Title Quantum - Inspired Boolean States for Bounding Engineering Network Reliability

Significant methodological progress has taken place to quantify the reliability of networked systems over the past decades. Both numerical and analytical methods have enjoyed improvements via a host of advanced Monte Carlo simulation strategies, state space partition methods, statistical learning, and Boolean functions among others. The latter approach exploits logic to approximate network reliability assessments efficiently while offering theoretical error guarantees. In parallel, physicists have made progress modeling complex systems via tensor networks (TNs), particularly quantum many-body systems. Inspired by the representation power of quantum TNs, this paper offers a new approach to efficiently bound network reliability (REL) classically. It does so by exactly solving a related network Boolean satisfiability counting problem (or #SATNET ), represented as a TN, which upper-bounds general all-terminal reliability (ATR) problems by counting configurations in which all network nodes are connected to at least a neighbor. Our #SATNET counting outperforms state-of-the-art approximate counters for the same problem as shown for challenging two-dimensional lattice networks of increasing size. While the over-counting from #SATNET increases exponentially relative to the number of configurations that satisfy (ATR) or #RELAT , the bias is predictable for ideal networks, such as lattices, and the upper-bound is guaranteed with 100% confidence—a desirable feature when other methods with error guarantees fail to scale. Clearly, our goal is not to solve the general stochastic network reliability problem, which remains a #P problem in the computational complexity hierarchy (i.e., a counting version of non-deterministic polynomial time [NP ] problems ∗Associate Professor, Department of Civil and Environmental Engineering, Rice University, Houston, Texas. Email: [email protected] †Professor, Department of Computer Science, Rice University, Houston, Texas. E-mail: [email protected] ‡Professor, Department of Statistics, Oregon State University. E-mail: [email protected]