Search for: All records

Abstract The SAT problem is a prototypical NP-complete problem of fundamental importance in computational complexity theory with many applications in science and engineering; as such, it has long served as an essential benchmark for classical and quantum algorithms. This study shows numerical evidence for a quadratic speedup of the Grover Quantum Approximate Optimization Algorithm (G-QAOA) over random sampling for finding all solutions to 3-SAT (All-SAT) and Max-SAT problems. G-QAOA is less resource-intensive and more adaptable for these problems than Grover’s algorithm, and it surpasses conventional QAOA in its ability to sample all solutions. We show these benefits by classical simulations of many-round G-QAOA on thousands of random 3-SAT instances. We also observe G-QAOA advantages on the IonQ Aria quantum computer for small instances, finding that current hardware suffices to determine and sample all solutions. Interestingly, a single-angle-pair constraint that uses the same pair of angles at each G-QAOA round greatly reduces the classical computational overhead of optimizing the G-QAOA angles while preserving its quadratic speedup. We also find parameter clustering of the angles. The single-angle-pair protocol and parameter clustering significantly reduce obstacles to classical optimization of the G-QAOA angles. 

Abstract It is widely acknowledged that distributed water systems (DWSs), which integrate distributed water supply and treatment with existing centralized infrastructure, can mitigate challenges to water security from extreme events, climate change, and aged infrastructure. However, it is unclear which are beneficial DWS configurations, i.e., where and at what scale to implement distributed water supply. We develop a mesoscale representation model that approximates DWSs with reduced backbone networks to enable efficient system emulation while preserving key physical realism. Moreover, system emulation allows us to build a multiobjective optimization model for computational policy search that addresses energy utilization and economic impacts. We demonstrate our models on a hypothetical DWS with distributed direct potable reuse (DPR) based on the City of Houston's water and wastewater infrastructure. The backbone DWS with greater thanlink and node reductions achieves satisfactory approximation of global flows and water pressures, to enable configuration optimization analysis. Results from the optimization model reveal case‐specific as well as general opportunities, constraints, and their interactions for DPR allocation. Implementing DPR can be beneficial in areas with high energy intensities of water distribution, considerable local water demands, and commensurate wastewater reuse capacities. The mesoscale modeling approach and the multiobjective optimization model developed in this study can serve as practical decision‐support tools for stakeholders to search for alternative DWS options in urban settings.