| dc.description.abstract | Groundwater plays a vital role in the water supply system. To understand the groundwater behavior, groundwater model was necessary to carry out. Previous studies prefer to use traditional computational methods to construct groundwater models for a long time. Recently, several studies have proven the efficiency of quantum computing in various applications including inverse problems, stochastic interpretation. It should be interesting to explore the possible implementation of quantum technology for the field of groundwater hydrology. This study aims to develop and test the solutions of groundwater equations for steady state and transient state in quantum computing. These groundwater equations were directly derived by finite difference method to find groundwater head variables. Python scriptings were built to calculate matrices of groundwater equations on classical computer. The other scriptings were continuously constructed QUBO (Quadratic Unconstrained Binary Optimization) equation of least square problem to solve discretized matrices in QPU (Quantum Processing Unit) direct solver and Iterative direct solver from D-Wave System. The results calculated by classical computing and quantum computing were presented for comparison purposes on grid sizes of 2x2, 3x3, 4x4, 9x9 in the steady-state, and 2x2 in the transient state. Our results indicated that the steady state model calculated by the simulated quantum annealer was consistent with classical computing results with grid sizes of 2x2 in QPU (Quantum Processing Unit) direct solver and grid sizes of 2x2, 3x3, 4x4 in Iterative solver. The instability was clearly shown in grid sizes of 9x9 with 100 variables in the matrices for both solvers. Transient state model with grid size of 2x2 also gained the same status as steady-state case. Generally, Iterative solver has performed better than QPU (Quantum Processing Unit) direct solver in testing examples on quantum computer. Based on our analysis, we conclude that quantum computing certainly achieves quality solutions in small-scale problems due to the limitations of qubits in the hardware machine. The results returned from Iterative solver were more stable than QPU (Quantum Processing Unit) direct solver in the calculation process. The research indicated that specific packages and API token authentication from D-Wave System should be prepared to directly run the problems in the local environment or D-Wave′s Leap online platform through SAPI (D-Wave′s Solver API) . Our research has proven that groundwater model is possible to solve by quantum computing in this period. Despite errors in large-scale problems, this research is considered as one of the initial studies in solving subsurface problems by quantum computing in its early stage.
Keywords: Groudwater model, finite difference method, quantum annealing method, QUBO, QPU direct solver , Iterative solver , Python scriptings. | en_US |