Super-bath Quantum Eigensolver

The simulation of the dynamics of a system coupled to a low-temperature environment is a promising application of quantum computers to determine ground-state properties of physical systems. However, this approach requires not only the $\textit{existence}$ of an environment that allows the system to dissipate energy and evolve to its ground state, but also the $\textit{detailed knowledge}$ of the properties of the bath. In this paper, we propose a polynomial-time algorithm for ground state preparation which only relies on the $\textit{existence}$ of a physical bath which achieves the same task, while a detailed description of the environment may remain $\textit{unknown}$. In particular, we show that this ``super-bath quantum eigensolver algorithm'' prepares the ground state of the system by combining a Gaussian stabilization dephasing procedure with the simulation of the interaction between the system and a super-bath which only requires minimal knowledge of the physical environment. Based on our algorithmic framework, we establish a partial order relation among environments. Supported by experimental lifetime data of nuclear metastable states, we suggest that our algorithm is applicable to determine nuclear ground states in polynomial time. These results highlight the potential advantage of quantum computing in addressing ground state problems in real-world physical systems.