PLQP & Company: Decidable Logics for Quantum Algorithms

Springer Science and Business Media LLC - Tập 53 - Trang 3628-3647 - 2014
Alexandru Baltag1, Jort Bergfeld1, Kohei Kishida2, Joshua Sack1, Sonja Smets1, Shengyang Zhong1
1ILLC, University of Amsterdam, Amsterdam, the Netherlands
2Department of Computer Science, University of Oxford, Oxford, UK

Tóm tắt

We introduce a probabilistic modal (dynamic-epistemic) quantum logic PLQP for reasoning about quantum algorithms. We illustrate its expressivity by using it to encode the correctness of the well-known quantum search algorithm, as well as of a quantum protocol known to solve one of the paradigmatic tasks from classical distributed computing (the leader election problem). We also provide a general method (extending an idea employed in the decidability proof in Dunn et al. (J. Symb. Log. 70:353–359, 2005)) for proving the decidability of a range of quantum logics, interpreted on finite-dimensional Hilbert spaces. We give general conditions for the applicability of this method, and in particular we apply it to prove the decidability of PLQP.

Tài liệu tham khảo

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