Recent progress on building quantum computers [1] envisages wide applications of quantum algorithms in the near future. With the advantage of quantum computer, one can speed up not only fundamental algorithms, e.g., unstructured search [6] and factoring [11], but recent machine learning algorithms [3] as well. In this paper, we study the quantum speedup on a canonical task of reinforcement learning-best arm identification in multi-armed bandits.
Recent progress on building quantum computers [1] envisages wide applications of quantum algorithms in the near future. With the advantage of quantum computer, one can speed up not only fundamental algorithms, e.g., unstructured search [6] and factoring [11], but recent machine learning algorithms [3] as well. In this paper, we study the quantum speedup on a canonical task of reinforcement learning-best arm identification in multi-armed bandits.
Identifying the best arm of a multi-armed bandit is a central problem in bandit optimization. We study a quantum computational version of this problem with coherent oracle access to states encoding the reward probabilities of each arm as quantum amplitudes. Specifically, we provide an algorithm to find the best arm with fixed confidence based on variable-time amplitude amplification and estimation. This algorithm gives a quadratic speedup compared to the best possible classical result in terms of query complexity. We also prove a matching quantum lower bound (up to poly-logarithmic factors).
We investigate the top-marm identification problem in a quantum multi-armed bandit (MAB) setting. GivenKarms whose rewards follow Bernoulli distributions with unknown means, the objective is to return themarms with the largest means with confidence at least1−δ. Many practical tasks-e.g., selecting the bestmrouting paths in a quantum network or the bestmquantum circuits for a given computation-fit naturally into this framework. We introduce Q-GapE, an elimination-based algorithm that queries each arm through a weak quantum oracle.Q- GapE attains the query complexity guaranteeO~(∑k=1K(1/Δk(m))log(1/δ)), whereΔk(m)denotes the gap between armk's mean and them-th largest mean. Compared with the best classical-oracle bound, this result offers a quadratic quantum speed-up. Extensive simulations confirm thatQ−GapEconsistently outperforms leading classical MAB algorithms in both query complexity and running time. These findings highlight the potential of quantum bandit algorithms to deliver substantial efficiency gains over their classical counterparts.
The convergence of quantum computing and robotics represents a paradigm shift in autonomous systems design, promising to overcome fundamental computational limitations that have constrained classical robotic capabilities. This comprehensive review surveys the rapidly evolving field of quantum machine learning (QML) for robotics, systematically analyzing 107 peer-reviewed contributions spanning quantum algorithms, machine learning techniques, and their robotic applications. We provide a detailed historical perspective on the field's development, from the early theoretical foundations established by Grover's search algorithm and quantum reinforcement learning proposals to current experimental implementations on noisy intermediate-scale quantum (NISQ) devices. The review systematically examines five major application domains: (1) quantum reinforcement learning for navigation and control, (2) quantum search and path planning algorithms, (3) quantum-enhanced localization and mapping, (4) quantum optimization for inverse kinematics and task allocation, and (5) multi-robot coordination and swarm intelligence. For each domain, we present detailed algorithmic formulations, computational complexity analyses, and critical assessments of experimental results. Our analysis reveals that while provable quantum advantage in robotics remains largely prospective, recent demonstrations show promising results: quantum deep reinforcement learning achieving 40\% parameter reduction in navigation tasks, Grover-based kinematic optimization demonstrating up to 93x speedups, and quantum annealing providing practical solutions for multi-robot routing. We identify key technical challenges, including barren plateaus in variational circuits, noise-induced performance degradation, and the quantum-classical integration bottleneck. Finally, we outline a strategic roadmap for quantum robotics research, distinguishing near-term opportunities in hybrid algorithms from long-term goals requiring fault-tolerant quantum computation. This paper serves as both an authoritative technical reference and a comprehensive guide for researchers working at the intersection of quantum computing and autonomous systems.
We study quantum multi-armed bandits (QMAB) and quantum linear bandits (QLB), where the learner queries each arm or action through a quantum reward oracle or its inverse. Prior work gives algorithms over horizon T with regret O(KlogT) for QMAB with K arms and O(d2polylogT) for d-dimensional QLB. This leaves open the optimal dependence on K and T and whether the dependence on d can be further improved. In this work, we prove the first tight minimax regret bound of Θ(Klog(1+T/K)) for QMAB and the first lower bound of Ω(dlog(1+T/d)) for finite-action QLB, ruling out regret independent of T. Our lower bounds rely on a high-confidence single-arm quantum testing lower bound for distinguishing a fixed reward mean from an interval of alternatives. A bandit-to-testing reduction then lifts it to the QMAB lower bound, while a linear embedding gives the finite-action QLB lower bound. The matching QMAB upper bound is obtained using a tail bound for the Quantum Monte Carlo (QMC) estimator. For finite-action QLB, we propose a phased elimination algorithm that combines a low-bias low-variance quantum mean estimator with a small-support G-optimal design through a query allocation matched to the design weights. When the action set has size poly(d), its regret is nearly linear in d and matches our lower bound up to polylogarithmic factors.
The convergence of quantum computing and robotics represents a paradigm shift in autonomous systems design, promising to overcome fundamental computational limitations that have constrained classical robotic capabilities. This comprehensive review surveys the rapidly evolving field of quantum machine learning (QML) for robotics, systematically analyzing 107 peer-reviewed contributions spanning quantum algorithms, machine learning techniques, and their robotic applications. We provide a detailed historical perspective on the field's development, from the early theoretical foundations established by Grover's search algorithm and quantum reinforcement learning proposals to current experimental implementations on noisy intermediate-scale quantum (NISQ) devices. The review systematically examines five major application domains: (1) quantum reinforcement learning for navigation and control, (2) quantum search and path planning algorithms, (3) quantum-enhanced localization and mapping, (4) quantum optimization for inverse kinematics and task allocation, and (5) multi-robot coordination and swarm intelligence. For each domain, we present detailed algorithmic formulations, computational complexity analyses, and critical assessments of experimental results. Our analysis reveals that while provable quantum advantage in robotics remains largely prospective, recent demonstrations show promising results: quantum deep reinforcement learning achieving 40\% parameter reduction in navigation tasks, Grover-based kinematic optimization demonstrating up to 93x speedups, and quantum annealing providing practical solutions for multi-robot routing. We identify key technical challenges including barren plateaus in variational circuits, noise-induced performance degradation, and the quantum-classical integration bottleneck. Finally, we outline a strategic roadmap for quantum robotics research, distinguishing near-term opportunities in hybrid algorithms from long-term goals requiring fault-tolerant quantum computation. This paper serves as both an authoritative technical reference and a comprehensive guide for researchers working at the intersection of quantum computing and autonomous systems.