Adiabatic quantum computing (AQC) is a promising quantum computing approach for discrete and often NP-hard optimization problems. Current AQCs allow to implement problems of research interest, which has sparked the development of quantum representations for many machine learning and computer vision tasks. Despite requiring multiple measurements from the noisy AQC, current approaches only utilize the best measurement, discarding information contained in the remaining ones. In this work, we explore the potential of using this information for probabilistic balanced k-means clustering. Instead of discarding non-optimal solutions, we propose to use them to compute calibrated posterior probabilities with little additional compute cost. This allows us to identify ambiguous solutions and data points, which we demonstrate on a D-Wave AQC on synthetic and real data.

The training of neural networks (NNs) is a computationally intensive task requiring significant time and resources. This paper presents a novel approach to NN training using Adiabatic Quantum Computing (AQC), a paradigm that leverages the principles of adiabatic evolution to solve optimisation problems. We propose a universal AQC method that can be implemented on gate quantum computers, allowing for a broad range of Hamiltonians and thus enabling the training of expressive neural networks. We apply this approach to various neural networks with continuous, discrete, and binary weights. Our results indicate that AQC can very efficiently find the global minimum of the loss function, offering a promising alternative to classical training methods.

Multi-Object Tracking (MOT) is most often approached in the tracking-by-detection paradigm, where object detections are associated through time. The association step naturally leads to discrete optimization problems. As these optimization problems are often NP-hard, they can only be solved exactly for small instances on current hardware. Adiabatic quantum computing (AQC) offers a solution for this, as it has the potential to provide a considerable speedup on a range of NP-hard optimization problems in the near future. However, current MOT formulations are unsuitable for quantum computing due to their scaling properties. In this work, we therefore propose the first MOT formulation designed to be solved with AQC. We employ an Ising model that represents the quantum mechanical system implemented on the AQC. We show that our approach is competitive compared with state-of-the-art optimization-based approaches, even when using of-the-shelf integer programming solvers. Finally, we demonstrate that our MOT problem is already solvable on the current generation of real quantum computers for small examples, and analyze the properties of the measured solutions.

Prime factorization is a difficult problem with classical computing, whose exponential hardness is the foundation of Rivest-Shamir-Adleman (RSA) cryptography. With programmable quantum devices, adiabatic quantum computing has been proposed as a plausible approach to solve prime factorization, having promising advantage over classical computing. Here, we find there are certain hard instances that are consistently intractable for both classical simulated annealing and un-configured adiabatic quantum computing (AQC). Aiming at an automated architecture for optimal configuration of quantum adiabatic factorization, we apply a deep reinforcement learning (RL) method to configure the AQC algorithm. By setting the success probability of the worst-case problem instances as the reward to RL, we show the AQC performance on the hard instances is dramatically improved by RL configuration. The success probability also becomes more evenly distributed over different problem instances, meaning the configured AQC is more stable as compared to the un-configured case. Through a technique of transfer learning, we find prominent evidence that the framework of AQC configuration is scalable -- the configured AQC as trained on five qubits remains working efficiently on nine qubits with a minimal amount of additional training cost.

Quantum computing promises fast solutions to a wide range of optimization problems and thus holds considerable potential for machine learning [1]-[3]. However, while the quantum machine learning literature so far mainly focused on the quantum gate paradigm, noticeable technological progress leading to commercial devices is happening in adiabatic quantum computing [4], [5]. Current adiabatic quantum computers are geared towards solving quadratic unconstrained binary optimization problems or Ising models. A simple strategy for setting up established learning algorithms to run on such devices is therefore to attempt to (re-)formulate or approximate their minimization or maximization objectives in terms of Ising models. In this paper, we apply this strategy to a simple unsupervised learning problem, namely binary clustering.