Exploring Parameter Redundancy in the Unitary Coupled-Cluster Ansätze for Hybrid Variational Quantum Computing

Mehendale, Shashank G.; Peng, Bo; Govind, Niranjan; Alexeev, Yuri

doi:10.1021/acs.jpca.3c00550

Exploring Parameter Redundancy in the Unitary Coupled-Cluster Ansätze for Hybrid Variational Quantum Computing

Journal Article · Tue May 16 00:00:00 EDT 2023 · Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory

DOI:https://doi.org/10.1021/acs.jpca.3c00550· OSTI ID:1985900

Mehendale, Shashank G. ^[1]; ^[2]; ^[2]; ^[3]

Indian Institute of Science Education and Research (IISER), Kolkata (India)
Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
Argonne National Laboratory (ANL), Argonne, IL (United States)

One of the commonly used chemical-inspired approaches in variational quantum computing is the unitary coupled-cluster (UCC) ansatze. Despite being a systematic way of approaching the exact limit, the number of parameters in the standard UCC ansatze exhibits unfavorable scaling with respect to the system size, hindering its practical use on near-term quantum devices. Efforts have been taken to propose some variants of UCC ansatze with better scaling. In this paper we explore the parameter redundancy in the preparation of unitary coupled-cluster singles and doubles (UCCSD) ansatze employing spin-adapted formulation, small amplitude filtration, and entropy-based orbital selection approaches. Numerical results of using our approach on some small molecules have exhibited a significant cost reduction in the number of parameters to be optimized and in the time to convergence compared with conventional UCCSD-VQE simulations. Further, we also discuss the potential application of some machine learning techniques in further exploring the parameter redundancy, providing a possible direction for future studies.

View Accepted Manuscript (DOE)

Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States); National Quantum Information Science (QIS) Research Centers (United States). Next Generation Quantum Science and Engineering (Q-NEXT); Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC02-06CH11357; AC05-76RL01830

OSTI ID:: 1985900

Alternate ID(s):: OSTI ID: 2203855

Report Number(s):: PNNL-SA-181544

Journal Information:: Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory, Journal Name: Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory Journal Issue: 20 Vol. 127; ISSN 1089-5639

Publisher:: American Chemical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (58)

A Synergistic Approach towards Optimization of Coupled Cluster Amplitudes by Exploiting Dynamical Hierarchy Patra, Chayan; Agarawal, Valay; Halder, Dipanjali ChemPhysChem, Vol. 24, Issue 4 https://doi.org/10.1002/cphc.202200633	journal	November 2022
New perspectives on unitary coupled-cluster theory Taube, Andrew G.; Bartlett, Rodney J. International Journal of Quantum Chemistry, Vol. 106, Issue 15 https://doi.org/10.1002/qua.21198	journal	January 2006
Orbital entanglement in quantum chemistry Boguslawski, Katharina; Tecmer, Paweł International Journal of Quantum Chemistry, Vol. 115, Issue 19 https://doi.org/10.1002/qua.24832	journal	December 2014
Reduced‐scaling coupled cluster response theory: Challenges and opportunities Crawford, T. Daniel; Kumar, Ashutosh; Bazanté, Alexandre P. Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 9, Issue 4 https://doi.org/10.1002/wcms.1406	journal	January 2019
Use of a unitary wavefunction in the calculation of static electronic properties Pal, Sourav Theoretica Chimica Acta, Vol. 66, Issue 3-4 https://doi.org/10.1007/BF00549670	journal	January 1984
Error analysis and improvements of coupled-cluster theory Kutzelnigg, Werner Theoretica Chimica Acta, Vol. 80, Issue 4-5 https://doi.org/10.1007/BF01117418	journal	January 1991
�ber das Paulische �quivalenzverbot Jordan, P.; Wigner, E. Zeitschrift f�r Physik, Vol. 47, Issue 9-10 https://doi.org/10.1007/BF01331938	journal	September 1928
Alternative coupled-cluster ansätze II. The unitary coupled-cluster method Bartlett, Rodney J.; Kucharski, Stanislaw A.; Noga, Jozef Chemical Physics Letters, Vol. 155, Issue 1 https://doi.org/10.1016/S0009-2614(89)87372-5	journal	February 1989
Measuring orbital interaction using quantum information theory Rissler, Jörg; Noack, Reinhard M.; White, Steven R. Chemical Physics, Vol. 323, Issue 2-3 https://doi.org/10.1016/j.chemphys.2005.10.018	journal	April 2006
Entanglement as measure of electron–electron correlation in quantum chemistry calculations Huang, Zhen; Kais, Sabre Chemical Physics Letters, Vol. 413, Issue 1-3 https://doi.org/10.1016/j.cplett.2005.07.045	journal	September 2005
Recurrence plots for the analysis of complex systems Marwan, N.; Carmenromano, M.; Thiel, M. Physics Reports, Vol. 438, Issue 5-6 https://doi.org/10.1016/j.physrep.2006.11.001	journal	January 2007
The Variational Quantum Eigensolver: A review of methods and best practices Tilly, Jules; Chen, Hongxiang; Cao, Shuxiang Physics Reports, Vol. 986 https://doi.org/10.1016/j.physrep.2022.08.003	journal	November 2022
Resource-Efficient Chemistry on Quantum Computers with the Variational Quantum Eigensolver and the Double Unitary Coupled-Cluster Approach Metcalf, Mekena; Bauman, Nicholas P.; Kowalski, Karol Journal of Chemical Theory and Computation, Vol. 16, Issue 10 https://doi.org/10.1021/acs.jctc.0c00421	journal	September 2020
Machine Learning-Assisted Selection of Active Spaces for Strongly Correlated Transition Metal Systems Golub, Pavlo; Antalik, Andrej; Veis, Libor Journal of Chemical Theory and Computation, Vol. 17, Issue 10 https://doi.org/10.1021/acs.jctc.1c00235	journal	September 2021
CNOT-Efficient Circuits for Arbitrary Rank Many-Body Fermionic and Qubit Excitations Magoulas, Ilias; Evangelista, Francesco A. Journal of Chemical Theory and Computation, Vol. 19, Issue 3 https://doi.org/10.1021/acs.jctc.2c01016	journal	January 2023
Qubit Coupled Cluster Method: A Systematic Approach to Quantum Chemistry on a Quantum Computer Ryabinkin, Ilya G.; Yen, Tzu-Ching; Genin, Scott N. Journal of Chemical Theory and Computation, Vol. 14, Issue 12 https://doi.org/10.1021/acs.jctc.8b00932	journal	November 2018
Generalized Unitary Coupled Cluster Wave functions for Quantum Computation Lee, Joonho; Huggins, William J.; Head-Gordon, Martin Journal of Chemical Theory and Computation, Vol. 15, Issue 1 https://doi.org/10.1021/acs.jctc.8b01004	journal	November 2018
Accuracy and Resource Estimations for Quantum Chemistry on a Near-Term Quantum Computer Kühn, Michael; Zanker, Sebastian; Deglmann, Peter Journal of Chemical Theory and Computation, Vol. 15, Issue 9 https://doi.org/10.1021/acs.jctc.9b00236	journal	August 2019
Iterative Qubit Coupled Cluster Approach with Efficient Screening of Generators Ryabinkin, Ilya G.; Lang, Robert A.; Genin, Scott N. Journal of Chemical Theory and Computation, Vol. 16, Issue 2 https://doi.org/10.1021/acs.jctc.9b01084	journal	January 2020
Projector-Based Quantum Embedding for Molecular Systems: An Investigation of Three Partitioning Approaches Waldrop, Jonathan M.; Windus, Theresa L.; Govind, Niranjan The Journal of Physical Chemistry A, Vol. 125, Issue 29 https://doi.org/10.1021/acs.jpca.1c03821	journal	July 2021
Orbital Entanglement in Bond-Formation Processes Boguslawski, Katharina; Tecmer, Paweł; Barcza, Gergely Journal of Chemical Theory and Computation, Vol. 9, Issue 7 https://doi.org/10.1021/ct400247p	journal	June 2013
Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets Kandala, Abhinav; Mezzacapo, Antonio; Temme, Kristan Nature, Vol. 549, Issue 7671 https://doi.org/10.1038/nature23879	journal	September 2017
A variational eigenvalue solver on a photonic quantum processor Peruzzo, Alberto; McClean, Jarrod; Shadbolt, Peter Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms5213	journal	July 2014
Barren plateaus in quantum neural network training landscapes McClean, Jarrod R.; Boixo, Sergio; Smelyanskiy, Vadim N. Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-07090-4	journal	November 2018
An adaptive variational algorithm for exact molecular simulations on a quantum computer Grimsley, Harper R.; Economou, Sophia E.; Barnes, Edwin Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-10988-2	journal	July 2019
Gate-free state preparation for fast variational quantum eigensolver simulations Meitei, Oinam Romesh; Gard, Bryan T.; Barron, George S. npj Quantum Information, Vol. 7, Issue 1 https://doi.org/10.1038/s41534-021-00493-0	journal	October 2021
Variational quantum eigensolver with reduced circuit complexity Zhang, Yu; Cincio, Lukasz; Negre, Christian F. A. npj Quantum Information, Vol. 8, Issue 1 https://doi.org/10.1038/s41534-022-00599-z	journal	August 2022
Error mitigation extends the computational reach of a noisy quantum processor Kandala, Abhinav; Temme, Kristan; Córcoles, Antonio D. Nature, Vol. 567, Issue 7749 https://doi.org/10.1038/s41586-019-1040-7	journal	March 2019
SciPy 1.0: fundamental algorithms for scientific computing in Python Virtanen, Pauli; Gommers, Ralf; Oliphant, Travis E. Nature Methods https://doi.org/10.1038/s41592-019-0686-2	journal	February 2020
Qubit-excitation-based adaptive variational quantum eigensolver Yordanov, Yordan S.; Armaos, V.; Barnes, Crispin H. W. Communications Physics, Vol. 4, Issue 1 https://doi.org/10.1038/s42005-021-00730-0	journal	October 2021
A quantum computing view on unitary coupled cluster theory Anand, Abhinav; Schleich, Philipp; Alperin-Lea, Sumner Chemical Society Reviews, Vol. 51, Issue 5 https://doi.org/10.1039/D1CS00932J	journal	January 2022
Quantum self-consistent equation-of-motion method for computing molecular excitation energies, ionization potentials, and electron affinities on a quantum computer Asthana, Ayush; Kumar, Ashutosh; Abraham, Vibin Chemical Science, Vol. 14, Issue 9 https://doi.org/10.1039/D2SC05371C	journal	January 2023
Benchmark studies of variational, unitary and extended coupled cluster methods Cooper, Bridgette; Knowles, Peter J. The Journal of Chemical Physics, Vol. 133, Issue 23 https://doi.org/10.1063/1.3520564	journal	December 2010
Correlation problems in atomic and molecular systems. V. Spin‐adapted coupled cluster many‐electron theory Paldus, Josef The Journal of Chemical Physics, Vol. 67, Issue 1 https://doi.org/10.1063/1.434526	journal	July 1977
The closed‐shell coupled cluster single and double excitation (CCSD) model for the description of electron correlation. A comparison with configuration interaction (CISD) results Scuseria, Gustavo E.; Scheiner, Andrew C.; Lee, Timothy J. The Journal of Chemical Physics, Vol. 86, Issue 5 https://doi.org/10.1063/1.452039	journal	March 1987
A unitary multiconfigurational coupled‐cluster method: Theory and applications Hoffmann, Mark R.; Simons, Jack The Journal of Chemical Physics, Vol. 88, Issue 2 https://doi.org/10.1063/1.454125	journal	January 1988
Properties of coupled-cluster equations originating in excitation sub-algebras Kowalski, Karol The Journal of Chemical Physics, Vol. 148, Issue 9 https://doi.org/10.1063/1.5010693	journal	March 2018
Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms Bauman, Nicholas P.; Bylaska, Eric J.; Krishnamoorthy, Sriram The Journal of Chemical Physics, Vol. 151, Issue 1 https://doi.org/10.1063/1.5094643	journal	July 2019
Exact parameterization of fermionic wave functions via unitary coupled cluster theory Evangelista, Francesco A.; Chan, Garnet Kin-Lic; Scuseria, Gustavo E. The Journal of Chemical Physics, Vol. 151, Issue 24 https://doi.org/10.1063/1.5133059	journal	December 2019
Sub-system quantum dynamics using coupled cluster downfolding techniques Kowalski, Karol; Bauman, Nicholas P. The Journal of Chemical Physics, Vol. 152, Issue 24 https://doi.org/10.1063/5.0008436	journal	June 2020
Accelerating coupled cluster calculations with nonlinear dynamics and supervised machine learning Agarawal, Valay; Roy, Samrendra; Chakraborty, Anish The Journal of Chemical Physics, Vol. 154, Issue 4 https://doi.org/10.1063/5.0037090	journal	January 2021
An approximate coupled cluster theory via nonlinear dynamics and synergetics: The adiabatic decoupling conditions Agarawal, Valay; Patra, Chayan; Maitra, Rahul The Journal of Chemical Physics, Vol. 155, Issue 12 https://doi.org/10.1063/5.0060087	journal	September 2021
A hybrid coupled cluster–machine learning algorithm: Development of various regression models and benchmark applications Agarawal, Valay; Roy, Samrendra; Shrawankar, Kapil K. The Journal of Chemical Physics, Vol. 156, Issue 1 https://doi.org/10.1063/5.0072250	journal	January 2022
Relativistic unitary coupled cluster theory and applications Sur, Chiranjib; Chaudhuri, Rajat K.; Sahoo, Bijaya K. Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 41, Issue 6 https://doi.org/10.1088/0953-4075/41/6/065001	journal	March 2008
Mutual information-assisted adaptive variational quantum eigensolver Zhang, Zi-Jian; Kyaw, Thi Ha; Kottmann, Jakob S. Quantum Science and Technology, Vol. 6, Issue 3 https://doi.org/10.1088/2058-9565/abdca4	journal	July 2021
Efficient quantum circuits for quantum computational chemistry Yordanov, Yordan S.; Arvidsson-Shukur, David R. M.; Barnes, Crispin H. W. Physical Review A, Vol. 102, Issue 6 https://doi.org/10.1103/PhysRevA.102.062612	journal	December 2020
Quantum circuits for strongly correlated quantum systems Verstraete, Frank; Cirac, J. Ignacio; Latorre, José I. Physical Review A, Vol. 79, Issue 3 https://doi.org/10.1103/PhysRevA.79.032316	journal	March 2009
Quantum Simulation of Electronic Structure with Linear Depth and Connectivity Kivlichan, Ian D.; McClean, Jarrod; Wiebe, Nathan Physical Review Letters, Vol. 120, Issue 11 https://doi.org/10.1103/PhysRevLett.120.110501	journal	March 2018
Orbital optimized unitary coupled cluster theory for quantum computer Mizukami, Wataru; Mitarai, Kosuke; Nakagawa, Yuya O. Physical Review Research, Vol. 2, Issue 3 https://doi.org/10.1103/PhysRevResearch.2.033421	journal	September 2020
Spin-projection for quantum computation: A low-depth approach to strong correlation Tsuchimochi, Takashi; Mori, Yuto; Ten-no, Seiichiro L. Physical Review Research, Vol. 2, Issue 4 https://doi.org/10.1103/PhysRevResearch.2.043142	journal	October 2020
Entanglement in many-body systems Amico, Luigi; Fazio, Rosario; Osterloh, Andreas Reviews of Modern Physics, Vol. 80, Issue 2 https://doi.org/10.1103/RevModPhys.80.517	journal	May 2008
VQE method: a short survey and recent developments Fedorov, Dmitry A.; Peng, Bo; Govind, Niranjan Materials Theory, Vol. 6, Issue 1 https://doi.org/10.1186/s41313-021-00032-6	journal	January 2022
Recurrence Plots of Dynamical Systems Eckmann, J. -P; Kamphorst, S. Oliffson; Ruelle, D. Europhysics Letters (EPL), Vol. 4, Issue 9 https://doi.org/10.1209/0295-5075/4/9/004	journal	November 1987
Unitary Selective Coupled-Cluster Method Fedorov, Dmitry A.; Alexeev, Yuri; Gray, Stephen K. Quantum, Vol. 6 https://doi.org/10.22331/q-2022-05-02-703	journal	May 2022
Classical and Quantum Algorithms for Orthogonal Neural Networks Kerenidis, Iordanis; Landman, Jonas; Mathur, Natansh arXiv https://doi.org/10.48550/arXiv.2106.07198	preprint	January 2021
Leveraging small scale quantum computers with unitarily downfolded Hamiltonians Huang, Renke; Li, Chenyang; Evangelista, Francesco A. arXiv https://doi.org/10.48550/arXiv.2208.08591	preprint	January 2022
Large-scale sparse wavefunction circuit simulator for applications with the variational quantum eigensolver Mullinax, J. Wayne; Tubman, Norm M. arXiv https://doi.org/10.48550/arXiv.2301.05726	preprint	January 2023
Modeling singlet fission on a quantum computer Claudino, Daniel; Peng, Bo; Kowalski, Karol arXiv https://doi.org/10.48550/arXiv.2301.05752	preprint	January 2023

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