Hydrodynamics successfully describes low-energy modes of a wide class of theories including QCD in the strongly-coupled regime. Some of the low energy constants in the hydrodynamic description of QCD, such as shear viscosity, are difficult to obtain from first principles on a classical computer due to the sign problem.
One long-standing way to address sign problems is to deform the contour of integration in the path integral to the complex plane. I will explain the conjectured existence of such deformed contours which solve the sign problem completely for a certain class of actions.
Quantum computing provides an alternative way to calculate the shear viscosity without a sign problem. Two necessary building blocks of the quantum algorithm are the construction of the energy momentum tensor in the Hamiltonian formalism, and a state preparation algorithm of thermal states.
Lastly, finite volume effects are always unavoidable and larger particularly for the foreseeable future in both classical and quantum calculations. We study such effects in molecule dynamics and $\mathcal{N}=4$ supersymmetric Yang-Mills theory.
