Quantum agents in the Gym: a variational quantum algorithm for deep Q-learning

Andrea Skolik1,2, Sofiene Jerbi3, and Vedran Dunjko1

1Leiden University, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
2Volkswagen Data:Lab, Ungererstraße 69, 80805 Munich, Germany
3Institute for Theoretical Physics, University of Innsbruck, Technikerstr. 21a, A-6020 Innsbruck, Austria

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Quantum machine learning (QML) has been identified as one of the key fields that could reap advantages from near-term quantum devices, next to optimization and quantum chemistry. Research in this area has focused primarily on variational quantum algorithms (VQAs), and several proposals to enhance supervised, unsupervised and reinforcement learning (RL) algorithms with VQAs have been put forward. Out of the three, RL is the least studied and it is still an open question whether VQAs can be competitive with state-of-the-art classical algorithms based on neural networks (NNs) even on simple benchmark tasks. In this work, we introduce a training method for parametrized quantum circuits (PQCs) that can be used to solve RL tasks for discrete and continuous state spaces based on the deep Q-learning algorithm. We investigate which architectural choices for quantum Q-learning agents are most important for successfully solving certain types of environments by performing ablation studies for a number of different data encoding and readout strategies. We provide insight into why the performance of a VQA-based Q-learning algorithm crucially depends on the observables of the quantum model and show how to choose suitable observables based on the learning task at hand. To compare our model against the classical DQN algorithm, we perform an extensive hyperparameter search of PQCs and NNs with varying numbers of parameters. We confirm that similar to results in classical literature, the architectural choices and hyperparameters contribute more to the agents' success in a RL setting than the number of parameters used in the model. Finally, we show when recent separation results between classical and quantum agents for policy gradient RL can be extended to inferring optimal Q-values in restricted families of environments.

Deep reinforcement learning has yielded remarkable successes over the past decade, achieving superhuman levels in many seminal "AI" benchmarks such as the game of Go, Chess, poker etc. In this work we explore how techniques from deep reinforcement learning can be transferred to the realm of variational quantum algorithms for a special type of reinforcement learning algorithm called Q-learning. In essence, we propose a quantum variant of deep reinforcement learning which substitutes the neural network with a quantum analogue – a parametrized quantum circuit. We show that with careful design choices such an architecture performs well on two classical benchmark tasks from the OpenAI Gym, perform comparisons of our model to a neural network-driven system on the same learning task, and analyse the theoretical perspectives and limitations of the model. We find that the quantum learner is competitive to its classical counterpart, and prove that in some task environments one can achieve a provable exponential separation between classical and quantum Q-learners.

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