Unitary Selective Coupled-Cluster Method

Dmitry A. Fedorov; Yuri Alexeev; Stephen K. Gray; Matthew Otten

doi:10.22331/q-2022-05-02-703

Unitary Selective Coupled-Cluster Method

Dmitry A. Fedorov^1,2, 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

Published:	2022-05-02, volume 6, page 703
Eprint:	arXiv:2109.12652v5
Doi:	https://doi.org/10.22331/q-2022-05-02-703
Citation:	Quantum 6, 703 (2022).

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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.}

► BibTeX data

@article{Fedorov2022unitaryselective,
  doi = {10.22331/q-2022-05-02-703},
  url = {https://doi.org/10.22331/q-2022-05-02-703},
  title = {Unitary {S}elective {C}oupled-{C}luster {M}ethod},
  author = {Fedorov, Dmitry A. and Alexeev, Yuri and Gray, Stephen K. and Otten, Matthew},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {703},
  month = may,
  year = {2022}
}

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[1] Matthew Otten, Matthew R. Hermes, Riddhish Pandharkar, Yuri Alexeev, Stephen K. Gray, and Laura Gagliardi, "Localized Quantum Chemistry on Quantum Computers", Journal of Chemical Theory and Computation 18 12, 7205 (2022).

[2] Ilias Magoulas and Francesco A. Evangelista, "CNOT-Efficient Circuits for Arbitrary Rank Many-Body Fermionic and Qubit Excitations", Journal of Chemical Theory and Computation 19 3, 822 (2023).

[3] 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).

[4] Tim Weaving, Alexis Ralli, William M. Kirby, Andrew Tranter, Peter J. Love, and Peter V. Coveney, "A Stabilizer Framework for the Contextual Subspace Variational Quantum Eigensolver and the Noncontextual Projection Ansatz", Journal of Chemical Theory and Computation 19 3, 808 (2023).

[5] Matt Menickelly, Yunsoo Ha, and Matthew Otten, "Latency considerations for stochastic optimizers in variational quantum algorithms", Quantum 7, 949 (2023).

[6] Mohammad Haidar, Marko J. Rančić, Yvon Maday, and Jean-Philip Piquemal, "Extension of the Trotterized Unitary Coupled Cluster to Triple Excitations", The Journal of Physical Chemistry A 127 15, 3543 (2023).

[7] Shashank G. Mehendale, Bo Peng, Niranjan Govind, and Yuri Alexeev, "Exploring Parameter Redundancy in the Unitary Coupled-Cluster Ansätze for Hybrid Variational Quantum Computing", The Journal of Physical Chemistry A 127 20, 4526 (2023).

[8] Benchen Huang, Nan Sheng, Marco Govoni, and Giulia Galli, "Quantum Simulations of Fermionic Hamiltonians with Efficient Encoding and Ansatz Schemes", Journal of Chemical Theory and Computation 19 5, 1487 (2023).

[9] Mark R. Hirsbrunner, Diana Chamaki, J. Wayne Mullinax, and Norm M. Tubman, "Beyond MP2 initialization for unitary coupled cluster quantum circuits", arXiv:2301.05666, (2023).

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

[11] 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, (2022).

[12] Ilias Magoulas and Francesco A. Evangelista, "Unitary Coupled Cluster: Seizing the Quantum Moment", arXiv:2305.01097, (2023).

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