Data-driven zone-agnostic imposition of boundary conditions in quantum transport methods

The proposed approach integrates data-driven classifiers with quantum circuit design. A supervised learning model is first trained to approximate the indicator function of the solid domain Ω. Candidate models include shallow neural networks. The trained model is then compiled into a quantum oracle circuit that maps position registers to an ancilla qubit, following the transformation , where is the learned classifier. This oracle replaces the analytically defined geometry in the ZA bounce back and specular reflection algorithms. The full QLBM circuit is constructed by combining streaming operators and the learned oracle. Emphasis is placed on maintaining reversibility and minimizing circuit depth through logic simplification and hybrid pre-processing of the data-driven model.

The correctness of the proposed approach is demonstrated using a combination of classical simulation and quantum circuit execution. First, synthetic geometries are generated, and datasets are constructed. The learned classifier is then translated into a quantum circuit and integrated into the QLBM framework. Validation will be performed by comparing particle dynamics obtained from the data-driven model with those from a classical lattice Boltzmann implementation with exact boundary conditions. Metrics include density conservation and reflection accuracy. The quantum circuits are executed using a simulator (Qiskit) to verify logical correctness and assess circuit depth and gate counts. Circuit diagrams are provided to illustrate the integration.

The proposed data-driven classifier enables a hybrid quantum-classical workflow for scaling QLBM. By offloading geometry learning, the quantum circuit complexity associated with oracle construction can be reduced, particularly for irregular or high-dimensional domains. This approach allows the quantum component to focus on transport dynamics, where potential advantages may emerge. A key aspect of scalability lies in the choice of learnable models that admit efficient reversible implementations. The hybrid strategy can potentially support adaptive scenarios where the geometry evolves over time, as the oracle can be retrained without redesigning the full circuit. While full quantum advantage is not expected in the near term, the method provides a pathway to reduce overhead in ZA-based imposition of boundary conditions within QLBM and highlights how data-driven abstractions can complement quantum algorithms in applied computational physics.