Robustness of near-thermal dynamics on digital quantum computers

Understanding how gate errors impact quantum circuits is crucial for assessing the utility of quantum computers, especially before the deployment of large-scale error correction. A promising near-term application of quantum computers is to simulate the dynamics of many-body quantum systems evolving under a Hamiltonian, a classically intractable problem with useful applications in materials science, chemistry, and physics. We present analytical arguments, supported by numerical and experimental evidence, that Trotterized Hamiltonian simulation near thermal equilibrium is more robust to gate and Trotter errors than commonly believed. We show that a two-qubit gate error probability that scales linearly with gate angle, observed on Quantinuum's quantum computers, is particularly helpful in performing accurate dynamics simulations. In our analysis, we make heavy use of a new theoretical tool, a statistical ensemble of random product states that approximates a thermal state, which can be used to design and optimize Hamiltonian simulation experiments on quantum hardware.