Algorithm for simulating ocean circulation on a quantum computer

The accurate and efficient simulation of ocean circulation is a fundamental topic in marine science; however, it is also a well-known and dauntingly difficult problem that requires solving nonlinear partial differential equations with multiple variables. In this paper, we present for the first time an algorithm for simulating ocean circulation on a quantum computer to achieve a computational speedup. Our approach begins with using primitive equations describing the ocean dynamics and then discretizing these equations in time and space. It results in several linear system of equations (LSE) with sparse coefficient matrices. We solve these sparse LSE using the variational quantum linear solver that enables the present algorithm to run easily on near-term quantum computers. Additionally, we develop a scheme for manipulating the data flow in the algorithm based on the quantum random access memory and l ∞ norm tomography technique. The efficiency of our algorithm is verified using multiple platforms, including MATLAB, a quantum virtual simulator, and a real quantum computer. The impact of the number of shots and the noise of quantum gates on the solution accuracy is also discussed. Our findings demonstrate that error mitigation techniques can efficiently improve the solution accuracy. With the rapid advancements in quantum computing, this work represents an important first step toward solving the challenging problem of simulating ocean circulation using quantum computers.