Cohomological description of contextual measurement-based quantum computations — the temporally ordered case

          @misc{ pirsa_PIRSA:24040091,
            doi = {10.48660/24040091},
            url = {https://pirsa.org/24040091},
            author = {Raussendorf, Robert},
            keywords = {Quantum Information},
            language = {en},
            title = {Cohomological description of contextual measurement-based quantum computations {\textemdash} the temporally ordered case},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {apr},
            note = {PIRSA:24040091 see, \url{https://pirsa.org}}
          }
          

Abstract

It is known that measurement-based quantum computations (MBQCs) which compute a non-linear Boolean function with sufficiently high probability of success are contextual, i.e., they cannot be described by a non-contextual hidden variable model. It is also known that contexuality has descriptions in terms of cohomology [1,2]. And so it seems in range to obtain a cohomological description of MBQC. And yet, the two connections mentioned above are not easily strung together. In a previous work [3], the cohomological description for MBQC was provided for the temporally flat case. Here we present the extension to the general temporally ordered case. [1] S. Abramsky, R. Barbosa, S. Mansfield, The Cohomology of Non-Locality and Contextuality, EPTCS 95, 2012, pp. 1-14 [2] C. Okay, S. Roberts, S.D. Bartlett, R. Raussendorf, Topological proofs of contextuality in quantum mechanics, Quant. Inf. Comp. 17, 1135-1166 (2017). [3] R. Raussendorf, Cohomological framework for contextual quantum computations, Quant. Inf. Comp. 19, 1141-1170 (2019) This is jount work with Polina Feldmann and Cihan Okay