Giuseppe Catalano

Quantum transport on structured networks is strongly influenced by interference effects, which can dramatically modify how information propagates through a system. We develop a quantum-information-theoretic framework for scattering on graphs in which a full network of connected scattering sites is treated as a quantum channel linking designated input and output ports. Using the Redheffer star product to construct global scattering matrices from local ones, we identify resonant concatenation, a nonlinear composition rule generated by internal back-reflections. In contrast to ordinary channel concatenation, resonant concatenation can suppress noise and even produce super-activation of the quantum capacity, yielding positive capacity in configurations where each constituent channel individually has zero capacity. We illustrate these effects through models exhibiting resonant-tunneling-enhanced transport. Our approach provides a general methodology for analyzing coherent information flow in quantum graphs, with relevance for quantum communication, control, and simulation in structured environments.

Efficient and coherent data retrieval and storage are essential for harnessing quantum algorithms' speedup. Such a fundamental task is addressed by a quantum Random Access Memory (qRAM). Despite their promising scaling properties, current qRAM proposals demand excessive resources and rely on operations beyond the capabilities of current hardware requirements, rendering their practical realization inefficient. We introduce a novel architecture that significantly reduces resource requirements while preserving optimal complexity scaling for quantum queries. Moreover, unlike previous proposals, our algorithm design leverages a simple, repeated operational block based exclusively on local unitary operations and short-range interactions between a limited number of quantum walkers traveling over a single binary tree. This novel approach not only simplifies experimental requirements by reducing the complexity of necessary operations but also enhances the architecture's scalability by ensuring a resource-efficient, modular design that maintains optimal quantum query performance.