Lost in Translation

          @misc{ pirsa_PIRSA:08050018,
            doi = {10.48660/08050018},
            url = {https://pirsa.org/08050018},
            author = {Kashefi, Elham},
            keywords = {Quantum Information},
            language = {en},
            title = {Lost in Translation },
            publisher = {Perimeter Institute},
            year = {2008},
            month = {may},
            note = {PIRSA:08050018 see, \url{https://pirsa.org}}
          }
          

Abstract

We consider the question of forward and backward translation between measurement-based quantum computing, called patterns, and quantum circuit computation. It is known that the class of patterns with a particular properties, having flow, is in one-to-one correspondence with quantum circuits. However we show that a more general class of patterns, those having generalised flow, will sometime translate to imaginary circuits, quantum circuits with time-like curves. Extending this approach, we first present the semantics of quantum circuits with time-like curves in terms of post-selection quantum computing and then characterise the class of curves with unitary or completely-positive semantic. Finally we present the re-write rules for opening the loops to transform an imaginary circuit to a normal circuit and discuss the connection between time-like curves and depth complexity.