Prospects for first-principle calculations of viscosity on a quantum computer

Applications of quantum computing to nuclear physics have been studied intensively in recent years. One natural application is the simulation of real-time dynamics of QCD matter via first principles, which is difficult on a classical computer due to the sign problem. In this talk, I propose a quantum algorithm for computing the shear viscosity, a central non-equilibrium property of QCD. I focus on the SU(3) Yang-Mills and describe the two building blocks of the algorithm: the preparation of a thermal state with temperature near the phase transition and the implementation of correlators of the energy-momentum tensor in the Hamiltonian formulation on a lattice. The shear viscosity is extracted from the correlators of the energy-momentum tensor. Due to the limitation of resources, such a calculation on a quantum computer is possible only for small-volume systems in the foreseeable future. I discuss finite-volume effects on the computation of the shear viscosity in the context of the quantum algorithm.