Evaluating thermal expectation values by almost ideal sampling with Trotter gates

We investigate the sampling efficiency for simulations of quantum many-body systems at finite temperatures when initial states are generated by applying Trotter gates to random phase product (RPPSs). restrict number applications be proportional system size, and thus preparation would easily accomplished in fault-tolerant computers. When made from a nonintegrable Hamiltonian, we observe that increases with size. This trend means almost ideal can achieved sufficiently large systems. also find is equal obtained typical pure (TPQ) state method utilizing Haar some cases. These findings suggest chaotic Hamiltonian dynamics transform RPPSs into an alternative TPQ evaluating thermal expectation values.