Algorithmic Analysis of Termination Problems for Quantum Programs
We introduce the notion of linear ranking super-martingale (LRSM) for quantum programs (with nondeterministic choices, namely angelic and demonic choices). Several termination theorems are established showing that the existence of the LRSMs of a quantum program implies its termination. Thus, the termination problems of quantum programs is reduced to realisability and synthesis of LRSMs. We further show that the realisability and synthesis problem of LRSMs for quantum programs can be reduced to an SDP (Semi-Definite Programming) problem, which can be settled with the existing SDP solvers. The techniques developed in this paper are used to analyse the termination of several example quantum programs, including quantum random walks and quantum Bernoulli factory for random number generation. This work is essentially a generalisation of constraint-based approach to the corresponding problems for probabilistic programs developed in the recent literature by adding two novel ideas: (1) employing the fundamental Gleason’s theorem in quantum mechanics to guide the choices of templates; and (2) a generalised Farkas’ lemma in terms of observables (Hermitian operators) in quantum physics.
Thu 11 JanDisplayed time zone: Tijuana, Baja California change
13:40 - 15:20 | |||
13:40 25mTalk | A new proof rule for almost-sure termination Research Papers Annabelle McIver Macquarie University, Carroll Morgan University of New South Wales; Data 61, Benjamin Lucien Kaminski RWTH Aachen University; University College London, Joost-Pieter Katoen RWTH Aachen University | ||
14:05 25mTalk | Lexicographic Ranking Supermartingales: An Efficient Approach to Termination of Probabilistic Programs Research Papers | ||
14:30 25mTalk | Algorithmic Analysis of Termination Problems for Quantum Programs Research Papers Yangjia Li Institute of Software, Chinese Academy of Sciences, Mingsheng Ying University of Technology Sydney | ||
14:55 25mTalk | Monadic refinements for relational cost analysis Research Papers Ivan Radicek TU Vienna, Gilles Barthe IMDEA Software Institute, Marco Gaboardi University at Buffalo, SUNY, Deepak Garg Max Planck Institute for Software Systems, Florian Zuleger TU Vienna |