Quantum simulation of non-equilibrium dynamics and thermalization in the
  Schwinger model
We present simulations of non-equilibrium dynamics of quantum field theories
on digital quantum computers. As a representative example, we consider the
Schwinger model, a 1+1 dimensional U(1) gauge theory, coupled through a
Yukawa-type interaction to a thermal environment described by a scalar field
theory. We use the Hamiltonian formulation of the Schwinger model discretized
on a spatial lattice. With the thermal scalar fields traced out, the Schwinger
model can be treated as an open quantum system and its real-time dynamics are
governed by a Lindblad equation in the Markovian limit. The interaction with
the environment ultimately drives the system to thermal equilibrium. In the
quantum Brownian motion limit, the Lindblad equation is related to a field
theoretical Caldeira-Leggett equation. By using the Stinespring dilation
theorem with ancillary qubits, we perform studies of both the non-equilibrium
dynamics and the preparation of a thermal state in the Schwinger model using
IBM's simulator and quantum devices. The real-time dynamics of field theories
as open quantum systems and the thermal state preparation studied here are
relevant for a variety of applications in nuclear and particle physics, quantum
information and cosmology.
Wibe A. de Jong Kyle Lee James Mulligan Mateusz Płoskoń Felix Ringer Xiaojun Yao