Who Earns the Safety? Intervention-Aware Quantum Predictive Control with Safety Attribution

The evolution of intelligent control systems has seen significant progress with the integration of machine learning and model predictive control (MPC), especially in building energy management. These systems aim to optimize comfort and energy efficiency simultaneously. However, safety remains a critical concern, particularly in systems with complex constraints and uncertainties. Traditional safety mechanisms rely heavily on external safety filters, such as control barrier functions (CBFs) and predictive safety filters, which modify proposed actions to ensure constraint satisfaction. While effective at runtime, these filters often mask the true safety capability of the underlying policy, making it difficult to assess whether the policy has learned safe behaviors.

Recent research in safe reinforcement learning (Safe RL) and shielding techniques has sought to incorporate safety into the learning process, but these methods typically focus on post-hoc action correction or constraint enforcement without explicitly promoting intrinsic safety. Moreover, most approaches are based on classical neural networks, which require large parameter counts and may lack interpretability. Quantum computing offers a promising alternative, with variational quantum circuits (VQCs) providing parameter-efficient models with Fourier structures that can potentially enhance expressivity in constrained control tasks.

Despite these advances, the application of quantum policies to safety-critical control remains underexplored. Existing work has demonstrated quantum advantages in small-scale tasks but has not addressed safety attribution or robustness in real-world scenarios. This gap motivates the development of a framework that not only trains quantum policies under safety constraints but also evaluates whether safety is genuinely learned or merely masked by external layers. The present study addresses this gap by proposing an intervention-aware training and evaluation protocol tailored for quantum control, with a focus on building energy management as a testbed.

Current safety control strategies often rely on external safety filters that correct unsafe actions during operation, which obscures whether the underlying policy has truly internalized safety principles. This leads to a fundamental challenge: how to measure and promote the intrinsic safety of learned policies. In particular, quantum policies, despite their parameter efficiency and Fourier structure, are susceptible to reliance on external safety layers, especially in constrained environments like building control.

The core problem is twofold: first, how to train policies that inherently respect safety constraints without over-reliance on external correction mechanisms; second, how to evaluate and attribute safety performance directly to the policy, rather than the safety layers. Existing metrics often conflate the two, making it difficult to assess the true safety learning capability of the policy. Moreover, the use of learned energy models as safety indicators introduces vulnerabilities, as these models can be exploited out-of-distribution, leading to physically implausible behaviors.

Addressing this problem requires a training framework that penalizes reliance on safety corrections, coupled with an evaluation protocol that decomposes trajectory corrections into policy-intrinsic and external components. This enables a clear attribution of safety performance, fostering the development of truly autonomous, safe policies suitable for real-world deployment.

The key innovations of this work include:

• �� The introduction of an intervention-aware training framework that employs primal-dual optimization to enforce a bounded reliance on safety layers, encouraging policies to learn safety intrinsically.
• �� The development of a safety attribution protocol that decomposes trajectory corrections into CBF-driven safety adjustments and runtime safety guards, providing a transparent measure of how much safety is earned by the policy itself.
• �� The application of a compact variational quantum circuit (VQC) with Fourier structure, leveraging data re-uploading to enhance expressivity while maintaining parameter efficiency, suitable for resource-constrained environments.
• �� The integration of a differentiable CBF layer via quadratic programming, enabling end-to-end training and real-time action projection.
• �� Extensive validation on high-fidelity building control simulations (BOPTEST), demonstrating significant reductions in violations and safety layer reliance, with the quantum policy outperforming classical counterparts of similar size in safety and comfort.
• �� The stress testing without runtime guards reveals the importance of combined safety mechanisms, emphasizing that learned energy models require distribution-aware runtime support to prevent exploitation.

These innovations collectively advance the state-of-the-art in safe, resource-efficient control, bridging quantum algorithms, differentiable optimization, and safety evaluation into a unified framework.

• �� Policy Representation: The control policy is modeled as a data re-uploading variational quantum circuit (VQC) with nq qubits, where classical encoder maps environment states to quantum angles, and multiple layers apply RX, RY, RZ rotations combined with CZ entangling gates. The output is a Pauli-Z expectation vector fed into a classical affine head, producing control actions.
• �� Safety Constraints: The system employs a differentiable control barrier function (CBF) layer, implemented via a quadratic programming (QP) problem, which projects proposed actions onto a safe set defined by signed temperature margins. Slack variables and penalty terms ensure soft constraint satisfaction.
• �� Intervention-aware Training: The training objective combines multiple components—behavior cloning of logged safe actions, a differentiable comfort loss based on system dynamics, a learned energy head predicting system energy, and a penalty on the reliance on safety layers (intervention). The primal-dual method optimizes the task loss while penalizing excessive reliance, with the intervention budget B controlling the trade-off.
• �� Optimization Process: The parameters of the quantum circuit and classical encoder are updated via Adam optimizer, with the dual variable λ updated through projected dual ascent to enforce reliance constraints.
• �� Safety Attribution: During evaluation, the trajectory corrections are decomposed into CBF correction (u_P - ˜u) and runtime guard correction (u - u_P). Violations before and after correction (Vpre, Vpost) are recorded, and stress tests are performed by disabling runtime guards to assess intrinsic policy safety.
• �� Experimental Setup: The training and evaluation are conducted on BOPTEST v0.9.0, focusing on single-zone hydronic systems. Multiple seeds and episodes ensure statistical significance. Comparisons include classical neural networks and quantum policies, with and without intervention-aware training.

The experimental setup involves simulating building control scenarios using BOPTEST v0.9.0, with 5 independent seeds and 60 episodes per method, totaling 420 guarded and 300 guard-off episodes. The control tasks involve regulating thermal states in hydronic systems with 15-minute steps. Baselines include rule-based controllers, classical MLPs of varying sizes, and the proposed quantum policies. Metrics include raw violation (Vpre), post-correction violation (Vpost), total correction (ctot), reliance on safety layers, energy consumption, and user comfort. The training hyperparameters involve a parameter budget of approximately 400, with dual ascent step size ηλ and penalty weights for behavior cloning, comfort, and energy head losses. Statistical significance is assessed via paired permutation tests with bootstrap confidence intervals, focusing on the impact of intervention-aware training and safety attribution. Additional stress tests disable runtime guards to evaluate policy intrinsic safety, revealing the importance of combined safety mechanisms.

The intervention-aware quantum policies achieve a significant reduction in raw violations, decreasing Vpre by approximately 0.0055 (p < 10^-4), and lower total safety reliance by about 0.068 (p < 10^-4). Energy consumption remains statistically unchanged, confirming no energy regression. Compared to classical models with similar parameter counts (~400), quantum policies outperform in safety and comfort metrics, with violations and reliance metrics favoring the quantum approach. Stress tests without runtime guards show that the policy’s safety is intrinsic, with violations remaining low, whereas unguarded learned energy heads can be exploited, leading to extreme energy states (~2.6 million kWh). These results demonstrate that intervention-aware training effectively promotes intrinsic safety in quantum policies, validated through rigorous attribution and stress testing.

This framework is directly applicable to safety-critical control in smart buildings, autonomous vehicles, and industrial automation, where safety and energy efficiency are paramount. The approach enables autonomous systems to learn safety structures internally, reducing reliance on external protective layers. It can be extended to multi-agent systems for coordinated safety, and integrated with real hardware for deployment in resource-constrained environments. The methodology also provides a foundation for developing interpretable, certifiable control policies that can be validated and trusted in real-world applications, fostering safer autonomous systems across industries.

The current validation relies heavily on high-fidelity simulation environments; real-world quantum hardware introduces noise, decoherence, and errors that may impact performance and robustness. The training process requires substantial computational resources, limiting scalability and real-time application. The learned energy head, while differentiable, is vulnerable to exploitation out-of-distribution, necessitating robust runtime guards. Extending the approach to multi-agent systems and more complex, uncertain environments remains an open challenge. Additionally, the assumptions of accurate differentiable models of system dynamics may not hold in practical scenarios, requiring further robustness and adaptation mechanisms.