DisQ: A Model of Distributed Quantum Processors

Abstract: The development of quantum computers has reached a great milestone in spite of restrictions on important quantum resources: the number of qubits being entangled at a single-location quantum computer. The next generation of distributed quantum processors combines single-location quantum computing and quantum networking techniques to permit large entangled qubit groups to be established through remote processors, and quantum algorithms can be executed distributively. We present Disq, as the first formal model of distributed quantum processors, and permit the analysis of distributed quantum programs in the new computation environment. The core of Disq is a distributed quantum programming language that combines the concepts of Chemical Abstract Machine (CHAM) and Markov Decision Processes (MDP) with the objective of providing clearly distinguishing quantum concurrent and distributed behaviors. Based on the Disq language, we develop a simulation relation to check the equivalence of a quantum algorithm and its distributed versions so that users can develop the distributed version of a sequential quantum program via a simulation check. We present several case studies, such as quantum addition and Shor's algorithm, to demonstrate their equivalent rewrites to distributed versions.