Quantum finite difference solvers for physics simulation

Physics systems are becoming increasingly complex and require more and more computing time. Quantum computing, which has shown its efficiency on some problems, such as the factorisation of a number with Shor's algorithm, may be the solution to reduce these computation times. Here, the authors propose two quantum numerical schemes for the simulation of physics phenomena, based on the finite difference method. The aim is to see if quantum versions of standard numerical schemes offer an advantage over their classical counterparts, either in accuracy, stability or computation time. First, the authors will present the different phenomena studied as well as the classical solution methods chosen. The authors will then describe the implementation of the quantum numerical schemes and present some results obtained on the different physics phenomena beforehand and then compare both approaches, classical and quantum.