Quantum adiabatic machine learning by zooming into a region of the energy surface

Recent work has shown that quantum annealing for machine learning, referred to as QAML, can perform comparably to state-of-the-art machine learning methods with a specific application to Higgs boson classification. We propose QAML-Z, an algorithm that iteratively zooms in on a region of the energy surface by mapping the problem to a continuous space and sequentially applying quantum annealing to an augmented set of weak classifiers. Results on a programmable quantum annealer show that QAML-Z matches classical deep neural network performance at small training set sizes and reduces the performance margin between QAML and classical deep neural networks by almost 50% at large training set sizes, as measured by area under the receiver operating characteristic curve. The significant improvement of quantum annealing algorithms for machine learning and the use of a discrete quantum algorithm on a continuous optimization problem both opens a class of problems that can be solved by quantum annealers and suggests the approach in performance of near-term quantum machine learning towards classical benchmarks

Efficiency of quantum versus classical annealing in non-convex learning problems

Quantum annealers aim at solving non-convex optimization problems by exploiting cooperative tunneling effects to escape local minima. The underlying idea consists in designing a classical energy function whose ground states are the sought optimal solutions of the original optimization problem and add a controllable quantum transverse field to generate tunneling processes. A key challenge is to identify classes of non-convex optimization problems for which quantum annealing remains efficient while thermal annealing fails. We show that this happens for a wide class of problems which are central to machine learning. Their energy landscapes is dominated by local minima that cause exponential slow down of classical thermal annealers while simulated quantum annealing converges efficiently to rare dense regions of optimal solutions.Comment: 31 pages, 10 figure

Quantum-enhanced reinforcement learning for finite-episode games with discrete state spaces

Quantum annealing algorithms belong to the class of metaheuristic tools, applicable for solving binary optimization problems. Hardware implementations of quantum annealing, such as the quantum annealing machines produced by D-Wave Systems, have been subject to multiple analyses in research, with the aim of characterizing the technology's usefulness for optimization and sampling tasks. Here, we present a way to partially embed both Monte Carlo policy iteration for finding an optimal policy on random observations, as well as how to embed (n) sub-optimal state-value functions for approximating an improved state-value function given a policy for finite horizon games with discrete state spaces on a D-Wave 2000Q quantum processing unit (QPU). We explain how both problems can be expressed as a quadratic unconstrained binary optimization (QUBO) problem, and show that quantum-enhanced Monte Carlo policy evaluation allows for finding equivalent or better state-value functions for a given policy with the same number episodes compared to a purely classical Monte Carlo algorithm. Additionally, we describe a quantum-classical policy learning algorithm. Our first and foremost aim is to explain how to represent and solve parts of these problems with the help of the QPU, and not to prove supremacy over every existing classical policy evaluation algorithm.Comment: 17 pages, 7 figure

Quantum adiabatic machine learning by zooming into a region of the energy surface

Recent work has shown that quantum annealing for machine learning, referred to as QAML, can perform comparably to state-of-the-art machine learning methods with a specific application to Higgs boson classification. We propose QAML-Z, an algorithm that iteratively zooms in on a region of the energy surface by mapping the problem to a continuous space and sequentially applying quantum annealing to an augmented set of weak classifiers. Results on a programmable quantum annealer show that QAML-Z matches classical deep neural network performance at small training set sizes and reduces the performance margin between QAML and classical deep neural networks by almost 50% at large training set sizes, as measured by area under the receiver operating characteristic curve. The significant improvement of quantum annealing algorithms for machine learning and the use of a discrete quantum algorithm on a continuous optimization problem both opens a class of problems that can be solved by quantum annealers and suggests the approach in performance of near-term quantum machine learning towards classical benchmarks

Nonnegative/binary matrix factorization with a D-Wave quantum annealer

D-Wave quantum annealers represent a novel computational architecture and have attracted significant interest, but have been used for few real-world computations. Machine learning has been identified as an area where quantum annealing may be useful. Here, we show that the D-Wave 2X can be effectively used as part of an unsupervised machine learning method. This method can be used to analyze large datasets. The D-Wave only limits the number of features that can be extracted from the dataset. We apply this method to learn the features from a set of facial images