On quantum circuits for quantum computation as (geodesic, if optimal) computational paths:
Michael A. Nielsen, Mark R. Dowling, Mile Gu, Andrew C. Doherty, Quantum Computation as Geometry, Science, 311 5764 (2006) 1133-1135 [doi:10.1126/science.1121541, arXiv:quant-ph/0603161]
Mark R. Dowling, Michael A. Nielsen, The geometry of quantum computation, Quantum Information & Computation 8 10 (2008) 861–899 [doi:10.5555/2016985.2016986, arXiv:quant-ph/0701004]
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