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Simulation of electronic structure Hamiltonians using quantum computers
Open accessAbstract
Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient methods for the exact simulation of quantum systems on classical computers presents a limitation of current computational approaches. We report, in detail, how a set of pre-computed molecular integrals can be used to explicitly create a quantum circuit, i.e. a sequence of elementary quantum operations, that, when run on a quantum computer, obtains the energy of a molecular system with fixed nuclear geometry using the quantum phase estimation algorithm. We extend several known results related to this idea and discuss the adiabatic state preparation procedure for preparing the input states used in the algorithm. With current and near future quantum devices in mind, we provide a complete example using the hydrogen molecule of how a chemical Hamiltonian can be simulated using a quantum computer.
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In the citing paper
“The time the quantum computer must remain coherent is determined by the necessity of O(p−1) successive applications of , each of which can require on the order of millions or billions of quantum gates for practical applications1719, as compared to the tens to hundreds of gates achievable in the short term.”
From A variational eigenvalue solver on a photonic quantum processor (2014) · cites this paper as [17]
Experimental — accuracy not yet measuredIn the citing paper
“Indeed, there are already proposals 200 for NISQ algorithms based on variational principles 201,202 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [201]
In the citing paper
“It is remarkable that the standard quantum-circuit treatment (e.g. see Ref.47) for implementing each involves as many as 2N two-qubit gates for simulating N fermionic modes; in our protocol one needs only two Mølmer-Sørensen gates, which are straightforwardly implementable with current trapped-ion technology.”
From From transistor to trapped-ion computers for quantum chemistry (2014) · cites this paper as [47]
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García-Álvarez, L., Heras, U. L., Mezzacapo, A., Sanz, M., Solano, E., & Lamata, L. (2016) · Scientific Reports · doi:10.1038/srep27836 · Cited by 23
The Geometry of Parallelism. Classical, Probabilistic, and Quantum EffectsPreprint
Lago, U. D., Faggian, C., Valiron, B., & Yoshimizu, A. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1610.09629 · Cited by 25
“Probabilistic and quantum computation are both justified by the very efficient algorithms they give rise to: think about Miller-Rabin primality test [3, 4], Shor’s factorization [5] but also the more recent algorithms for quantum chemistry [6] or for solving linear systems of equations [7].”
MethodSparse Quantum State Preparation for Strongly Correlated Systems
Feniou, C., Adjoua, O., Claudon, B., Zylberman, J., Giner, E., & Piquemal, J. (2024) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.3c03159 · Cited by 27
Hagan, M., & Wiebe, N. (2023) · Quantum · doi:10.22331/q-2023-11-14-1181 · Cited by 33
“The simulation of quantum systems remains one of the most compelling applications for future digital quantum computers [1, 2, 3, 4, 5, 6].”
BackgroundImproved Accuracy for Trotter Simulations Using Chebyshev Interpolation
Rendon, G., Watkins, J., & Wiebe, N. (2024) · Quantum · doi:10.22331/q-2024-02-26-1266 · Cited by 34
Simulating the transverse Ising model on a quantum computer: Error correction with the surface code
You, H., Geller, M. R., & Stancil, P. C. (2013) · Physical Review A · doi:10.1103/physreva.87.032341 · Cited by 20
Tunneling, decoherence, and entanglement of two spins interacting with a dissipative bath
Sahrapour, M. M., & Makri, N. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4795159 · Cited by 21
Stability of the Trotter–Suzuki decomposition
Dhand, I., & Sanders, B. C. (2014) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/47/26/265206 · Cited by 21
Jordan–Wigner transformations for tree structures
Backens, S., Shnirman, A., & Makhlin, Y. (2019) · Scientific Reports · doi:10.1038/s41598-018-38128-8 · Cited by 21
Sugisaki, K., Toyota, K., Sato, K., Shiomi, D., & Takui, T. (2022) · Communications Chemistry · doi:10.1038/s42004-022-00701-8 · Cited by 23
Innan, N., Khan, M. A.-Z., & Bennai, M. (2023) · Materials Today Communications · doi:10.1016/j.mtcomm.2023.107760 · Cited by 24
Kudrow, D., Bier, K., Deng, Z., Franklin, D. M., Tomita, Y., Brown, K. R., & Chong, F. T. (2013) · Proceedings - International Symposium on Computer Architecture/Proceedings · doi:10.1145/2485922.2485937 · Cited by 21
“This is accomplished using quantum phase estimation[33].”
A simulational model for witnessing quantum effects of gravity using IBM quantum computer
Manabputra, Behera, B. K., & Panigrahi, P. K. (2020) · Quantum Information Processing · doi:10.1007/s11128-020-2617-7 · Cited by 28
“3 Circuit corresponding the four unitary matrices [64].”
BackgroundA diagrammatic approach to variational quantum ansatz construction
Herasymenko, Y., & O’Brien, T. E. (2021) · Quantum · doi:10.22331/q-2021-12-02-596 · Cited by 22
“In the rest of the text, we will refer to Pauli-type ansatzes as fundamentally digital: note that Pauli rotations can be directly implemented in a quantum circuit via the techniques of [13].”
MethodQuantum Algorithm for the Direct Calculations of Vertical Ionization Energies
Sugisaki, K., Toyota, K., Sato, K., Shiomi, D., & Takui, T. (2021) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.1c00283 · Cited by 20
Manenti, R., & Motta, M. (2023) · Oxford University Press eBooks · doi:10.1093/oso/9780198787488.005.0002 · Cited by 20
Recompilation-enhanced simulation of electron–phonon dynamics on IBM quantum computers
Jaderberg, B., Eisfeld, A., Jaksch, D., & Mostame, S. (2022) · New Journal of Physics · doi:10.1088/1367-2630/ac8a69 · Cited by 19
Haidar, M., Rančić, M. J., Ayral, T., Maday, Y., & Piquemal, J. (2023) · Wiley Interdisciplinary Reviews Computational Molecular Science · doi:10.1002/wcms.1664 · Cited by 30
Niemann, P., Zulehner, A., Drechsler, R., & Wille, R. (2020) · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · doi:10.1109/tcad.2020.2977603 · Cited by 19
“2 shows the size of the QMDD through simulating the ground state estimation (GSE) [33] quantum algorithm.”
BackgroundInfluentialImplementation of measurement reduction for the variational quantum eigensolver
Ralli, A., Love, P. J., Tranter, A., & Coveney, P. V. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.033195 · Cited by 22
“Quantum circuit to perform a unitary operator given as an exponentiated n-fold tensor product of Pauli operators [49].”
BackgroundMethodGeneralized Zeno Effect and Entanglement Dynamics Induced by Fermion Counting
Starchl, E., Fischer, M. H., & Sieberer, L. M. (2025) · PRX Quantum · doi:10.1103/jppz-vdgn · Cited by 19
Smart, S. E., & Mazziotti, D. A. (2022) · Physical Review A · doi:10.1103/physreva.105.062424 · Cited by 17
“Simulations on quantum computers have a potentially exponential advantage for the computation of many-fermion quantum systems such as molecules and materials [1, 2].”
BackgroundSynthesizing efficient circuits for Hamiltonian simulation
Mukhopadhyay, P., Wiebe, N., & Zhang, H. T. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00697-6 · Cited by 20
“Much work has been done for the construction of quantum circuits for the evolution of molecular systems 16,53 – 59 and the Heisenberg model 60 .”
BackgroundMethodInfluentialOptimizing Shot Assignment in Variational Quantum Eigensolver Measurement
Zhu, L., Liang, S., Yang, C., & Li, X. (2024) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.3c01113 · Cited by 28
Driven multiphoton qubit-resonator interactions
Ayyash, M., Xu, X., Ashhab, S., & Mariantoni, M. (2024) · Physical Review A · doi:10.1103/physreva.110.053711 · Cited by 23
Quantum simulation of Lindbladian dynamics via repeated interactions
Pocrnic, M., Segal, D., & Wiebe, N. (2025) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/adebc4 · Cited by 18
“The latter is more useful when non-unitary algorithms are used to implement each of the U n such that amplitude amplification can be used at the end.”
Analyzing Many-Body Localization with a Quantum Computer
Bauer, B., & Nayak, C. (2014) · Physical Review X · doi:10.1103/physrevx.4.041021 · Cited by 18
Fault-tolerant fermionic quantum computation based on color code
Li, Y. (2018) · Physical Review A · doi:10.1103/physreva.98.012336 · Cited by 21
Using quantum annealers to calculate ground state properties of molecules
Copenhaver, J., Wasserman, A., & Wehefritz-Kaufmann, B. (2021) · The Journal of Chemical Physics · doi:10.1063/5.0030397 · Cited by 19
Magic state distillation and gate compilation in quantum algorithms for quantum chemistry
Trout, C. J., & Brown, K. R. (2015) · International Journal of Quantum Chemistry · doi:10.1002/qua.24856 · Cited by 17
O’Brien, T. E., Ioffe, L. B., Su, Y., Fushman, D., Neven, H., Babbush, R., & Smelyanskiy, V. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.030345 · Cited by 25
“From accurate knowledge of the dipolar couplings between different spins, one can infer the real-space molecular structure.”
BackgroundTao, Y., Zeng, X., Fan, Y., Liu, J., Li, Z., & Yang, J. (2022) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.2c01738 · Cited by 19
A model of randomly-coupled Pauli spins
Hanada, M., Jevicki, A., Liu, X., Rinaldi, E., & Tezuka, M. (2024) · Journal of High Energy Physics · doi:10.1007/jhep05(2024)280 · Cited by 19
“Let us note that having Pauli strings with several terms that are exponentiated is a very common occurrence in quantum chemistry applications [39], such as in the Unitary Coupled-Cluster ansatz, and there exist numerous techniques to synthesize the corresponding quantum circuits, such as those…”
MethodRelation between fermionic and qubit mean fields in the electronic structure problem
Ryabinkin, I. G., Genin, S. N., & Izmaylov, A. F. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5055357 · Cited by 17
Iterative quantum-phase-estimation protocol for shallow circuits
Smith, J. G., Barnes, C. H. W., & Arvidsson-Shukur, D. R. M. (2022) · Physical Review A · doi:10.1103/physreva.106.062615 · Cited by 16
Toward perturbation theory methods on a quantum computer
Li, J., Jones, B., & Kais, S. (2023) · Science Advances · doi:10.1126/sciadv.adg4576 · Cited by 16
“1H, and more details can be found in (35).”
Quantum-assisted Monte Carlo algorithms for fermions
Xu, X., & Li, Y. (2023) · Quantum · doi:10.22331/q-2023-08-03-1072 · Cited by 16
“An established quantum-computing (QC) approach combines Hamiltonian simulation and quantum phase estimation [26, 27].”
MethodBaker, T. E., & Poulin, D. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.043238 · Cited by 20
Computational complexity of time-dependent density functional theory
Whitfield, J. D., Yung, M.-H., Tempel, D. G., Boixo, S., & Aspuru-Guzik, A. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/8/083035 · Cited by 15
Self-citationCarleman-lattice-Boltzmann quantum circuit with matrix access oracles
Sanavio, C., Simon, W., Ralli, A., Love, P. J., & Sauro Succi, A. (2025) · Physics of Fluids · doi:10.1063/5.0254588 · Cited by 15
Digital Quantum Simulation of the Spin-Boson Model under Markovian Open-System Dynamics
Burger, A., Kwek, L. C., & Poletti, D. (2022) · Entropy · doi:10.3390/e24121766 · Cited by 20
Extension of the Trotterized Unitary Coupled Cluster to Triple Excitations
Haidar, M., Rančić, M. J., Maday, Y., & Piquemal, J. (2023) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.3c01753 · Cited by 17
Xiao, X., Zhao, H., Ren, J., Fang, W., & Li, Z. (2024) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.3c00966 · Cited by 21
A query‐based quantum eigensolver
Jin, S., Wu, S., Zhou, G., Li, Y., Li, L., Li, B., & Wang, X. (2020) · Quantum Engineering · doi:10.1002/que2.49 · Cited by 15
A unified framework of transformations based on the Jordan–Wigner transformation
Li, Q.-S., Liu, H., Wang, Q., Wu, Y.-C., & Guo, G. (2022) · The Journal of Chemical Physics · doi:10.1063/5.0107546 · Cited by 16
Meister, R. J., Benjamin, S. C., & Campbell, E. T. (2022) · Quantum · doi:10.22331/q-2022-02-02-637 · Cited by 16
“Following the first concepts for such simulations [2, 3], there have been numerous proposed algorithms to simulate these systems using quantum computers [4–12], often with variations of Trotter-Suzuki product formulas [13, 14].”
MethodVariational quantum algorithms for simulation of Lindblad dynamics
Watad, T., & Lindner, N. H. (2023) · Quantum Science and Technology · doi:10.1088/2058-9565/ad17d8 · Cited by 18
“It is important to note that this is an upper bound and the number of single-qubit and CNOT gates needed for the realization of Pauli-generated rotation operations is significantly smaller as shown in [40, 41].”
BackgroundResultQuantum Approximate Optimization Algorithm for Test Case Optimization
Wang, X., Ali, S., Yue, T., & Arcaini, P. (2024) · IEEE Transactions on Software Engineering · doi:10.1109/tse.2024.3479421 · Cited by 22
“To simulate the problem Hamiltonian in a quantum circuit, we need to create the unitary operator: According to [14], to create the unitary operator e − jγY j σ zj related to the j -th test case (i.e., the j -th qubit), we use the Rz ( θ ) defined in Table 1 in Sect.”
Compiler Management of Communication and Parallelism for Quantum Computation
Heckey, J., Patil, S. R., Javadi-Abhari, A., Holmes, A. A., Kudrow, D., Brown, K. R., Franklin, D. M., Chong, F. T., & Martonosi, M. (2015) · ACM SIGARCH Computer Architecture News · doi:10.1145/2786763.2694357 · Cited by 16
Iterative quantum phase estimation with variationally prepared reference state
Halder, D., Prasannaa, V. S., Agarawal, V., & Maitra, R. (2022) · International Journal of Quantum Chemistry · doi:10.1002/qua.27021 · Cited by 14
Dynamical mean-field theory for the Hubbard-Holstein model on a quantum device
Backes, S., Murakami, Y., 酒井, 志., & Arita, R. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.165155 · Cited by 19
“Using the Jordan-Wigner transformation[4, 42], we represent the electronic creation and annihilation operators by corresponding Pauli operators X,Y, Z via”
MethodHolmes, A. A., Ding, Y., Javadi-Abhari, A., Franklin, D. M., Martonosi, M., & Chong, F. T. (2019) · Microprocessors and Microsystems · doi:10.1016/j.micpro.2019.02.007 · Cited by 14
“We look at two representative benchmarks for the quantum chemistry and quantum simulation fields, the Ising Model [25] and Ground State Estimation [23] algorithms, as well as how performance of these architectures changes as the benchmarks scale up in size.”
BackgroundMethodInfluentialSugisaki, K., Nakazawa, S., Toyota, K., Sato, K., Shiomi, D., & Takui, T. (2019) · Physical Chemistry Chemical Physics · doi:10.1039/c9cp02546d · Cited by 13
Manenti, R., & Motta, M. (2023) · doi:10.1093/oso/9780198787488.001.0001 · Cited by 15
Digital Quantum Simulation of Linear and Nonlinear Optical Elements
Sabín, C. (2020) · Quantum Reports · doi:10.3390/quantum2010013 · Cited by 16
Graph optimization perspective for low-depth Trotter-Suzuki decomposition
Schmitz, A. T., Sawaya, N. P. D., Johri, S., & Matsuura, A. Y. (2024) · Physical Review A · doi:10.1103/physreva.109.042418 · Cited by 28
“All terms smaller than 10 − 6 Hartrees in the second quantized Hamiltonian were removed.”
BackgroundInfluentialDirect application of the phase estimation algorithm to find the eigenvalues of the Hamiltonians
Daskin, A., & Kais, S. (2018) · Chemical Physics · doi:10.1016/j.chemphys.2018.01.002 · Cited by 13
Sugisaki, K., Toyota, K., Sato, K., Shiomi, D., & Takui, T. (2020) · Chemical Science · doi:10.1039/d0sc04847j · Cited by 14
Explicit Quantum Circuit for Simulating the Advection–Diffusion–Reaction Dynamics
Sanavio, C., Mauri, E., & Sauro Succi, A. (2025) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2025.3544839 · Cited by 12
“In fact, when the number of Pauli terms is low, one can implement the corresponding circuit by using a low number of gates exploiting standard tools from Hamiltonian simulation techniques [22].”
Quantum Gaussian process model of potential energy surface for a polyatomic molecule
Dai, J. F., & Krems, R. V. (2022) · The Journal of Chemical Physics · doi:10.1063/5.0088821 · Cited by 16
“Several algorithms have been recently developed for solving electronic structure [1–16] and nuclear dynamics [17– 22] problems on noisy intermediate-scale quantum (NISQ) computers.”
BackgroundResource estimations for the Hamiltonian simulation in correlated electron materials
Kanno, S., Endo, S., Utsumi, T., & Tada, T. (2022) · Physical Review A · doi:10.1103/physreva.106.012612 · Cited by 11
HamLib: A Library of Hamiltonians for Benchmarking Quantum Algorithms and Hardware
Sawaya, N. P. D., Marti-Dafcik, D., Ho, Y., Tabor, D. P., Bernal, D. E., Magann, A. B., Premaratne, S., Dubey, P. K., Matsuura, A. Y., Bishop, N. C., et al. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.10296 · Cited by 12
Materia, D., Ratini, L., Angeli, C., & Guidoni, L. (2024) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.4c03756 · Cited by 15
“One of the most representative examples is the Unitary Coupled Cluster (UCC) method 10;11;12;13;14;15;16 which is a unitary implementation of the widely used Coupled Cluster classical method.”
MethodQudit-based quantum simulation of fermionic systems
Chizzini, M., Tacchino, F., Chiesa, A., Tavernelli, I., Carretta, S., & Santini, P. M. (2024) · Physical Review A · doi:10.1103/physreva.110.062602 · Cited by 11
Quantum computing quantum Monte Carlo algorithm
Zhang, Y., Huang, Y., Sun, J., Lv, D., & Yuan, X. (2025) · Physical Review A · doi:10.1103/jt8s-hzhd · Cited by 27
“In addition to the advanced algorithms, we also consider two types of textbook algorithms, i.e quantum phase estimation (QPE) method [25, 27] and iterative quantum phase estimation (IQPE) [111, 112].”
Sun, S., Marinelli, B., Koh, J. M., Kim, Y., Nguyen, L. B., Chen, L., Kreikebaum, J. M., Santiago, D., Siddiqi, I. A., & Minnich, A. J. (2024) · npj Quantum Information · doi:10.1038/s41534-024-00850-9 · Cited by 15
“To apply the single- or double-controlled gates, we follow the standard multi-qubit Pauli gate decomposition [53] with the base gate as CZ or CCZ and use CNOT gates consisting of native CZ gates dressed by Hadamard gates to extend the weights of the Pauli strings.”
Bondonic Chemistry: Physical Origins and Entanglement Prospects
Putz, M. V., & Ori, O. (2015) · Carbon materials: chemistry and physics/Carbon materials · doi:10.1007/978-94-017-9567-8_10 · Cited by 11
A Randomized Method for Simulating Lindblad Equations and Thermal State Preparation
Chen, H., Li, B., Lu, J., & Ying, L. (2025) · Quantum · doi:10.22331/q-2025-11-20-1917 · Cited by 12
“For the middle term, we apply Trotterization once more, reducing the problem to simulating Hamiltonians formed by Pauli strings.”
The electron density: a fidelity witness for quantum computation
Skogh, M., Dobrautz, W., Lolur, P., Warren, C., Biznárová, J., Osman, A., Tancredi, G., Bylander, J., & Rahm, M. (2023) · Chemical Science · doi:10.1039/d3sc05269a · Cited by 12
Ino, Y., Yonekawa, M., Yuzawa, H., Minato, Y., & Sugisaki, K. (2024) · Physical Chemistry Chemical Physics · doi:10.1039/d4cp03454f · Cited by 11
“63”
Quantum Zeno effect in noisy integrable quantum circuits for impurity models
Tang, Y., Kattel, P., Pixley, J. H., & Andrei, N. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.054313 · Cited by 10
Alfonso, D. R., Lee, Y., Paudel, H. P., & Duan, Y. (2025) · Applied Physics Reviews · doi:10.1063/5.0245874 · Cited by 11
Quantum simulation of the ground-state Stark effect in small molecules: a case study using IBM Q
Tavares, C., Oliveira, S., Fernandes, V., Postnikov, A. V., & Vasilevskiy, M. I. (2021) · Soft Computing · doi:10.1007/s00500-020-05492-5 · Cited by 11
Quantum chemistry on a quantum computer
Fano, G., & Blinder, S. M. (2018) · Elsevier eBooks · doi:10.1016/b978-0-12-813651-5.00011-5 · Cited by 10
Quantum computing for the Lipkin model with unitary coupled cluster and structure learning ansatz *
Chikaoka, A., & Liang, H. (2021) · Chinese Physics C · doi:10.1088/1674-1137/ac380a · Cited by 10
Position Papers for the ASCR Workshop on Basic Research Needs in Quantum Computing and Networking
Lougovski, P., Parekh, O., Broz, J., Byrd, M., Chembo, Y. K., de Jong, W. A., Figueroa, E. V., Humble, T. S., Larson, J. M., Quiroz, G., et al. (2023) · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · doi:10.2172/2283320 · Cited by 10
Composite Qdrift-product formulas for quantum and classical simulations in real and imaginary time
Pocrnic, M., Hagan, M., Carrasquilla, J., Segal, D., & Wiebe, N. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.013224 · Cited by 14
Scalable simulation of nonequilibrium quantum dynamics via classically optimized unitary circuits
Causer, L., Jung, F., Mitra, A., Pollmann, F., & Gammon-Smith, A. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.033062 · Cited by 13
“For rotations of Pauli strings on three qubits, it is well understood how to efficiently implement such gates using only single-qubit gates and CNOTs [101].”
BackgroundQuantum algorithms for computational nuclear physics
Višňák, J. (2015) · EPJ Web of Conferences · doi:10.1051/epjconf/201510001008 · Cited by 9
Sugisaki, K., WAKIMOTO, H., Toyota, K., Sato, K., Shiomi, D., & Takui, T. (2022) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.2c02737 · Cited by 9
Sugisaki, K., Prasannaa, V. S., Ohshima, S., Katagiri, T., Mochizuki, Y., Sahoo, B. K., & Das, B. P. (2023) · Electronic Structure · doi:10.1088/2516-1075/acf909 · Cited by 10
“Subsequently, the quantum circuit corresponding to the time evolution operators is constructed [38] using second-order Trotter–Suzuki decomposition [39–41].”
MethodVariational Quantum Eigensolver Boosted by Adiabatic Connection
Matoušek, M., Pernal, K., Pavošević, F., & Veis, L. (2024) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.3c07590 · Cited by 10
Shortcut to chemically accurate quantum computing via density-based basis-set correction
Traoré, D., Adjoua, O., Feniou, C., Lygatsika, I.-M., Maday, Y., Posenitskiy, E., Hammernik, K., Peruzzo, A., Toulouse, J., Giner, E., et al. (2024) · Communications Chemistry · doi:10.1038/s42004-024-01348-3 · Cited by 10
Iterative method to improve the precision of the quantum-phase-estimation algorithm
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Measuring Trotter error and its application to precision-guaranteed Hamiltonian simulations
Ikeda, T. N., Kono, H., & Fujii, K. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.033285 · Cited by 10
Representation of the fermionic boundary operator
Akhalwaya, I. Y., He, Y., Lior Horesh, C., Jejjala, V., Kirby, W., Naidoo, K., & Ubaru, S. (2022) · Physical Review A · doi:10.1103/physreva.106.022407 · Cited by 8
Adiabatic quantum algorithm for artificial graphene
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Casares, P. A. M., Campos, R., & Martin-Delgado, M. A. (2022) · Quantum · doi:10.22331/q-2022-07-20-768 · Cited by 11
Back to The Future: A Roadmap for Quantum Simulation From Vintage Quantum Chemistry
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“Using the recursive phase estimation procedure define in [2, 42, 98] we can repeat this calculation to estimate E one bit at a time.”
BackgroundMethodInfluentialLight‐Cone Feature Selection for Quantum Machine Learning
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“For example, the Hamiltonian for H 2 in a 4-qubit space appears as [52], with the complete list given in Table I.”
BackgroundChatterjee, A., Rappaport, S., Giri, A., Johri, S., Proctor, T. J., Neira, D. E. B., Sathe, P., & Lubinski, T. (2025) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2025.3558090 · Cited by 12
“In addition, encodings that better manage fermionic antisymmetry, like BK and Parity, might require extra SWAP gates, further increasing circuit depth when implemented on hardware [107], [108].”
Nonvariational ADAPT algorithm for quantum simulations
Tang, H. L., Chen, Y., Biswas, P., Magann, A. B., Arenz, C., & Economou, S. E. (2025) · Physical Review Research · doi:10.1103/x8g1-7h1k · Cited by 13
Kudrow, D., Bier, K., Deng, Z., Franklin, D. M., Tomita, Y., Brown, K. R., & Chong, F. T. (2013) · ACM SIGARCH Computer Architecture News · doi:10.1145/2508148.2485937 · Cited by 7
Numerical simulations of noisy quantum circuits for computational chemistry
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“The advent of quantum computers has motivated the development and testing of new methods for solving familiar problems by using quantum mechanics itself to perform the computation [1, 2, 3, 4].”
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“…involved the transfer of concepts from quantum chemistry to quantum computing 22 , such as, for instance, the Uni-tary Coupled Cluster (UCC) method, which adapts the concept of excitations from the Coupled Cluster method into a variational circuit suitable for quantum devices 23;24;25;26;27;28;29 .”
Simulating Electronic Structure on Bosonic Quantum Computers
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Charged string tensor networks
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Self-citationEngineering analog quantum chemistry Hamiltonians using cold atoms in optical lattices
Argüello-Luengo, J., Shi, T., & González-Tudela, A. (2021) · Physical Review A · doi:10.1103/physreva.103.043318 · Cited by 7
“[22] James D Whitfield, Jacob Biamonte, and Alán AspuruGuzik, “Simulation of electronic structure Hamiltonians using quantum computers,” Molecular Physics 109, 735–750 (2011).”
A Partially Random Trotter Algorithm for Quantum Hamiltonian Simulations
Jin, S., & Li, X. (2023) · Communications on Applied Mathematics and Computation · doi:10.1007/s42967-023-00336-z · Cited by 8
Metadata
- Authors
- Whitfield, J. D., Biamonte, J., & Aspuru-Guzik, A.
- Affiliations
- Harvard University (US)
- Corresponding author
- Whitfield, James D.
- Biamonte, Jacob
- ORCID
- Biamonte, Jacob
- Venue
- Molecular Physics
- Publisher
- Informa UK Limited
- Published
- 2011-03-10
- Volume
- 109
- Issue
- 5
- Pages
- 735-750
- ISSN
- 0026-8976 (ISSN-L)
- 1362-3028
- OpenAlex
- W2103373613
- Cited by
- 472
- References
- 36
- Citations by year
- 2026: 33 · 2025: 54 · 2024: 54 · 2023: 64 · 2022: 49 · 2021: 36 · 2020: 43 · 2019: 23 · 2018: 29 · 2017: 13 · 2016: 14 · 2015: 14 · 2014: 19 · 2013: 11 · 2012: 12
- FWCI
- 13.55
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Molecular Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Engineering and Physical Sciences Research Council (EP/G003017/1)
- 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, quantum circuits, molecular integrals, adiabatic state preparation, molecular hydrogen, quantum chemistry, quantum computing
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