  Simulating the nonequilibrium dynamics of thermal states is a fundamental
problem across scales from high energy to condensed matter physics. Quantum
computers may provide a way to solve this problem efficiently. Preparing a
thermal state on a quantum computer is challenging, but there exist methods to
circumvent this by computing a weighted sum of time-dependent matrix elements
in a convenient basis. While the number of basis states can be large, in this
work we show that it can be reduced by simulating only the largest density
matrix elements by weight, capturing the density matrix to a specified
precision. Leveraging Hamiltonian symmetries enables further reductions. This
approach paves the way to more accurate thermal-state dynamics simulations on
near-term quantum hardware.
