A query‐based quantum eigensolver. Issue 3 (24th August 2020) - Jin, Shan; Wu, Shaojun; Zhou, Guanyu; Li, Ying; Li, Lvzhou; Li, Bo; Wang, Xiaoting
Summary: Solving eigenvalue problems is crucially important for both classical and quantum applications. Many well‐known numerical eigensolvers have been developed, including the QR and the power methods for classical computers, as well as the quantum phase estimation (QPE) method and the variational quantum eigensolver for quantum computers. In this work, we present a different type of quantum method that uses fixed‐point quantum search to solve Type II eigenvalue problems. This method serves as an important complement to the QPE method, which is a Type I eigensolver. We show that the quantum oracle of our query‐based method can be efficiently constructed from the QPE gate, which is crucial for analyzing the total gate complexity of our method. In addition, compared with the QPE method, our query‐based method achieves a quadratic speedup in solving Type II problems. As two applications, we then discuss how to apply our method to solve Type II eigenvalue problems for the Heisenberg model and the hydrogen molecule.