Evolutionary Quantum Autoencoders for Adaptive Teleportation-Mediated Gate Synthesis

We propose a novel framework for teleportation-mediated non-local gate synthesis by integrating evolutionary learning with a quantum variational autoencoder (QVAE). The conventional approaches to quantum teleportation often rely on static entanglement resources and fixed measurement bases, which limit adaptability and efficiency. The proposed method addresses these limitations through a symmetry-preserving QVAE that dynamically compresses quantum states while preserving teleportation-critical features, combined with an evolutionary optimizer to refine protocol performance. The QVAE employs a parameterized quantum circuit with SU(3)-symmetric layers to encode two-qubit states into a compressed latent representation, then reconstructs them via a Bell-basis measurement decoder. The evolutionary component optimizes a multi-objective fitness function balancing teleportation fidelity and entanglement efficiency, adapting parameters in real-time through Gaussian mutations and annealing. Moreover, the system integrates seamlessly with existing teleportation protocols by replacing traditional Bell-state generation with adaptive state preparation and post-teleportation error correction. Implemented on a superconducting quantum processor with classical co-processing, our framework achieves high fidelity (above 0.99) while reducing classical communication overhead by 50%. The hybrid architecture operates at a 10 kHz update rate, ensuring compatibility with current quantum networking standards without additional hardware requirements. This work demonstrates the potential of evolutionary quantum autoencoders to enhance teleportation-based gate synthesis, offering a scalable and adaptive solution for future quantum communication systems.