2021/09/06 by Andre Kornell, Bert Lindenhovius, Michael Mislove
Computer Science · #cs.PL #cs.ET
paper · pdf · doi:10.4204/eptcs.340.9
published as EPTCS 340, 2021, pp. 174-187 · In Proceedings QPL 2020, arXiv:2109.01534
arxiv created 2021/09/06 · arxiv updated 2021/09/07
We introduce the monoidal closed category qCPO of quantum cpos, whose objects are "quantized" analogs of omega-complete partial orders (cpos). The category qCPO is enriched over the category CPO of cpos, and contains both CPO, and the opposite of the category FdAlg of finite-dimensional von Neumann algebras as monoidal subcategories. We use qCPO to construct a sound model for the quantum programming language Proto-Quipper-M (PQM) extended with term recursion, as well as a sound and computationally adequate model for the Linear/Non-Linear Fixpoint Calculus (LNL-FPC), which is both an extension of the Fixpoint Calculus (FPC) with linear types, and an extension of a circuit-free fragment of PQM that includes recursive types.