PIRSA:06080007

Quantum computation as geometry

Nielsen, M. (2006). Quantum computation as geometry. Perimeter Institute. https://pirsa.org/06080007

Nielsen, Michael. Quantum computation as geometry. Perimeter Institute, Aug. 02, 2006, https://pirsa.org/06080007 

          @misc{ pirsa_PIRSA:06080007,
            doi = {10.48660/06080007},
            url = {https://pirsa.org/06080007},
            author = {Nielsen, Michael},
            keywords = {Quantum Information, Quantum Foundations},
            language = {en},
            title = {Quantum computation as geometry},
            publisher = {Perimeter Institute},
            year = {2006},
            month = {aug},
            note = {PIRSA:06080007 see, \url{https://pirsa.org}}
          }

Michael Nielsen

Talk numberPIRSA:06080007
DOI10.48660/06080007
Collection
Talk Type Scientific Series
Subject

Abstract

How should we think about quantum computing? The usual answer to this question is based on ideas inspired by computer science, such as qubits, quantum gates, and quantum circuits. In this talk I will explain an alternate geometric approach to quantum computation. In the geometric approach, an optimal quantum computation corresponds to "free falling" along the minimal geodesics of a certain Riemannian manifold. This reformulation opens up the possibility of using tools from geometry to understand the strengths and weaknesses of quantum computation, and perhaps to understand what makes certain physical operations difficult (or easy) to synthesize.