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Abstract: We introduce an algebra qCCS of pure quantum processes in which no classicaldata is involved, communications by moving quantum states physically areallowed, and computations is modeled by super-operators. An operationalsemantics of qCCS is presented in terms of non-probabilistic labeledtransition systems. Strong bisimulation between processes modeled in qCCS isdefined, and its fundamental algebraic properties are established, includinguniqueness of the solutions of recursive equations. To model sequentialcomputation in qCCS, a reduction relation between processes is defined. Bycombining reduction relation and strong bisimulation we introduce the notion ofstrong reduction-bisimulation, which is a device for observing interaction ofcomputation and communication in quantum systems. Finally, a notion of strongapproximate bisimulation equivalently, strong bisimulation distance and itsreduction counterpart are introduced. It is proved that both approximatebisimilarity and approximate reduction-bisimilarity are preserved by variousconstructors of quantum processes. This provides us with a formal tool forobserving robustness of quantum processes against inaccuracy in theimplementation of its elementary gates.



Author: Mingsheng Ying, Yuan Feng, Runyao Duan, Zhengfeng Ji

Source: https://arxiv.org/







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