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Simulated Quantum Computation of Molecular Energies
Open accessAbstract
The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical interest using modest numbers of quantum bits. Calculations of the water and lithium hydride molecular ground-state energies have been carried out on a quantum computer simulator using a recursive phase-estimation algorithm. The recursive algorithm reduces the number of quantum bits required for the readout register from about 20 to 4. Mappings of the molecular wave function to the quantum bits are described. An adiabatic method for the preparation of a good approximate ground-state wave function is described and demonstrated for a stretched hydrogen molecule. The number of quantum bits required scales linearly with the number of basis functions, and the number of gates required grows polynomially with the number of quantum bits.
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In the citing paper
“Previous quantum algorithms to find the ground state of a given Hamiltonian H were based on adiabatic state preparation and quantum phase estimation subroutines [104, 105], both of which have circuit depth requirements beyond those available in the NISQ era.”
From Variational quantum algorithms (2021) · cites this paper as [105]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“The QPE algorithm offers an exponential speedup over classical methods and requires a number of quantum operations O(p−1) to obtain an estimate with precision p (refs 13, 14, 15, 16, 17, 18).”
From A variational eigenvalue solver on a photonic quantum processor (2014) · cites this paper as [15]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“The initial application for chemistry was to obtain molecular energies via quantum phase estimation on a quantum computer (Aspuru-Guzik et al. , 2005).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Aspuru-Guzik et al. , 2005
Experimental — accuracy not yet measuredIn the citing paper
“By exploiting their quantum mechanical properties, quantum computers have been proposed to simulate quantum systems efficiently [9–13].”
From Drug design on quantum computers (2024) · cites this paper as [9]
In the citing paper
“Around the same time, Wiesner 40 and Zalka 41 also suggested using quantum computers for simulating the dynamics of many-body systems.”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [41]
In the citing paper
“Early proposals 40,41 for representing wave functions of quantum systems consider a real-space representation where the spatial wave function ψ ( x ) is discretized into grid points ∑ i ψ i | i 〉 with each | i 〉 being a computational basis state.”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [41]
In the citing paper
“the ability to manipulate a discretization of the wave function directly opened a floodgate of new results in quantum algorithms for quantum chemistry 37,40,41,75,233 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [41]
In the citing paper
“In his pioneering work, Zalka 41 considered discretizing the wave function and initializing simulation through a series of controlled rotations.”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [41]
In the citing paper
“Therefore, the number of terms in He scales polynomially in N, and the integrals {hpq, hpqrs} can be numerically calculated by a classical computer with polynomial resources9.”
From From transistor to trapped-ion computers for quantum chemistry (2014) · cites this paper as [9]
In the citing paper
“On a fault-tolerant computer, one may directly measure the full-CI energy by first preparing a wave function ansatz on the quantum hardware (as in VQE) and then applying the Quantum Phase Estimation algorithm, which projects a prepared state into an energy eigenstate of the Hamiltonian.[111,[132][133][134][135][136]”
From Quantum Computing for Molecular Biology** (2023) · cites this paper as [132]
In the citing paper
“Indeed, the electronic structure problem is considered to be among the first practical applications of QC [91].”
From Quantum computing algorithms: getting closer to critical problems in computational biology (2022) · cites this paper as [91]
In the citing paper
“In particular, it is possible that for some classes of nUDQSs the problems of Trotterization are not as severe as in the case of UDQSs [101].”
From Can one trust quantum simulators? (2012) · cites this paper as [101]
In the citing paper
“But, due to purely dissipative nature of the process, this type of simulation has a certain intrinsic robustness and built-in 'error correction.'”
From Can one trust quantum simulators? (2012) · cites this paper as [101]
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Citations
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Flagged first, then by citations
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- A. Y. Kitaev arXiv e-print ; www.arxiv.org/abs/quant-ph/9511026 (1995). · arXiv
- T. Helgaker P. Jorgensen J. Olsen Molecular Electronic-Structure Theory (Wiley Sussex 2002).
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Brown, K. R., Clark, R. J., & Chuang, I. L. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.050504 · Cited by 98
Quantum Computing for Molecular Biology**
Baiardi, A., Christandl, M., & Reiher, M. (2023) · ChemBioChem · doi:10.1002/cbic.202300120 · Cited by 93
Grimsley, H. R., Barron, G. S., Barnes, E., Economou, S. E., & Mayhall, N. J. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00681-0 · Cited by 93
Biology and medicine in the landscape of quantum advantages
Cordier, B. A., Sawaya, N. P. D., Guerreschi, G. G., & McWeeney, S. K. (2022) · Journal of The Royal Society Interface · doi:10.1098/rsif.2022.0541 · Cited by 87
Klein tunneling and Dirac potentials in trapped ions
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Classical variational simulation of the Quantum Approximate Optimization Algorithm
Medvidović, M., & Carleo, G. (2021) · npj Quantum Information · doi:10.1038/s41534-021-00440-z · Cited by 79
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Liu, H., Low, G. H., Steiger, D. S., Häner, T., Reiher, M., & Troyer, M. (2022) · Materials Theory · doi:10.1186/s41313-021-00039-z · Cited by 73
Orbital-optimized pair-correlated electron simulations on trapped-ion quantum computers
Zhao, L., Goings, J., Shin, K., Kyoung, W., Fuks, J. I., Kevin Rhee, J.-K., Rhee, Y. M., Wright, K., Nguyen, J., Kim, J., et al. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00730-8 · Cited by 73
Mitigating algorithmic errors in a Hamiltonian simulation
Endo, S., Zhao, Q., Li, Y., Benjamin, S., & Yuan, X. (2019) · Physical Review A · doi:10.1103/physreva.99.012334 · Cited by 72
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Computational complexity in electronic structure
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Fault-Tolerant Operation of a Quantum Error-Correction Code
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Li, Z., Yung, M.-H., Chen, H., Lu, D., Whitfield, J. D., Peng, X., Aspuru-Guzik, A., & Du, J. (2011) · Scientific Reports · doi:10.1038/srep00088 · Cited by 63
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Ward, N. J., Kassal, I., & Aspuru-Guzik, A. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3115177 · Cited by 54
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“Indeed, the electronic structure problem is considered to be among the first practical applications of QC [91].”
BackgroundTowards the simulation of large scale protein–ligand interactions on NISQ-era quantum computers
Malone, F. D., Parrish, R. M., Welden, A. R., Fox, T., Degroote, M., Kyoseva, E., Moll, N., Santagati, R., & Streif, M. (2022) · Chemical Science · doi:10.1039/d1sc05691c · Cited by 48
Modelling chemical reactions using semiconductor quantum dots
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Approximating vibronic spectroscopy with imperfect quantum optics
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Babbush, R., Huggins, W. J., Berry, D. W., Ung, S. F., Zhao, A., Reichman, D. R., Neven, H., Baczewski, A. D., & Lee, J. (2023) · Nature Communications · doi:10.1038/s41467-023-39024-0 · Cited by 32
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Self-citationQuantum Information and Computation for Chemistry
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“…and Computation for Chemistry from these tools, Aspuru-Guzik et al. developed a quantum algorithm for computing molecular electronic ground state energies in polynomial time, paving the way for a variety of subsequent developments in quantum computing for chemistry (Aspuru-Guzik et al., 2005).”
BackgroundMethodSelf-citationQuantum computation of eigenvalues within target intervals
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Quantum error correction and fault tolerance: A comprehensive tutorial
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Metadata
- Authors
- Aspuru-Guzik, A., Dutoi, A. D., Love, P. J., & Head-Gordon, M.
- Affiliations
- Department of Chemistry, University of California, Berkeley, CA, USA.
- D-Wave Systems (Canada) (CA)
- Corresponding author
- Dutoi, Anthony D.
- Venue
- Science
- Published
- 2005-09-09
- Volume
- 309
- Issue
- 5741
- Pages
- 1704-1707
- ISSN
- 0036-8075 (ISSN-L)
- 1095-9203
- OpenAlex
- W2052891002
- Cited by
- 1,418
- References
- 13
- Citations by year
- 2026: 125 · 2025: 197 · 2024: 145 · 2023: 175 · 2022: 132 · 2021: 140 · 2020: 100 · 2019: 75 · 2018: 54 · 2017: 27 · 2016: 29 · 2015: 31 · 2014: 33 · 2013: 17 · 2012: 31
- FWCI
- 15.81
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Science (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Digital Access to Scholarship at Harvard (DASH) (Harvard University) (submittedVersion, cc-by)
- Scholarly Commons (University of the Pacific) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- quantum phase estimation, ground state energy, water molecules, lithium hydride, molecular wave functions
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