which updates the partial preference matrix each time data comes in and can, based on such matrix, provides a recommendation in time polylog to the matrix-dimension, exponentially faster than classical recommendation systems.

Solving a discrete multi-period portfolio optimisation problem using a quantum annealer

Solving a discrete multi-period portfolio optimisation problem using a quantum annealer

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. 

Quantum algorithms: an overview (2015)

Quantum algorithms: an overview (2015)

In this paper, Ashley Montanaro, gives a broad overview of quantum algorithms, focusing on algorithms with clear applications and rigorous performance bounds, and including recent progress in the field. The paper does not a detailed discussion of how the quantum algorithms mentioned work, but aims to provide structure to the different classes of quantum-algorithms, which were known in November 2015

Ising formulations of many NP problems

Ising formulations of many NP problems

In this paper, Andrew Lucas provides Ising formulations for many NP-complete and NP-hard problems, including all of Karp's 21 NP-complete problems. In each case, the required number of spins is at most cubic in the size of the problem. This work may be useful in designing adiabatic quantum optimization algorithms.

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