Quantum feedback control requires acting on noisy continuous measurement records without direct access to the underlying quantum state. We propose Kraus-Parameterized Belief Reinforcement Learning, a pipeline in which a recurrent encoder, constrained to the Stiefel manifold, produces density-matrix estimates that are guaranteed positive-semidefinite and trace-normalized by construction, embedding quantum state geometry directly into the learning loop. A Proximal Policy Optimization (PPO) actor then maps these physically valid belief states to continuous control actions. On a simulated continuously monitored qubit, the resulting policy achieves stable feedback control, maintaining a measurement-conditioned belief fidelity of approximately 0.77-0.80 and exhibiting substantially lower return variance than a parameter-matched LSTM-history baseline across both nominal and out-of-distribution conditions. Although gains in raw target fidelity are modest, the geometric constraint guarantees a physically valid, interpretable belief representation and yields markedly more stable control under measurement inefficiency and abrupt dynamics switches. These results indicate that physics-informed neural memory is a practical inductive bias for reliable quantum feedback control.
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Accepted at the QCE26 International Workshop on Quantum Computing & Reinforcement Learning (QCRL26), IEEE Quantum Week 2026
Quantum feedback control requires acting on noisy continuous measurement records without direct access to the underlying quantum state. We propose Kraus-Parameterized Belief Reinforcement Learning, a pipeline in which a recurrent encoder, constrained to the Stiefel manifold, produces density-matrix estimates that are guaranteed positive-semidefinite and trace-normalized by construction, embedding quantum state geometry directly into the learning loop. A Proximal Policy Optimization (PPO) actor then maps these physically valid belief states to continuous control actions. On a simulated continuously monitored qubit, the resulting policy achieves stable feedback control, maintaining a measurement-conditioned belief fidelity of approximately 0.77-0.80 and exhibiting substantially lower return variance than a parameter-matched LSTM-history baseline across both nominal and out-of-distribution conditions. Although gains in raw target fidelity are modest, the geometric constraint guarantees a physically valid, interpretable belief representation and yields markedly more stable control under measurement inefficiency and abrupt dynamics switches. These results indicate that physics-informed neural memory is a practical inductive bias for reliable quantum feedback control.
The effectiveness of measurement-based feedback control protocols is hampered by the presence of measurement noise, which affects the ability to accurately infer the underlying dynamics of a quantum system from noisy continuous measurement records to determine an accurate control strategy. To circumvent such limitations, this Letter explores a real-time stochastic state estimation approach that enables noise-free monitoring of the conditional dynamics including the full density matrix of the quantum system using noisy measurement records within a single quantum trajectory-a method we name as "conditional state tomography." This, in turn, enables the development of precise measurement-based feedback control strategies that lead to effective control of quantum systems by essentially mitigating the constraints imposed by measurement noise and has potential applications in various feedback quantum control scenarios. This approach is particularly useful for reinforcement-learning-(RL) based control, where the RL-agent can be trained with arbitrary conditional averages of observables, and/or the full density matrix as input (observation), to quickly and accurately learn control strategies.
This paper presents a novel Lyapunov-Based Quantum Reinforcement Learning (LQRL) framework that integrates quantum policy optimization with Lyapunov stability analysis for continuous-time vehicle control. The proposed approach combines the representational power of variational quantum circuits (VQCs) with a stability-aware policy gradient mechanism to ensure asymptotic convergence and safe decision-making under dynamic environments. The vehicle longitudinal control problem was formulated as a continuous-state reinforcement learning task, where the quantum policy network generates control actions subject to Lyapunov stability constraints. Simulation experiments were conducted in a closed-loop adaptive cruise control scenario using a quantum-inspired policy trained under stability feedback. The results demonstrate that the LQRL framework successfully embeds Lyapunov stability verification into quantum policy learning, enabling interpretable and stability-aware control performance. Although transient overshoot and Lyapunov divergence were observed under aggressive acceleration, the system maintained bounded state evolution, validating the feasibility of integrating safety guarantees within quantum reinforcement learning architectures. The proposed framework provides a foundational step toward provably safe quantum control in autonomous systems and hybrid quantum-classical optimization domains.
Quantum network routing requires online decisions under probabilistic entanglement generation, finite quantum memories, decoherence, imperfect operations, and classical feedback, while the controller has incomplete knowledge of the physical state. This paper develops a robust belief-state routing framework based on a quantum partially observable Markov decision process (q-POMDP) and a feasibility-masked graph neural network (GNN). The model uses atomic micro-epochs in which each selected operation completes before the next decision boundary. This enables explicit accounting of memory reservations, pair-instance inventories, purification consumption, swapping outcomes, release decisions, queue service, and completion-time delivery fidelity. The controller maintains a classical belief over hidden physical states, including latent environmental conditions, and uses this belief to evaluate feasible actions and update posterior pair states. To make planning scalable, we introduce feasibility-stratified prototypes, identifier-free signatures, and role-aware action matching, which preserve hard resource constraints while enabling value transfer across structurally similar information states. A cached q-POMDP planner is then fused with a role-aware GNN policy through an adaptive trust rule, with a safe fallback for previously unseen feasibility signatures. We provide theoretical guarantees on feasibility, value approximation, policy performance, robustness, regret, and learning variance. Simulations over finite-memory quantum-network topologies show that the proposed hybrid controller improves high-fidelity goodput, reduces below-threshold deliveries, and maintains lower online decision cost than planner-only control, while outperforming heuristic, purification-aware, and learning-based baselines.
Reinforcement learning for robot navigation requires representations that capture spatial geometry, long-horizon dependencies, and goal-conditioned structure. Classical neural networks provide flexible function approximators, but their representations are ultimately limited by classical feature transformations. We investigate quantum representation learning as a mechanism for encoding state–goal pairs in goal-conditioned reinforcement learning. We formulate navigation as a finite-horizon Markov decision process and introduce a quantum variational feature map that embeds continuous states into a high-dimensional Hilbert space. This representation is optimized jointly with a Q-learning objective, yielding a hybrid quantum–classical value function. Classical networks serve only as baselines to validate the environment and evaluation protocol. After correcting subtle issues in reward shaping and success detection, we observe that quantum representations produce coherent value structures, stable optimization dynamics, and competitive success rates relative to classical baselines. Rather than aiming to improve navigation performance, our objective is to provide a controlled and reproducible framework for analyzing how quantum feature geometry shapes value estimation and goal-conditioned behavior in offline RL. Our analysis highlights how quantum feature geometry influences value estimation and navigation behavior, establishing a reproducible foundation for studying quantum-enhanced representations in reinforcement learning for robotics.
This paper presents an Adaptive Quantum Feedback Control Algorithm (AQFCA) designed to achieve high-precision control of quantum systems. The core of the algorithm lies in utilizing quantum measurements to generate feedback signals, which are then employed to dynamically adjust the parameters of the quantum system. This approach leverages the principles of reinforcement learning to optimize the control strategy, addressing the inherent precision challenges associated with traditional quantum feedback control. The AQFCA offers a novel solution for enhancing the accuracy and reliability of quantum control, thereby providing a crucial foundation for the practical application of quantum technologies. The algorithm's implementation involves a closed-loop system where a measurement of the quantum state is continuously fed back, and the control parameters are adjusted based on this feedback. The use of reinforcement learning allows the system to adapt to the specific characteristics of the quantum system, further improving control accuracy.
Attention-based neural networks such as transformers have revolutionized various fields such as natural language processing, genomics, and vision. Here, we demonstrate the use of transformers for quantum feedback control through both a supervised and a reinforcement learning approach. In particular, due to the transformer's ability to capture long-range temporal correlations and training efficiency, we show that it can surpass some of the limitations of previous control approaches, e.g., those based on recurrent neural networks trained using a similar approach or policy-based reinforcement learning. We numerically show, for the example of state stabilization of a two-level system, that our bespoke transformer architecture can achieve near-unit fidelity to a target state in a short time even in the presence of inefficient measurement and Hamiltonian perturbations that were not included in the training set as well as the control of non-Markovian systems. We also demonstrate that our transformer can perform energy minimization of nonintegrable many-body quantum systems when trained for reinforcement learning tasks. Our approach can be used for quantum error correction, fast control of quantum states in the presence of colored noise, as well as real-time tuning, and characterization of quantum devices.