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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Previous quantum algorithms to find the ground state of a given Hamiltonian H were based on adiabatic state preparation and quantum phase estimation subroutines, both of which have circuit depth requirements beyond those available in the NISQ era.
“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]
Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredThe 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.
“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]
The Abstract (p. 2) says molecular-energy calculations scale exponentially with system size classically but polynomially using quantum algorithms, and identifies recursive phase estimation as the method used. The discussion on p. 6 and Figure 2 caption (p. 14) describe gaining one phase bit per iteration, but our copy does not state that obtaining precision p requires O(p−1) quantum operations. (LLM, conf=0.83)
Experimental — accuracy not yet measuredThe initial application for chemistry was to obtain molecular energies via quantum phase estimation on a quantum computer.
“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
The Abstract (p. 2) reports calculating H2O and LiH molecular ground-state energies on a quantum-computer simulator using recursive phase estimation. The paper supports the application described, but it does not establish that this was the initial application for chemistry; nor does it report a calculation on a physical quantum computer. (LLM, conf=0.84)
Experimental — accuracy not yet measuredQuantum computers have been proposed to simulate quantum systems efficiently.
“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]
Wiesner and Zalka suggested using quantum computers for simulating the dynamics of many-body systems.
“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]
Early proposals for representing wave functions of quantum systems consider a real-space representation where the spatial wave function is discretized into grid points.
“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]
The ability to manipulate a discretization of the wave function directly opened a floodgate of new results in quantum algorithms for quantum chemistry.
“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]
Zalka considered discretizing the wave function and initializing simulation through a series of controlled rotations.
“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]
The number of terms in the electronic Hamiltonian He scales polynomially in N, and the integrals {hpq, hpqrs} can be numerically calculated by a classical computer with polynomial resources.
“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]
On a fault-tolerant computer, full-CI energy can be measured by preparing a wave function ansatz and applying Quantum Phase Estimation, which projects into an energy eigenstate.
“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]
The electronic structure problem is considered to be among the first practical applications of quantum computing.
“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]
It is possible that for some classes of non-universal digital quantum simulators the problems of Trotterization are not as severe as in the case of universal digital quantum simulators.
“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]
OSDQSs have a certain intrinsic robustness and built-in error correction due to the purely dissipative nature of the process.
“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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Accelerated Variational Quantum Eigensolver
Wang, D., Higgott, O., & Brierley, S. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.140504 · Cited by 241 · see citing works
From transistor to trapped-ion computers for quantum chemistry
Yung, M.-H., Casanova, J., Mezzacapo, A., McClean, J., Lamata, L., Aspuru-Guzik, A., & Solano, E. (2014) · Scientific Reports · doi:10.1038/srep03589 · Cited by 221 · see citing works
Self-citationQubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization
Berry, D. W., Gidney, C., Motta, M., McClean, J. R., & Babbush, R. (2019) · Quantum · doi:10.22331/q-2019-12-02-208 · Cited by 222 · see citing works
The prospects of quantum computing in computational molecular biology
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Witnessing eigenstates for quantum simulation of Hamiltonian spectra
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Chemical basis of Trotter-Suzuki errors in quantum chemistry simulation
Babbush, R., McClean, J., Wecker, D., Aspuru-Guzik, A., & Wiebe, N. (2015) · Physical Review A · doi:10.1103/physreva.91.022311 · Cited by 199 · see citing works
Self-citationQuantum simulations of materials on near-term quantum computers
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Adiabatic Quantum Simulation of Quantum Chemistry
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Self-citationDesigning metamaterials with quantum annealing and factorization machines
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Challenges and opportunities in quantum optimization
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Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems
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A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons
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Adding control to arbitrary unknown quantum operations
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Self-citationApplication of fermionic marginal constraints to hybrid quantum algorithms
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A non-orthogonal variational quantum eigensolver
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Faster quantum chemistry simulation on fault-tolerant quantum computers
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Self-citationAnalogue quantum chemistry simulation
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Exponentially more precise quantum simulation of fermions in second quantization
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Self-citationGoings, J. J., White, A., Lee, J., Tautermann, C. S., Degroote, M., Gidney, C., Shiozaki, T., Babbush, R., & Rubin, N. C. (2022) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2203533119 · Cited by 127 · see citing works
Drug design on quantum computers
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Exploiting Locality in Quantum Computation for Quantum Chemistry
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Self-citationUsing Quantum Computers for Quantum Simulation
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Fault-tolerant quantum simulations of chemistry in first quantization
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Self-citationLow-depth circuit ansatz for preparing correlated fermionic states on a quantum computer
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Self-citationConstrained Variational Quantum Eigensolver: Quantum Computer Search Engine in the Fock Space
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Measurements as a roadblock to near-term practical quantum advantage in chemistry: resource analysis
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Measurement reduction in variational quantum algorithms
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Self-citationA study of heuristic guesses for adiabatic quantum computation
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Self-citationQuantum algorithm for obtaining the energy spectrum of molecular systems
Wang, H., Kais, S., Aspuru-Guzik, A., & Hoffmann, M. R. (2008) · Physical Chemistry Chemical Physics · doi:10.1039/b804804e · Cited by 109 · see citing works
Self-citationQuantum Algorithm for Spectral Measurement with a Lower Gate Count
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Quantum algorithm for simulating the dynamics of an open quantum system
Wang, H., Ashhab, S., & Nori, F. (2011) · Physical Review A · doi:10.1103/physreva.83.062317 · Cited by 106 · see citing works
Optimal layout synthesis for quantum computing
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Mostame, S., Rebentrost, P., Eisfeld, A., Kerman, A. J., Tsomokos, D. I., & Aspuru-Guzik, A. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/10/105013 · Cited by 104 · see citing works
Self-citation$O(N^3)$ Measurement Cost for Variational Quantum Eigensolver on Molecular Hamiltonians
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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 · see citing works
Quantum Computing for Molecular Biology**
Baiardi, A., Christandl, M., & Reiher, M. (2023) · ChemBioChem · doi:10.1002/cbic.202300120 · Cited by 93 · see citing works
- 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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