Near-term quantum algorithms for linear systems of equations with regression loss functions

Abstract Solving linear systems of equations is essential for many problems in science and technology, including machine learning. Existing quantum algorithms have demonstrated the potential large speedups, but required resources are not immediately available on near-term devices. In this work, we study equations, with a focus two-norm Tikhonov regression settings. We investigate use variational analyze their optimization landscapes. There exist types which designed to avoid barren plateaus, such as properly-initialized imaginary time evolution adiabatic-inspired optimization, suffer from different plateau problem. To circumvent issue, design based core idea: classical combination states (CQS). exhibit several provable guarantees these algorithms, supported by representation system so-called ansatz tree. The CQS approach tree also admit systematic application heuristic approaches, gradient-based search. conducted numerical experiments solving 2 300 × considering cases where can simulate algorithm efficiently computer. Our methods may provide benefits within reach