Benchmark of quantum algorithms for ground state preparation in the presence of noise

Preparing ground states of many-body Hamiltonians is a central task in quantum simulation and computation. Various strategies have been developed, including adiabatic evolution [3], variational algorithms, such as the Quantum Approximate Optimization Algorithm (QAOA) [2, 4, 5], and dissipative or cooling protocols [1, 6–21]. In current experimental settings, all these approaches are limited by the presence of noise, including decoherence and imperfections, which degrades the quality of the prepared states and imposes limits on the reachable energies. Thus, the following questions naturally arise: how does the achievable energy scale with the noise rate, and which strategy performs best for given hardware constraints? The adiabatic algorithm [3] prepares the target ground state by slowly evolving the system from the ground state of a simple initial Hamiltonian to the target Hamiltonian, relying on the adiabatic theorem to keep the state close to the instantaneous ground state throughout the evolution. Its performance is often limited by the minimum spectral gap along the interpolation path, which closes at quantum phase transitions and demands impractically long runtimes [22, 23]. Variational algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) [2, 5] circumvent some of those issues by optimizing the parameters of a fixed-depth quantum circuit…