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

Jingwei Wen1,2, Zhengan Wang3, Chitong Chen4,5, Junxiang Xiao1, Hang Li3, Ling Qian2, Zhiguo Huang2, Heng Fan3,4, Shijie Wei3, and Guilu Long1,3,6,7

1State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
2China Mobile (Suzhou) Software Technology Company Limited, Suzhou 215163, China
3Beijing Academy of Quantum Information Sciences, Beijing 100193, China
4Institude of Physics, Chinese Academy of Sciences, Beijing 100190, China
5School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
6Frontier Science Center for Quantum Information, Beijing 100084, China
7Beijing National Research Center for Information Science and Technology, Beijing 100084, China

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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.

We propose a full quantum excited-state solver (FQESS) algorithm for determining the spectrum of chemistry Hamiltonian efficiently and steadily for future fault-tolerant quantum computation. Compared with classical-quantum hybrid variational algorithms, our method removes the optimization process in classical computers, and the parameter updating for different energy-levels can be simply realized by modifying the state preparation process of ancillary system based on the energy measurement of previous energy-level, which is experimentally friendly. Moreover, the non-variational nature can ensure that the algorithm converges to the target states along the direction of the fastest gradient descent, avoiding barren plateau phenomenon. Our work fills the last step of solving quantum chemistry problems based on different algorithm frames.

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