Breakthroughs in Higher Order Quantum Algorithms Unveiled by Prof. Mio Murao

Prof. Mio Murao from the University of Tokyo delivered a landmark talk on higher order quantum algorithms for learning quantum objects at a recent IVADO seminar in Montreal. As a leading expert in quantum programming, Prof. Murao emphasized the emerging era of "quantum civilization," where quantum computers enable the direct learning of quantum objects without converting quantum properties to classical data.

Her presentation introduced “fully-quantum” learning algorithms that operate entirely on quantum computers, offering quantum advantage by sidestepping traditional, measurement-heavy, classical approaches. Two significant algorithms were featured: universal isometry adjointation and learning singular value moments of unknown quantum channels. Prof. Murao also distinguished quantum learning from quantum machine learning, focusing on using quantum computers to learn about quantum maps and processes, not merely extracting classical information.

The lecture delved into higher order quantum computation, wherein quantum computers process not just states but quantum operations themselves sometimes called "super maps" to enable sophisticated learning and transformation tasks. These breakthroughs position quantum learning as an essential tool for advanced quantum technologies, potentially impacting fields ranging from error correction to channel analysis.

The event concluded with active discussion on algorithmic complexity, physical representability, and future application areas. Prof. Murao’s talk highlighted how mathematical rigor and group theory underpin these innovations, setting the agenda for the next phase of quantum algorithm research.

Reference / Source:

IVADO Seminar, "Higher Order Quantum Algorithms for Learning Quantum Objects" by Prof. Mio Murao, University of Tokyo (Nov 4, 2025).