Unitary Selective Coupled-Cluster Method

Dmitry A. Fedorov1,2, Yuri Alexeev1, Stephen K. Gray3, and Matthew Otten4

1Computational Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Lemont, IL 60439, USA
2Oak Ridge Associated Universities, Oak Ridge, TN 37830
3Center for Nanoscale Materials, Argonne National Laboratory, 9700 S. Cass Ave, Lemont, IL 60439, USA
4HRL Laboratories, LLC, 3011 Malibu Canyon Road, Malibu, CA 90265

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Abstract

Simulating molecules using the Variational Quantum Eigensolver method is one of the promising applications for NISQ-era quantum computers. Designing an efficient ansatz to represent the electronic wave function is crucial in such simulations. Standard unitary coupled-cluster with singles and doubles (UCCSD) ansatz tends to have a large number of insignificant terms that do not lower the energy of the system. In this work, we present a unitary selective coupled-cluster method, a way to construct a unitary coupled-cluster ansatz iteratively using a selection procedure with excitations up to fourth order. This approach uses the electronic Hamiltonian matrix elements and the amplitudes for excitations already present in the ansatz to find the important excitations of higher order and to add them to the ansatz. The important feature of the method is that it systematically reduces the energy error with increasing ansatz size for a set of test molecules. {The main advantage of the proposed method is that the effort to increase the ansatz does not require any additional measurements on a quantum computer.}

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Cited by

[1] Jules Tilly, Hongxiang Chen, Shuxiang Cao, Dario Picozzi, Kanav Setia, Ying Li, Edward Grant, Leonard Wossnig, Ivan Rungger, George H. Booth, and Jonathan Tennyson, "The Variational Quantum Eigensolver: A review of methods and best practices", Physics Reports 986, 1 (2022).

[2] Benchen Huang, Marco Govoni, and Giulia Galli, "Simulating the Electronic Structure of Spin Defects on Quantum Computers", PRX Quantum 3 1, 010339 (2022).

[3] Ashutosh Kumar, Ayush Asthana, Conner Masteran, Edward F. Valeev, Yu Zhang, Lukasz Cincio, Sergei Tretiak, and Pavel A. Dub, "Accurate quantum simulation of molecular ground and excited states with a transcorrelated Hamiltonian", arXiv:2201.09852.

[4] Matt Menickelly, Yunsoo Ha, and Matthew Otten, "Latency considerations for stochastic optimizers in variational quantum algorithms", arXiv:2201.13438.

The above citations are from Crossref's cited-by service (last updated successfully 2022-10-04 07:32:46) and SAO/NASA ADS (last updated successfully 2022-10-04 07:32:47). The list may be incomplete as not all publishers provide suitable and complete citation data.