MADQRL: Distributed Quantum Reinforcement Learning Framework for Multi-Agent Environments

Quantum reinforcement learning (QRL) is a promising approach to learn effective decision strategies across several applications with stochastic environments. Instead of directly modeling the random variables that govern these environments, existing QRL architectures indirectly approximate environment behavior by estimating expected outcomes, which limits their expressive power and adaptive potential. Overcoming such challenges requires a novel QRL approach that exploits the distributional nature of quantum computers to directly model environment random variables as quantum state distributions. Hence, in this paper, a novel framework dubbed quantum-native reinforcement learning (QnRL) is proposed. QnRL is a distributional RL framework that learns conditional distributions naturally in Hilbert space via superimposed and entangled quantum states. Thus, QnRL can directly model the behavior of stochastic learning environments via the natural properties of quantum systems. QnRL accomplishes this via a novel, proposed quantum amplitude kickback (QuAK) algorithm that enables comparing the $n$-th power of the $m$-th moment of multiple superimposed distributions. It is theoretically proven that a conditional action policy distribution is distilled from the moments of a quantum generative model entirely within Hilbert space via QuAK, and optimized via QnRL. This complex distribution composition is also shown to provide extra dimensions for expressing environment correlations that are unknown to purely classical and classically-sampled quantum distributional models. Experimental results across diverse environments show that QnRL achieves up to $82.9\%$ higher evaluation scores, with up to $94.3\%$ fewer parameters on average, more accurately estimates the expected return for unseen observations, and better adapts to varying stochastic conditions compared to the baseline.

We present an empirical evaluation of quantum entanglement in agent coordination within quantum multi agent reinforcement learning (QMARL). While QMARL has attracted growing interest recently, most prior work evaluates quantum policies without provable baselines, making it impossible to rigorously distinguish quantum advantage from algorithmic coincidence. We address this directly by evaluating a decentralized QMARL framework with variational quantum circuit (VQC) actors with shared entangled states. In the CHSH game, which has a mathematically proven classical performance ceiling of 0.75 win rate, we show that entangled QMARL agents approach the Tsirelson limit of 0.854, providing clear evidence of their quantum advantage. We show that unentangled quantum circuits match the classical baseline, confirming that entanglement and not the quantum circuit itself is the active coordination mechanism. We also explore the effect of specific entanglement structures, as some Bell states enable coordination gains while others actively harm performance. On cooperative navigation (CoopNav), QMARL without entanglement achieves $\sim2\times$ improvement in success rate over classical MAA2C ($\sim$0.85 versus $\sim$0.40), with the hybrid configuration, quantum actor paired with a classical centralised critic, outperforming both fully classical and fully quantum solutions. We present our experimental analysis and discuss future work.

Reinforcement learning (RL) provides a principled framework for decision-making in partially observable environments, which can be modeled as Markov decision processes and compactly represented through dynamic decision Bayesian networks. Recent advances demonstrate that inference on sparse Bayesian networks can be accelerated using quantum rejection sampling combined with amplitude amplification, leading to a computational speedup in estimating acceptance probabilities. Building on this result, we introduce Quantum Bayesian Reinforcement Learning (QBRL), a hybrid quantum-classical look-ahead algorithm for model-based RL in partially observable environments. We present a rigorous, oracle-free time complexity analysis under fault-tolerant assumptions for the quantum device. Unlike standard treatments that assume a black-box oracle, we explicitly specify the inference process, allowing our bounds to more accurately reflect the true computational cost. We show that, for environments whose dynamics form a sparse Bayesian network, horizon-based near-optimal planning can be achieved sub-quadratically faster through quantum-enhanced belief updates. On the other hand, we show that there is no quantum speed-up for environments that are either fully observable, or characterized by Bayesian networks whose maximum in-degree is not small. Furthermore, we present numerical experiments benchmarking QBRL against its classical counterpart on simple yet illustrative decision-making tasks. Our results offer a detailed analysis of how the quantum computational advantage translates into decision-making performance, highlighting that the magnitude of the advantage can vary significantly across different deployment settings.