Mutual information-assisted adaptive variational quantum eigensolver
Open accessAbstract
Adaptive construction of ansatz circuits offers a promising route towards applicable variational quantum eigensolvers on near-term quantum hardware. Those algorithms aim to build up optimal circuits for a certain problem and ansatz circuits are adaptively constructed by selecting and adding entanglers from a predefined pool. In this work, we propose a way to construct entangler pools with reduced size by leveraging classical algorithms. Our method uses mutual information between the qubits in classically approximated ground state to rank and screen the entanglers. The density matrix renormalization group method is employed for classical precomputation in this work. We corroborate our method numerically on small molecules. Our numerical experiments show that a reduced entangler pool with a small portion of the original entangler pool can achieve same numerical accuracy. We believe that our method paves a new way for adaptive construction of ansatz circuits for variational quantum algorithms.
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Cites
SciPy 1.0: fundamental algorithms for scientific computing in Python
Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., et al. (2020) · Nature Methods · doi:10.1038/s41592-019-0686-2 · Cited by 38,430 · see citing works
<i>Quantum Computation and Quantum Information</i>
Nielsen, M. A., Chuang, I., & Grover, L. K. (2002) · American Journal of Physics · doi:10.1119/1.1463744 · Cited by 21,895 · see citing works
SciPy 1.0: fundamental algorithms for scientific computing in Python
Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., et al. (2019) · Apollo - University of Cambridge Repository · doi:10.17863/cam.64134 · Cited by 10,460 · see citing works
Quantum Computing in the NISQ era and beyond
Preskill, J. (2018) · Quantum · doi:10.22331/q-2018-08-06-79 · Cited by 8,830 · see citing works
Algorithms for quantum computation: discrete logarithms and factoring
Shor, P. W. (2002) · Proceedings 35th Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1994.365700 · Cited by 8,713 · see citing works
Quantum supremacy using a programmable superconducting processor
Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J. C., Barends, R., Biswas, R., Boixo, S., Brandao, F. G. S. L., Buell, D. A., et al. (2019) · Nature · doi:10.1038/s41586-019-1666-5 · Cited by 7,720 · see citing works
A variational eigenvalue solver on a photonic quantum processor
Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.-H., Zhou, X.-Q., Love, P. J., Aspuru-Guzik, A., & O’Brien, J. L. (2014) · Nature Communications · doi:10.1038/ncomms5213 · Cited by 4,552 · cited 1× · see citing works
“There exists a number of quantum algorithms [11–16] for solving the electronic structure problem; and the variational quantum eigensolver (VQE) [13, 14] is one of them which requires a feasible number of quantum gates for near-term devices and has noise resilient feature.”
BackgroundSelf-citationEntanglement in many-body systems
Amico, L., Fazio, R., Osterloh, A., & Vedral, V. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.517 · Cited by 3,745 · see citing works
Quantum Algorithm for Linear Systems of Equations
Harrow, A. W., Hassidim, A., & Lloyd, S. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.150502 · Cited by 3,325 · see citing works
Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets
Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J. M., & Gambetta, J. M. (2017) · Nature · doi:10.1038/nature23879 · Cited by 2,982 · see citing works
�ber das Paulische �quivalenzverbot
Jordan, P., & Wigner, E. (1928) · Zeitschrift f�r Physik · doi:10.1007/bf01331938 · Cited by 2,597 · cited 1× · see citing works
“In this work, Jordan-Wigner (JW) [25], parity and Bravyi-Kitaev (BK) [26] transformations are used and compared.”
MethodThe theory of variational hybrid quantum-classical algorithms
McClean, J. R., Romero, J., Babbush, R., & Aspuru-Guzik, A. (2016) · New Journal of Physics · doi:10.1088/1367-2630/18/2/023023 · Cited by 2,227 · see citing works
Self-citationP y SCF: the Python‐based simulations of chemistry framework
Sun, Q., Berkelbach, T. C., Blunt, N. S., Booth, G. H., Guo, S., Li, Z., Liu, J., McClain, J. D., Sayfutyarova, E. R., Sharma, S., et al. (2017) · Wiley Interdisciplinary Reviews Computational Molecular Science · doi:10.1002/wcms.1340 · Cited by 1,795 · see citing works
Quantum computational chemistry
McArdle, S., Endo, S., Aspuru-Guzik, A., Benjamin, S. C., & Yuan, X. (2020) · Reviews of Modern Physics · doi:10.1103/revmodphys.92.015003 · Cited by 1,621 · see citing works
Self-citationQuantum Chemistry in the Age of Quantum Computing
Cao, Y., Romero, J., Olson, J. P., Degroote, M., Johnson, P. D., Kieferová, M., Kivlichan, I. D., Menke, T., Peropadre, B., Sawaya, N. P. D., et al. (2019) · Chemical Reviews · doi:10.1021/acs.chemrev.8b00803 · Cited by 1,560 · see citing works
Self-citationSimulated Quantum Computation of Molecular Energies
Aspuru-Guzik, A., Dutoi, A. D., Love, P. J., & Head-Gordon, M. (2005) · Science · doi:10.1126/science.1113479 · Cited by 1,418 · see citing works
Self-citationQuantum Chemistry in the Age of Quantum Computing
Cao, Y., Romero, J., Olson, J., Degroote, M., Johnson, P., Kieferová, M., Kivlichan, I., Menke, T., Peropadre, B., Sawaya, N., et al. (n.d.) · OPUS - Open Publications of UTS Scholars (University of Technology Sydney) · Cited by 1,265 · see citing works
Self-citationThe ITensor Software Library for Tensor Network Calculations
Fishman, M., White, S., & Stoudenmire, E. M. (2022) · SciPost Physics Codebases · doi:10.21468/scipostphyscodeb.4 · Cited by 1,084 · see citing works
Bravyi, S. B., & Kitaev, A. Y. (2002) · Annals of Physics · doi:10.1006/aphy.2002.6254 · Cited by 1,033 · see citing works
An adaptive variational algorithm for exact molecular simulations on a quantum computer
Grimsley, H. R., Economou, S. E., Barnes, E., & Mayhall, N. J. (2019) · Nature Communications · doi:10.1038/s41467-019-10988-2 · Cited by 1,033 · see citing works
About the Pauli exclusion principle
Jordán, P., & Wigner, E. P. (1928) · Cited by 951 · see citing works
The Density Matrix Renormalization Group in Quantum Chemistry
Chan, G. K.-L., & Sharma, S. (2011) · Annual Review of Physical Chemistry · doi:10.1146/annurev-physchem-032210-103338 · Cited by 822 · see citing works
Quantum Algorithm Providing Exponential Speed Increase for Finding Eigenvalues and Eigenvectors
Abrams, D. S., & Lloyd, S. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.5162 · Cited by 817 · see citing works
Elucidating reaction mechanisms on quantum computers
Reiher, M., Wiebe, N., Svore, K. M., Wecker, D., & Troyer, M. (2017) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1619152114 · Cited by 745 · see citing works
Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz
Romero, J., Babbush, R., McClean, J. R., Hempel, C., Love, P. J., & Aspuru-Guzik, A. (2019) · Quantum Science and Technology · doi:10.1088/2058-9565/aad3e4 · Cited by 726 · see citing works
Self-citationEnergy Landscapes: Applications to Clusters, Biomolecules and Glasses
Wales, D. J. (2004) · Cited by 637 · see citing works
OpenFermion: the electronic structure package for quantum computers
McClean, J. R., Rubin, N. C., Sung, K. J., Kivlichan, I., Bonet-Monroig, X., Cao, Y., Dai, C., Fried, E., Gidney, C., Gimby, B., et al. (2020) · Quantum Science and Technology · doi:10.1088/2058-9565/ab8ebc · Cited by 525 · see citing works
Benchmarking an 11-qubit quantum computer
Wright, K., Beck, K. M., Debnath, S., Amini, J., Nam, Y., Grzesiak, N., Chen, J.-S., Pisenti, N. C., Chmielewski, M., Collins, C., et al. (2019) · Nature Communications · doi:10.1038/s41467-019-13534-2 · Cited by 521 · see citing works
ProjectQ: An open source software framework for quantum computing
Steiger, D. S., Häner, T., & Troyer, M. (2018) · Quantum · doi:10.22331/q-2018-01-31-49 · Cited by 428 · see citing works
Libcint: An efficient general integral library for Gaussian basis functions
Sun, Q. (2015) · Journal of Computational Chemistry · doi:10.1002/jcc.23981 · Cited by 356 · see citing works
Sichtig, H., Minogue, T. D., Yan, Y., Stefan, C. P., Hall, A. T., Tallon, L. J., Sadzewicz, L., Nadendla, S., Klimke, W. A., Hatcher, E., et al. (2019) · Nature Communications · doi:10.1038/s41467-019-11306-6 · Cited by 328 · see citing works
Optimizing the density-matrix renormalization group method using quantum information entropy
Legeza, Ö., & Sólyom, J. (2003) · Physical review. B, Condensed matter · doi:10.1103/physrevb.68.195116 · Cited by 315 · see citing works
Qubit Coupled Cluster Method: A Systematic Approach to Quantum Chemistry on a Quantum Computer
Ryabinkin, I. G., Yen, T.-C., Genin, S. N., & Izmaylov, A. F. (2018) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.8b00932 · Cited by 287 · see citing works
Measuring orbital interaction using quantum information theory
Rissler, J., Noack, R. M., & White, S. R. (2005) · Chemical Physics · doi:10.1016/j.chemphys.2005.10.018 · Cited by 265 · see citing works
Genuine 12-Qubit Entanglement on a Superconducting Quantum Processor
Gong, M., Chen, M.-C., Zheng, Y., Wang, S., Zha, C., Deng, H., Yan, Z., Rong, H., Wu, Y., Li, S., et al. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.110501 · Cited by 201 · see citing works
Tapering off qubits to simulate fermionic HamiltoniansPreprint
Bravyi, S. B., Gambetta, J., Mezzacapo, A., & Temme, K. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1701.08213 · Cited by 172 · see citing works
Iterative Qubit Coupled Cluster Approach with Efficient Screening of Generators
Ryabinkin, I. G., Lang, R. A., Genin, S. N., & Izmaylov, A. F. (2020) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.9b01084 · Cited by 170 · see citing works
Is the Trotterized UCCSD Ansatz Chemically Well-Defined?
Grimsley, H. R., Claudino, D., Economou, S. E., Barnes, E., & Mayhall, N. J. (2019) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.9b01083 · Cited by 158 · see citing works
The ITensor Software Library for Tensor Network CalculationsPreprint
Fishman, M., White, S. R., & Stoudenmire, E. M. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2007.14822 · Cited by 129 · see citing works
Tranter, A., Love, P. J., Mintert, F., & Coveney, P. V. (2018) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.8b00450 · Cited by 120 · see citing works
autoCAS : A Program for Fully Automated Multiconfigurational Calculations
Stein, C. J., & Reiher, M. (2019) · Journal of Computational Chemistry · doi:10.1002/jcc.25869 · Cited by 104 · see citing works
MADNESS: A Multiresolution, Adaptive Numerical Environment for Scientific Simulation
Harrison, R. J., Beylkin, G., Bischoff, F. A., et al. (2016) · SIAM Journal on Scientific Computing · doi:10.1137/15m1026171 · Cited by 96 · see citing works
MADNESS: A Multiresolution, Adaptive Numerical Environment for Scientific Simulation
Harrison, R. J., Beylkin, G., Bischoff, F. A., et al. (2016) · eScholarship (California Digital Library) · Cited by 92 · see citing works
Tkachenko, N. V., Sud, J., Zhang, Y., Tretiak, S., Anisimov, P. M., Arrasmith, A. T., Coles, P. J., Cincio, L., & Dub, P. A. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.020337 · Cited by 73 · see citing works
TEQUILA: a platform for rapid development of quantum algorithms
Kottmann, J. S., Alperin-Lea, S., Chaney, S., Kesibi, M., Curnow, N. G., Solo, B., Tsilimigkounakis, G., Zendejas-Morales, C., Izmaylov, A. F., Aspuru‐Guzik, A., et al. (2021) · RWTH Publications (RWTH Aachen) · Cited by 68 · see citing works
Self-citationKottmann, J. S., Schleich, P., Tamayo-Mendoza, T., & Aspuru‐Guzik, A. (2021) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.0c03410 · Cited by 48 · see citing works
Self-citationKottmann, J. S., Bischoff, F. A., & Valeev, E. F. (2020) · The Journal of Chemical Physics · doi:10.1063/1.5141880 · Cited by 20 · see citing works
Self-citation
Flagged first, then by citations
Research works printed but not linked: 7
- [8]8. P. W. Atkins and R. S. Friedman, Molecular quantum mechan- ics (Oxford university press, 2011).
- [9]9. T. Helgaker, P. Jorgensen, and J. Olsen, Molecular electronic- structure theory (John Wiley & Sons, 2014).
- [22]22. H. L. Tang, V. Shkolnikov, G. S. Barron, H. R. Grimsley, N. J. Mayhall, E. Barnes, and S. E. Economou, "qubit- adapt-vqe: An adaptive algorithm for constructing hardware- efficient ansatze on a quantum processor," arXiv preprint arXiv:1911.10205 (2019). · arXiv
- [29]29. E. P. Wigner and P. Jordan, " Über das paulische äquivalenzver- bot," Z. Phys 47, 631 (1928).
- [30]30. S. B. Bravyi and A. Y. Kitaev, "Fermionic quantum computa- tion," Ann. Phys. 298, 210 (2002).
- [36]36. Q. Sun, T. C. Berkelbach, N. S. Blunt, G. H. Booth, S. Guo, Z. Li, J. Liu, J. D. McClain, E. R. Sayfutyarova, S. Sharma, et al., "PySCF: the Python-based simulations of chemistry framework," Wiley Interdiscip. Rev. Comput. Mol. Sci. 8, e1340 (2018).
- [43]43. N. V. Tkachenko, J. Sud, Y. Zhang, S. Tretiak, P. M. Anisi- mov, A. T. Arrasmith, P. J. Coles, L. Cincio, and P. A. Dub, "Correlation-informed permutation of qubits for reducing ansatz depth in vqe," arXiv preprint arXiv:2009.04996 (2020). · arXiv
Cited by
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Bharti, K., Cervera-Lierta, A., Kyaw, T. H., Haug, T., Alperin-Lea, S., Anand, A., Degroote, M., Heimonen, H., Kottmann, J. S., Menke, T., et al. (2022) · Reviews of Modern Physics · doi:10.1103/revmodphys.94.015004 · Cited by 1,726 · see citing works
Self-citationThe Variational Quantum Eigensolver: A review of methods and best practices
Tilly, J., Chen, H., Cao, S., Picozzi, D., Setia, K., Li, Y., Grant, E., Wossnig, L., Rungger, I., Booth, G. H., et al. (2022) · Physics Reports · doi:10.1016/j.physrep.2022.08.003 · Cited by 1,031 · see citing works
Noise-induced barren plateaus in variational quantum algorithms
Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., & Coles, P. J. (2021) · Nature Communications · doi:10.1038/s41467-021-27045-6 · Cited by 773 · see citing works
Limitations of Quantum Hardware for Molecular Energy Estimation Using VQE
Carreras, A., Orús, R., & Casanova, D. (2026) · Physical Chemistry Chemical Physics · doi:10.1039/d5cp03907j · Cited by 5 · see citing works
- Authors
- Zhang, Z.-J., Kyaw, T. H., Kottmann, J. S., Degroote, M., & Aspuru-Guzik, A.
- Affiliations
- University of Toronto (CA)
- Venue
- Quantum Science and Technology
- Publisher
- IOP Publishing
- Published
- 2021-07-01
- Volume
- 6
- Issue
- 3
- Pages
- 035001
- ISSN
- 2058-9565 (ISSN-L)
- OpenAlex
- W3121441853
- Semantic Scholar
- 88e8e75586922fe84d4d5f8576f7b566d997ca69
- Cited by
- 52
- References
- 47
- Citations by year
- 2026: 3 · 2025: 10 · 2024: 9 · 2023: 11 · 2022: 11 · 2021: 8
- FWCI
- 3.45
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Quantum Science and Technology (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- OPUS (Augsburg University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Office of Science (Quantum Algorithms Teams Program)
- Google (Google Focused Award)
- Canada 150 Research Chairs Program
- Anders G. Frøseth
- U.S. Department of Energy (DE-SC0019374)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
- Keywords
- variational quantum eigensolver, mutual information, density matrix renormalization group, ground state approximation, small molecules, variational quantum algorithms
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