A system-bath quantum thermal gradient descent algorithm for local minima search

Recently a quantum advantage has been proven for searching local minima under thermal perturbations by Chen et al. (2023). The authors propose a Thermal Gradient Descent quantum

algorithm that uses non-unitary thermal perturbations to efficiently find local minima of the energy.

We propose and study a new approach to a thermal gradient descent, the system-bath thermal-gradient descent, that can be used on both NISQ and error corrected quantum computers.

The approach uses noisy bath qubits to cool down system qubits until a local minimum is reached. The algorithm uses inherent bath qubits noise to fit a continuous bath spectral function. This

allows the bath to absorb energy from the system without previous knowledge of the system's energy levels.

We present promising results for the longitudinal-field Ising model, and show that with this approach we are able to cool the system to its ground state.