Hybrid quantum-classical simulations of relativistic charged fluids

Extreme plasmas, which are both quantum and relativistic, are relevant in several contexts ranging from Astrophysics to Inertial Fusion. I will present the first steps in a research program aiming at simulating these plasmas on quantum computers. The approach is based on the Dirac equation and relies on two key results. First, a generalization of the so-called Madelung transform shows that the Dirac equation actually describes a quantum relativistic fluid of spin 1/2 particles. Second, the Dirac equation can be discretized into quantum walks, which are a standard tool of quantum computing and also constitute a universal quantum computational primitive. Our first results are simulations of shocks in extreme fluids immersed in a uniform electric field. The simulations have been first performed on a classical computer, but we have also developed a new quantum-classical hybrid algorithm tailor-made for current Noisy Intermediate-Scale Quantum (NISQ) computers and run the simulations on IBM’s quantum processors. The next steps, including the introduction of self-consistent electromagnetic fields, will be also discussed.