The Problem
Large water distribution system operators like Vitens are faced with network models that are intractable to simulate in their full scale in short time periods and must instead simulate smaller networks over larger time periods. These models are important for understanding e.g., pipe friction parameters, determining least-cost designs, finding leaks, developing digital twins and more.
Traditional methods may struggle with the complexity of predicting and managing water flow, especially under varying loading conditions and for large networks. The use of quantum computing may improve decision-making processes and enhance the development of water distribution resources.
The Quantum Solution
Quantum computing offers new approaches for WDN management by leveraging its ability to process complex optimization problems and simulate systems with high accuracy. Two different solutions were developed in this project. In the first, a quantum adaptation was made to the well-known Newton-Raphson algorithm, dubbed Quantum Newton-Raphson (QNR). In QNR one of three different quantum linear solvers can be used in a classical iterative modelling process. In the second solution, we worked towards a more concrete use-case of hydraulic modelling and developed a quantum annealing algorithm for water distribution network design, which finds the optimal combination of pipe-diameters when installing a new water distribution network.
Simulated annealing results for our Water Distribution Network design algorithm. On the x-axis, 5 different pairs of pipe diameters, with the left-most pair representing the known optimal design.
The Benefits
For QNR we found that the QUBO linear solver and Variational linear solvers performed the best, whereas the HHL linear solver required too large a qubit count to be feasible on the near-term. We performed accurate simulations of small 2-loop networks on quantum emulators, determining feasibility of our application. The implementation is found on our Github, here.
Our quantum annealing algorithm for network design led to a highly complex annealing formulation, allowing us to solve networks of up to size 3 for using simulated annealing, the results are depicted in the above image. The implementation is also found on our Github, here.
This work is supported by the Dutch National Growth Fund (NGF), as part of the Quantum Delta NL programme
