Quantum Computing for CFD

Quantum computing (QC) is experiencing rapid developments and is widely expected to provide algorithmic scaling performance with polynomial, or even exponential advantages over what is currently possible on classical computers. Work is in progress to assess the performance of numerical methods that will enable the use of QC for computational fluid dynamics (CFD). As a step toward achieving this capability, a demonstration is made of the use of matrix product states (MPS), a subset of tensor network methods borrowed from many-body physics, to provide a low-rank approximation of the discretized Burger's equation. The corresponding MPS structure is solved on IBM's cloud computing platforms. Simulations are conducted on IBM's quantum simulators and noisy intermediate-scale quantum (NISQ) computers. The results are assessed via comparison with those obtained via classical simulations of the full-ranked equation.