Researchers have compared the performance of various quantum algorithms designed for ground-state preparation in the presence of noise. The study focused on an exactly solvable family of quadratic fermionic Hamiltonians subjected to depolarizing noise. The goal was to determine how the noise rate affects the achievable relative energy for cooling, adiabatic, and optimization algorithms. This analysis is crucial for the development of quantum computing, where the preparation of specific quantum states is a fundamental task and the presence of noise is an unavoidable reality.

The results indicate that the performance of the algorithms depends on the quantum phase of the system. In the trivial phase, adiabatic evolution proved to be more effective. However, in the topological phase, where gap-closing limits adiabatic protocols, a multi-frequency cooling algorithm became competitive or even superior. The quantum approximate optimization algorithm (QAOA) was also evaluated, showing comparable performance to cooling in the trivial phase but being outperformed in the topological regime.

The study also revealed that the cooling protocol exhibits enhanced robustness to parameter imperfections, highlighting its potential advantage for realistic implementations of noisy quantum state preparation. This analytical approach, combined with numerical validation, establishes an extendable methodology for benchmarking ground-state preparation algorithms, providing a solid foundation for future advancements in quantum computing and material simulation.