We are entering an era where quantum hardware capabilities are beginning to meet the requirements of theoretical quantum protocols. This development brings new urgency to a fundamental question in quantum information processing theory: for which tasks do quantum information processing devices outperform their conventional counterparts?
This project addresses the above challenge in the context of information processing with interacting parties, a natural framework for cryptography, communication, and distributed computing. We take a two-pronged approach, with each prong tackling a fundamental aspect of interactive information processing while maintaining a shared focus on efficiency. We focus on two key areas: entanglement-enabled information processing and efficiency in quantum computations.
The first objective explores entanglement, a uniquely quantum phenomenon that enables powerful advantages in multi-party information processing. We aim to deepen the theoretical foundation of entanglement-enabled computations by developing methods to analyze them, identifying practical scenarios where entanglement can be efficiently utilized, and comparing different models of entanglement to understand their computational potential.
The second objective focuses on improving efficiency in quantum computations, particularly for problems with symmetric quantum inputs, which frequently appear in quantum information theory. While much of quantum theory studies the ultimate capabilities of quantum systems, we aim to make these processes more efficient. Specifically, we will develop optimized algorithms for the quantum Schur transform, a widely used quantum tool. Our approach includes creating a streaming implementation of Schur sampling that can run on small-scale quantum devices, designing error-mitigation techniques for real-world quantum hardware, and constructing efficient quantum circuits for port-based teleportation and related applications.
