A full circuit-based quantum algorithm for excited-states in quantum chemistry

TL;DR

This paper introduces a full circuit-based quantum algorithm for excited-state spectrum determination in quantum chemistry, eliminating classical optimization, reducing resource costs, and demonstrating robustness and practical applicability on superconducting quantum hardware.

Contribution

The paper presents a non-variational, full circuit-based quantum algorithm for excited-states that improves efficiency and robustness over previous methods, with experimental validation.

Findings

Successful simulation of molecules like H2, LiH, H2O, NH3

Good agreement between experimental results and theory

Algorithm shows robustness against noise

Abstract

Utilizing quantum computer to investigate quantum chemistry is an important research field nowadays. In addition to the ground-state problems that have been widely studied, the determination of excited-states plays a crucial role in the prediction and modeling of chemical reactions and other physical processes. Here, we propose a non-variational full circuit-based quantum algorithm for obtaining the excited-state spectrum of a quantum chemistry Hamiltonian. Compared with previous classical-quantum hybrid variational algorithms, our method eliminates the classical optimization process, reduces the resource cost caused by the interaction between different systems, and achieves faster convergence rate and stronger robustness against noise without barren plateau. The parameter updating for determining the next energy-level is naturally dependent on the energy measurement outputs of the previous energy-level and can be realized by only modifying the state preparation process of ancillary system, introducing little additional resource overhead. Numerical simulations of the algorithm with hydrogen, LiH, H2O and NH3 molecules are presented. Furthermore, we offer an experimental demonstration of the algorithm on a superconducting quantum computing platform, and the results show a good agreement with theoretical expectations. The algorithm can be widely applied to various Hamiltonian spectrum determination problems on the fault-tolerant quantum computers.