Measurement Pattern Interpolation: Theory, and potential applications

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Quantum computation by single-qubit measurements was proposed by Raussendorf and Briegel [PRL 86, 5188] as a potential scheme for implementing quantum computers. It also offers an unusual means of describing unitary transformations. To better understand which measurement-based procedures perform unitary operations, we may consider the following problem: under what circumstances can a measurement-based procedure for a unitary U be found, provided a similar procedure for U which relies on post-selection? In this talk, I describe the so-called \'Measurement Pattern Interpolation\' problem, the intuition behind the solved special cases, and possible applications of a general solution to this problem.