Abstract
We introduce a family of variational quantum algorithms, which we coin as quantum iterative
power algorithms (QIPAs), and demonstrate their capabilities as applied to global-optimization
numerical experiments. Specifically, we demonstrate the QIPA based on a double exponential
oracle as applied to ground state optimization of the H2 molecule, search for the transmon qubit
ground-state, and biprime factorization. Our results indicate that QIPA outperforms quantum
imaginary time evolution (QITE) and requires a polynomial number of queries to reach
convergence even with exponentially small overlap between an initial quantum state and the final
desired quantum state, under some circumstances. We analytically show that there exists an
exponential amplitude amplification at every step of the variational quantum algorithm, provided
the initial wavefunction has non-vanishing probability with the desired state and that the unique
maximum of the oracle is given by λ1 > 0, while all other values are given by the same value
0 < λ2 < λ1 (here λ can be taken as eigenvalues of the problem Hamiltonian). The generality of the
global-optimization method presented here invites further application to other problems that
currently have not been explored with QITE-based near-term quantum computing algorithms.
Such approaches could facilitate identification of reaction pathways and transition states in
chemical physics, as well as optimization in a broad range of machine learning applications. The
method also provides a general framework for adaptation of a class of classical optimization
algorithms to quantum computers to further broaden the range of algorithms amenable to
implementation on current noisy intermediate-scale quantum computers.