Although global optimization algorithms play a central role in a wide variety of chemical disciplines, from quantum control to electronic structure theory; today's global optimization algorithms frequently become “trapped” in local minima. We present the iterative power algorithm (IPA) and provide a formal proof that the method successfully bypasses local minimum traps to converge to the global minima, both for discrete and continuous global search. In IPA, the function to be optimized is represented as a potential energy surface. A density is placed in the potential energy surface and acted upon by an oracle function that localizes the density at the locations of the global minima. We demonstrate the quantics tensor-train implementation of the method successfully identifies global minima in model potential energy surfaces with up to 2<sup>50</sup> local minima. We also show the method can be employed on quantum computers via the McLachlan variational principle. The resulting quantum iterative power method is found to outperform one of the foremost quantum computing approaches for hydrogen ground state optimization, as well as quantum processor design and prime factorization.

Iterative power algorithm for global optimization of molecular systems via quantum computing and quantics tensor trains

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