Reconstructing Thermal Quantum Quench Dynamics from Pure States

Simulating the nonequilibrium dynamics of thermal states is a fundamental problem across scales from high energy to condensed matter physics. The exponential complexity of time-evolving such states suggests that quantum computers could solve this problem efficiently. However, even on a quantum computer, this requires evolving an exponentially large number of pure states, one for each element of the density matrix. In this work we show that the necessary number of pure-state evolutions can be reduced to simulating the largest density matrix elements by weight, capturing the density matrix to a specified precision. The number of quantum simulations can be further reduced by leveraging symmetries of the Hamiltonian. This approach paves the way to more accurate thermal-state dynamics simulations on near-term quantum hardware with reduced resources.