Quantum-accelerated constraint programming

Constraint programming (CP) is a paradigm used to model and solve constraint satisfaction and combinatorial optimization problems. In CP, problems are modeled with constraints that describe acceptable solutions and solved with backtracking tree search augmented with logical inference. In this paper, we show how quantum algorithms can accelerate CP, at both the levels of inference and search. Leveraging existing quantum algorithms, we introduce a quantum-accelerated filtering algorithm for the $\texttt{alldifferent}$ global constraint and discuss its applicability to a broader family of global constraints with similar structure. We propose frameworks for the integration of quantum filtering algorithms within both classical and quantum backtracking search schemes, including a novel hybrid classical-quantum backtracking search method. This work suggests that CP is a promising candidate application for early fault-tolerant quantum computers and beyond.Comment: published in Quantu

Formal Generation of Executable Assertions for Application-Oriented Fault Tolerance

Executable assertions embedded into a distributed computing system can provide run-time assurance by ensuring that the program state, in the actual run-time environment, is consistent with the logical stage specified in the assertions; if not, then an error has occurred and a reliable communication of this diagnostic information is provided to the system such that reconfiguration and recovery can take place. Application- oriented fault tolerance is a method that provides fault detection using executable assertions based on the natural constraints of the application. This paper focuses on giving application-oriented fault tolerance a theoretical foundation by providing a mathematical model for the generation of executable assertions which detect faults in the presence of arbitrary failures. The mathematical model of choice was axiomatic program verification. A method was developed that translates a concurrent verification proof outline into an error-detecting concurrent program. This paper shows the application of the developed method to several applications