Global Optimization with the Iterative Power Algorithm via Quantum Computing and Quantics Tensor Trains*

Although global optimization is essential to many disciplines of science, from quantum control to machine learning, today's global optimization algorithms frequently become mired in local minima traps. We present the iterative power algorithm (IPA) and prove the method circumvents local minimum traps to converge to global minima. In IPA, the function to be optimized is represented as a potential energy surface (PES). A density is placed in the PES and acted on by an oracle that localizes the density at the global minimum locations. We demonstrate the quantics tensor-train implementation of IPA successfully identifies global minima in model potential energy surfaces with up to 2⁵⁰ local minima. We also show the method can be employed on quantum computers via the McLachlan variational principle. The resulting method is found to outperform one of the foremost quantum computing approaches for H₂ ground state optimization, quantum processor design, and prime factorization.