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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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“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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Quantum Algorithm for Calculating Molecular Vibronic Spectra
Sawaya, N. P. D., & Huh, J. (2019) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.9b01117 · Cited by 79
“Many quantum algorithms have been proposed for practical problems in chemistry, chiefly for solving the fermionic problem of determining the lowest-energy configuration of Ne electrons, given the presence of a set of clamped atomic nuclei [15, 16, 17, 18, 19, 20, 21, 22, 23].”
BackgroundComputational complexity in electronic structure
Whitfield, J. D., Love, P. J., & Aspuru-Guzik, A. (2013) · Phys. Chem. Chem. Phys. · doi:10.1039/c2cp42695a · Cited by 71
Self-citationExact and efficient Lanczos method on a quantum computer
Kirby, W., Motta, M., & Mezzacapo, A. (2023) · Quantum · doi:10.22331/q-2023-05-23-1018 · Cited by 81
“Many quantum algorithms for the task have been proposed (see for example [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]) that avoid this representation problem by encoding the system’s Hilbert space in the Hilbert space of a register of qubits, whose dimensi…”
MethodEntanglement spectroscopy on a quantum computer
Johri, S., Steiger, D. S., & Troyer, M. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.96.195136 · Cited by 65
Single-particle digitization strategy for quantum computation of a ϕ4 scalar field theory
Barata, J., Mueller, N., Tarasov, A., & Raju Venugopalan, B. (2021) · Physical Review A · doi:10.1103/physreva.103.042410 · Cited by 78
Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance
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
Self-citationRossmannek, M., Barkoutsos, P. K., Ollitrault, P. J., & Tavernelli, I. (2021) · The Journal of Chemical Physics · doi:10.1063/5.0029536 · Cited by 73
Impact of qubit connectivity on quantum algorithm performance
Holmes, A., Johri, S., Guerreschi, G. G., Clarke, J. S., & Matsuura, A. Y. (2020) · Quantum Science and Technology · doi:10.1088/2058-9565/ab73e0 · Cited by 67
Fixed Depth Hamiltonian Simulation via Cartan Decomposition
Kökcü, E., Steckmann, T., Wang, Y., Freericks, J. K., Dumitrescu, E., & Kemper, A. F. (2022) · Physical Review Letters · doi:10.1103/physrevlett.129.070501 · Cited by 77
Nearly tight Trotterization of interacting electrons
Su, Y., Huang, H.-Y., & Campbell, E. T. (2021) · Quantum · doi:10.22331/q-2021-07-05-495 · Cited by 79
“[3] using phase estimation; later developments have dramatically reduced the cost through various techniques [6, 13, 19, 41, 51, 54, 60, 63, 69, 73, 76].”
MethodDaskin, A., & Kais, S. (2011) · The Journal of Chemical Physics · doi:10.1063/1.3575402 · Cited by 60
Moll, N., Fuhrer, A., Staar, P., & Tavernelli, I. (2016) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/49/29/295301 · Cited by 58
“(1), f1 = h11 − h1212 2 + h1221 + h1441 4 + h22 + h2332 4 , f2 = h1221 4 − h1212 4 , f3 = h1221 4 , f4 = h2332 4 , f5 = h1441 4 , f6 = h1212 4 , f7 = − h11 2 + h1212 4 − h1221 2 − h1441 4 , f8 = h1212 4 − h1221 2 − h22 2 − h2332 4 (32) and can be precomputed using a classical computer [7].”
BackgroundMethodInfluentialOptimized surface code communication in superconducting quantum computers
Javadi-Abhari, A., Gokhale, P., Holmes, A. A., Franklin, D. M., Brown, K. R., Martonosi, M., & Chong, F. T. (2017) · IEEE/ACM International Symposium on Microarchitecture (MICRO) · doi:10.1145/3123939.3123949 · Cited by 69
Variational Quantum-Neural Hybrid Eigensolver
Zhang, S., Wan, Z., Lee, C., Hsieh, C., Zhang, S., & Yao, H. (2022) · Physical Review Letters · doi:10.1103/physrevlett.128.120502 · Cited by 65
“Equipped with error resilient logical qubits in the fault-tolerant quantum computation regime [2], we can efficiently and arbitrarily precisely prepare the ground state of any given Hamiltonian by combining adiabatic evolution with quantum phase estimation [3, 4].”
MethodSugisaki, K., Yamamoto, S., Nakazawa, S., Toyota, K., Sato, K., Shiomi, D., & Takui, T. (2016) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.6b04932 · Cited by 55
Veis, L., Višňák, J., Nishizawa, H., Nakai, H., & Pittner, J. (2016) · International Journal of Quantum Chemistry · doi:10.1002/qua.25176 · Cited by 55
Biamonte, J., Bergholm, V., Whitfield, J. D., Fitzsimons, J., & Aspuru‐Guzik, A. (2011) · AIP Advances · doi:10.1063/1.3598408 · Cited by 56
Self-citationUse of global interactions in efficient quantum circuit constructions
Maslov, D., & Nam, Y. (2017) · New Journal of Physics · doi:10.1088/1367-2630/aaa398 · Cited by 59
“ection 3.1, since it is relevant to our more advanced constructions. Reference [14, Figure 5] shows a two-GMS gate construction of the number excitation operator used in quantum chemistry simulations [15,16]. References [7,17] study the ways to implement quantum algorithms eciently on a trapped ion quantum computer wi…”
MethodInfluentialA dynamic programming approach for distributing quantum circuits by bipartite graphs
Davarzani, Z., Moghadam, M. Z., Houshmand, M., & Nouri-Baygi, M. (2020) · Quantum Information Processing · doi:10.1007/s11128-020-02871-7 · Cited by 53
Solving Quantum Chemistry Problems with a D-Wave Quantum Annealer
Streif, M., Neukart, F., & Leib, M. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-14082-3_10 · Cited by 63
Simulating Periodic Systems on a Quantum Computer Using Molecular Orbitals
Liu, J., Wan, L., Li, Z., & Yang, J. (2020) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.0c00881 · Cited by 54
Opportunities and Challenges of Quantum Computing for Engineering Optimization
Wang, Y., Kim, J. E., & Suresh, K. (2023) · Journal of Computing and Information Science in Engineering · doi:10.1115/1.4062969 · Cited by 55
Variational Quantum Simulation for Quantum Chemistry
Li, Y., Hu, J., Zhang, X., Song, Z., & Yung, M. (2019) · Advanced Theory and Simulations · doi:10.1002/adts.201800182 · Cited by 56
Compilation by stochastic Hamiltonian sparsification
Ouyang, Y., White, D. R., & Campbell, E. T. (2020) · Quantum · doi:10.22331/q-2020-02-27-235 · Cited by 66
Introduction to Quantum Algorithms for Physics and Chemistry
Yung, M. H., Whitfield, J. D., Boixo, S., Tempel, D. G., & Aspuru‐Guzik, A. (2014) · Advances in chemical physics · doi:10.1002/9781118742631.ch03 · Cited by 60
“The explicit circuits for simulating the time evolution operators can be found in Whitfield et al. (2011).”
BackgroundSelf-citationHuang, K., Cai, X., Li, H., Ge, Z.-Y., Hou, R., Li, H., Liu, T., Shi, Y., Chen, C.-T., Zheng, D., et al. (2022) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.2c02381 · Cited by 52
qTorch: The quantum tensor contraction handler
Fried, E., Sawaya, N. P. D., Cao, Y., Kivlichan, I., Romero, J., & Aspuru‐Guzik, A. (2018) · PLoS ONE · doi:10.1371/journal.pone.0208510 · Cited by 48
Self-citationVariational quantum simulation for periodic materials
Yoshioka, N., Sato, T., Nakagawa, Y. O., Ohnishi, Y.-Y., & Mizukami, W. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.013052 · Cited by 54
“[46] for a detailed description of how to realize a UCC ansatz on a quantum circuit.”
BackgroundLi, A., Fang, B., Granade, C., Prawiroatmodjo, G., Heim, B., Roetteler, M., & Krishnamoorthy, S. (2021) · International Conference for High Performance Computing, Networking, Storage and Analysis (SC) · doi:10.1145/3458817.3476169 · Cited by 46
Say NO to Optimization: A Nonorthogonal Quantum Eigensolver
Baek, U., Hait, D., Shee, J., Leimkuhler, O., Huggins, W. J., Stetina, T. F., Head‐Gordon, M., & Whaley, K. B. (2023) · PRX Quantum · doi:10.1103/prxquantum.4.030307 · Cited by 52
“[58] James D Whitfield, Jacob Biamonte, and Alán AspuruGuzik, “Simulation of electronic structure Hamiltonians using quantum computers,” Mol.”
BackgroundLiu, J., Li, Z., & Yang, J. (2021) · The Journal of Chemical Physics · doi:10.1063/5.0054822 · Cited by 53
Subspace methods for electronic structure simulations on quantum computers
Motta, M., Kirby, W., Liepuoniute, I., Sung, K. J., Cohn, J. F., Mezzacapo, A., Klymko, K., Nguyen, N., Yoshioka, N., & Rice, J. E. (2024) · Electronic Structure · doi:10.1088/2516-1075/ad3592 · Cited by 61
Nearly tight Trotterization of interacting electrons
Su, Y., Huang, H.-Y., & Campbell, E. T. (2020) · CaltechAUTHORS (California Institute of Technology) · Cited by 49
Algebraic compression of quantum circuits for Hamiltonian evolution
Kökcü, E., Camps, D., Oftelie, L. B., Freericks, J. K., de Jong, W. A., Beeumen, R. V., & Kemper, A. F. (2022) · Physical Review A · doi:10.1103/physreva.105.032420 · Cited by 46
Hybrid Quantum-Classical Neural Network for Calculating Ground State Energies of Molecules
Xia, R., & Kais, S. (2020) · Entropy · doi:10.3390/e22080828 · Cited by 48
“Many quantum algorithms have been proposed to solve quantum chemistry problems [2–4], such as the Phase Estimation Algorithm; [5–8] to calculate eigenstate energies of simple molecules; the Variational Quantum Eigensolver (VQE) [9–11] to solve electronic structure problems; quantum algorithms for open quantum dynamics…”
MethodFormal Verification of Quantum Programs: Theory, Tools, and Challenges
Lewis, M., Soudjani, S., & Zuliani, P. (2023) · ACM Transactions on Quantum Computing · doi:10.1145/3624483 · Cited by 65
“The hardest algorithms to implement would be some of the 7 algorithms implemented in Quipper [61], which includes quantum walks on Binary Welded Trees [32] and the Ground State Estimation algorithm [101].”
MethodContextuality Test of the Nonclassicality of Variational Quantum Eigensolvers
Kirby, W. M., & Love, P. J. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.200501 · Cited by 47
Multiscale quantum algorithms for quantum chemistry
Ma, H., Liu, J., Shang, H., Fan, Y., Li, Z., & Yang, J. (2023) · Chemical Science · doi:10.1039/d2sc06875c · Cited by 47
Programming the quantum future
Valiron, B., Ross, N. J., Selinger, P., Alexander, D. S., & Smith, J. M. (2015) · Communications of the ACM · doi:10.1145/2699415 · Cited by 43
Compilation by stochastic Hamiltonian sparsification
Ouyang, Y., White, D. R., & Campbell, E. T. (2020) · White Rose Research Online (University of Leeds, The University of Sheffield, University of York) · Cited by 41
Arbitrary controlled-phase gate on fluxonium qubits using differential ac Stark shifts
Xiong, H., Ficheux, Q., Somoroff, A., Nguyen, L. B., Dogan, E., Rosenstock, D., Wang, C., Nesterov, K., Vavilov, M., & Manucharyan, V. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.023040 · Cited by 46
Preparing Bethe Ansatz Eigenstates on a Quantum Computer
Dyke, J. S. V., Barron, G. S., Mayhall, N. J., Barnes, E., & Economou, S. E. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.040329 · Cited by 44
“formed using any of the known algorithms for quantum simulation, whether by Trotterization [16, 77, 78], Taylor expansions [52, 79], or other approaches [51, 80].”
Daskin, A., & Kais, S. (2016) · Cited by 41
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) · International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS) · doi:10.1145/2694344.2694357 · Cited by 43
“• Ground State Estimation (GSE): Uses quantum phase estimation algorithm to estimate the ground state energy of a molecule [48].”
BackgroundConstruction of Green's functions on a quantum computer: Quasiparticle spectra of molecules
Kosugi, T., & Matsushita, Y. (2020) · Physical Review A · doi:10.1103/physreva.101.012330 · Cited by 45
Quantum computing for chemistry and physics applications from a Monte Carlo perspective
Mazzola, G. (2024) · The Journal of Chemical Physics · doi:10.1063/5.0173591 · Cited by 48
“38 As we will see, the choice of second quantization introduces non-locality in the Hamiltonian, which is translated as a sum of tensor products of Pauli matrices (qubits are not fermionic particles) and therefore requires very long circuits.”
BackgroundQuantum computing methods for electronic states of the water molecule
Bian, T., Murphy, D., Xia, R., Daskin, A., & Kais, S. (2019) · Molecular Physics · doi:10.1080/00268976.2019.1580392 · Cited by 44
“[11] James D Whitfield, Jacob Biamonte, and Alán Aspuru-Guzik, “Simulation of electronic structure hamiltonians using quantum computers,” Molecular Physics 109, 735–750 (2011).”
BackgroundVariational quantum eigensolver for dynamic correlation functions
Chen, H., Nusspickel, M., Tilly, J., & Booth, G. H. (2021) · Physical Review A · doi:10.1103/physreva.104.032405 · Cited by 42
Koridon, E., Yalouz, S., Senjean, B., Buda, F., O’Brien, T. E., & Visscher, L. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.033127 · Cited by 44
Quantum Resilience and Distributed Trust: The Promise of Blockchain and Quantum Computing in Defense
Akhai, S., & Kumar, V. (2024) · Contributions to environmental sciences & innovative business technology · doi:10.1007/978-981-97-0088-2_7 · Cited by 39
Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation
Sawaya, N. P. D., Smelyanskiy, M., McClean, J. R., & Aspuru‐Guzik, A. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b00220 · Cited by 37
Self-citationStabilizing multiple topological fermions on a quantum computer
Koh, J. M., Tai, T., Phee, Y. H., Ng, W. E., & Lee, C. H. (2022) · npj Quantum Information · doi:10.1038/s41534-022-00527-1 · Cited by 40
Relativistic quantum chemistry on quantum computers
Veis, L., Višňák, J., Fleig, T., Knecht, S., Saue, T., Visscher, L., & Pittner, J. (2012) · Physical Review A · doi:10.1103/physreva.85.030304 · Cited by 36
Optimized Quantum Phase Estimation for Simulating Electronic States in Various Energy Regimes
Kang, C., Bauman, N. P., Krishnamoorthy, S., & Kowalski, K. (2022) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c00577 · Cited by 41
“One technique, phase estimation-based Hamiltonian simulation, requires only a linear number of qubits relative to the number of orbitals [51].”
BackgroundMethodQuantum entanglement patterns in the structure of atomic nuclei within the nuclear shell model
Pérez-Obiol, A., Masot-Llima, S., Romero, A. M., Menéndez, J., Rios, A., García-Sáez, A., & Juliá-Díaz, B. (2023) · The European Physical Journal A · doi:10.1140/epja/s10050-023-01151-z · Cited by 36
Nakazawa, S., Nishida, S., Ise, T., Yoshino, T., Mori, N., Rahimi, R. D., Sato, K., Morita, Y., Toyota, K., Shiomi, D., et al. (2012) · Angewandte Chemie · doi:10.1002/ange.201204489 · Cited by 35
Tilly, J., Jones, G. A., Chen, H., Wossnig, L., & Grant, E. (2020) · Physical Review A · doi:10.1103/physreva.102.062425 · Cited by 43
Realization of higher-order topological lattices on a quantum computer
Koh, J. M., Tai, T., & Lee, C. H. (2024) · Nature Communications · doi:10.1038/s41467-024-49648-5 · Cited by 46
Heisenberg-limited quantum phase estimation of multiple eigenvalues with few control qubits
Dutkiewicz, A., Terhal, B. M., & Brien, T. E. O. A. (2022) · Quantum · doi:10.22331/q-2022-10-06-830 · Cited by 32
Kang, M., Nuomin, H., Chowdhury, S. N., Yuly, J. L., Sun, K., Whitlow, J., Valdiviezo, J., Zhang, Z., Zhang, P., Beratan, D. N., et al. (2024) · Nature Reviews Chemistry · doi:10.1038/s41570-024-00595-1 · Cited by 40
Castaldo, D., Rosa, M., & Corni, S. (2021) · Physical Review A · doi:10.1103/physreva.103.022613 · Cited by 32
“[26] consisting in the application of a phase gate on each qubit with the phase specified by θ kk ( t j ).”
MethodA stochastic approach to unitary coupled cluster
Filip, M.-A., & Thom, A. J. W. (2020) · The Journal of Chemical Physics · doi:10.1063/5.0026141 · Cited by 39
Hidden Inverses: Coherent Error Cancellation at the Circuit Level
Zhang, B., Majumder, S., Leung, P. H., Crain, S., Wang, Y., Fang, C., Debroy, D. M., Kim, J., & Brown, K. R. (2022) · Physical Review Applied · doi:10.1103/physrevapplied.17.034074 · Cited by 33
“This structure is common in quantum simulation and quantum optimization algorithms [26, 35].”
BackgroundCastaldo, D., Rosa, M., & Corni, S. (2020) · arXiv · doi:10.48550/arxiv.2007.00368 · Cited by 32
Optimal quantum reservoir computing for the noisy intermediate-scale quantum era
Domingo, L., Carlo, G. G., & Borondo, F. (2022) · Physical review. E · doi:10.1103/physreve.106.l043301 · Cited by 36
Hémery, K., Ghanem, K., Crane, E., Campbell, S., Dreiling, J., Figgatt, C., Foltz, C., Gaebler, J., Johansen, J., Mills, M., et al. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.030323 · Cited by 40
“Z can be implemented using staircase circuit using 2( n − 1) two qubit gates [41, 42].”
MethodQuantum computation for periodic solids in second quantization
Ivanov, A. V., Sünderhauf, C., Holzmann, N., Ellaby, T., Kerber, R. N., Jones, G. A., & Camps, J. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.013200 · Cited by 39
Sugisaki, K., Yamamoto, S., Nakazawa, S., Toyota, K., Sato, K., Shiomi, D., & Takui, T. (2018) · Chemical Physics Letters · doi:10.1016/j.cpletx.2018.100002 · Cited by 30
Hybrid quantum-classical algorithm for computing imaginary-time correlation functions
Sakurai, R., Mizukami, W., & Shinaoka, H. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.023219 · Cited by 33
Pastori, L., Olsacher, T., Kokail, C., & Zoller, P. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.030324 · Cited by 39
“Finally, we emphasize that while the examples considered in the present work have focused on DQS of quantum many-body models motivated by condensed matter physics, the technique finds immediate application to the simulation of quantum chemistry problems [80], or the real time dynamics of lattice gauge theories [24, 68…”
BackgroundSelf-Healing of Trotter Error in Digital Adiabatic State Preparation
Kovalsky, L. K., Calderon-Vargas, F. A., Grace, M., Magann, A. B., Larsen, J. B., Baczewski, A., & Sarovar, M. (2023) · Physical Review Letters · doi:10.1103/physrevlett.131.060602 · Cited by 31
Universal programmable quantum circuit schemes to emulate an operator
Daskin, A., Grama, A. Y., Kollias, G., & Kais, S. (2012) · The Journal of Chemical Physics · doi:10.1063/1.4772185 · Cited by 30
A stochastic approach to unitary coupled cluster.
Filip, M.-A., & Thom, A. J. W. (2020) · Apollo (University of Cambridge) · doi:10.17863/cam.60181 · Cited by 29
Sugisaki, K., Sakai, C., Toyota, K., Sato, K., Shiomi, D., & Takui, T. (2021) · Physical Chemistry Chemical Physics · doi:10.1039/d1cp03156b · Cited by 31
Propagation of errors and quantitative quantum simulation with quantum advantage
Flannigan, S., Pearson, N., Low, G. H., Buyskikh, A. S., Bloch, I., Zoller, P., Troyer, M., & Daley, A. J. (2022) · Quantum Science and Technology · doi:10.1088/2058-9565/ac88f5 · Cited by 48
Reordering and Partitioning of Distributed Quantum Circuits
Dadkhah, D., Moghadam, M. Z., Hosseini, S. E., Pławiak, P., & Zhou, X. (2022) · IEEE Access · doi:10.1109/access.2022.3186485 · Cited by 29
“In this paper, as a benchmark, quantum circuits were selected from the RevLib website [10] and Quipper’s library [11], [12] to test the proposed optimization.”
MethodLinear and Logarithmic Time Compositions of Quantum Many-Body Operators
Motzoi, F., Kaicher, M., & Wilhelm, F. K. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.160503 · Cited by 29
Measures of quantum computing speedup
Papageorgiou, A., & Traub, J. F. (2013) · Physical Review A · doi:10.1103/physreva.88.022316 · Cited by 28
Wang, Q., Li, M., Monroe, C. R., & Nam, Y. (2021) · Quantum · doi:10.22331/q-2021-07-26-509 · Cited by 27
“A standard circuit that implements a Trotter term is readily available in [47].”
BackgroundMethodInfluentialBenfenati, F., Mazzola, G., Capecci, C., Barkoutsos, P. K., Ollitrault, P. J., Tavernelli, I., & Guidoni, L. (2021) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.1c00091 · Cited by 34
Quantum simulation of real-space dynamics
Childs, A. M., Leng, J., Li, T., Liu, J.-P., & Zhang, C. (2022) · Quantum · doi:10.22331/q-2022-11-17-860 · Cited by 55
QuRE: The Quantum Resource Estimator toolbox
Suchara, M., Kubiatowicz, J., Faruque, A., Chong, F. T., Lai, C.-Y., & Paz, G. (2013) · 2013 IEEE 31st International Conference on Computer Design (ICCD) · doi:10.1109/iccd.2013.6657074 · Cited by 45
“FOR THE GROUND STATE ESTIMATION ALGORITHM [7].”
InfluentialLocal Convertibility and the Quantum Simulation of Edge States in Many-Body Systems
Franchini, F., Cui, J., Luigi Amico, A., Fan, H., Gu, M., Korepin, V. E., Kwek, L. C., & Vedral, V. (2014) · Physical Review X · doi:10.1103/physrevx.4.041028 · Cited by 29
“[7,8]).”
Accuracy and Compactness in Decision Diagrams for Quantum Computation
Zulehner, A., Niemann, P., Drechsler, R., & Wille, R. (2019) · Design, Automation, and Test in Europe · doi:10.23919/date.2019.8715040 · Cited by 27
“2 shows the size of the state vector (by means of QMDD nodes) while simulating the Ground State Estimation (GSE, [20]) quantum algorithm.”
MethodHamLib: 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. (2024) · Quantum · doi:10.22331/q-2024-12-11-1559 · Cited by 39
“For instance, when researchers wish to test a novel Hamiltonian simulation algorithm [Llo96, WBAG11, LC17, CST + 21] for chemistry, they must first go through the tedious and non-trivial process of preparing a set of chemical Hamiltonians on their own.”
Variational quantum simulation of ultrastrong light-matter coupling
Paolo, A. D., Barkoutsos, P. K., Tavernelli, I., & Blais, A. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.033364 · Cited by 28
“Figure 5(b) provides the compilation of the controlled two-qubit gates in elementary single-and two-qubit gates [42].”
BackgroundQuantum algorithm for the simulation of open-system dynamics and thermalization
Su, H.-Y., & Li, Y. (2020) · Physical Review A · doi:10.1103/physreva.101.012328 · Cited by 27
“where NT is the number of Trotter steps, and each exponential of k-qubit Pauli operator can be implemented on the quantum computer with up to 2(k− 1) CNOT gates and 2k + 1 single-qubit gates [41].”
MethodOptimization of Simultaneous Measurement for Variational Quantum Eigensolver Applications
Gokhale, P., Angiuli, O., Ding, Y., Gui, K., Tomesh, T., Suchara, M., Martonosi, M., & Chong, F. T. (2020) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce49297.2020.00054 · Cited by 29
“These terms are asymptotically dominant [53].”
Divide and conquer approach to quantum Hamiltonian simulation
Hadfield, S., & Papageorgiou, A. (2018) · New Journal of Physics · doi:10.1088/1367-2630/aab1ef · Cited by 25
Simulation of molecular spectroscopy with circuit quantum electrodynamics
Hu, L., Ma, Y.-C., Xu, Y., Wang, W.-T., Ma, Y.-W., Liu, K., Wang, H.-Y., Song, Y.-P., Yung, M.-H., & Sun, L.-Y. (2018) · 中国科学通报：英文版 · doi:10.1016/j.scib.2018.02.001 · Cited by 24
Exponential Improvements in the Simulation of Lattice Gauge Theories Using Near-Optimal Techniques
Rhodes, M. L., Kreshchuk, M., & Pathak, S. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.040347 · Cited by 59
Continuous-variable gate decomposition for the Bose-Hubbard model
Kalajdzievski, T. Z., Weedbrook, C., & Rebentrost, P. (2018) · Physical Review A · doi:10.1103/physreva.97.062311 · Cited by 27
Switchable Next-Nearest-Neighbor Coupling for Controlled Two-Qubit Operations
Zhao, P., Xu, P., Lan, D., Tan, X., Yu, H., & Yu, Y. (2020) · Physical Review Applied · doi:10.1103/physrevapplied.14.064016 · Cited by 25
“These native implementations of three-qubit gates may find useful application for reducing circuit depth of NISQ algorithms [6] and for performing quantum simulations [38, 39].”
MethodAccelerated variational algorithms for digital quantum simulation of many-body ground states
Lyu, C., Montenegro, V., & Bayat, A. (2020) · Quantum · doi:10.22331/q-2020-09-16-324 · Cited by 27
“To overcome these obstacles, the VQE method, a hybrid combination of a quantum circuit and a classical optimizer, has been theoretically investigated [4, 52, 53, 55, 65, 82, 83, 88] and experimentally implemented on various NISQ simulators, including photonic chips [61], ion traps [33, 44, 73], nuclear magnetic resona…”
MethodSimulating Effective QED on Quantum Computers
Stetina, T. F., Ciavarella, A. N., Li, X., & Wiebe, N. (2022) · Quantum · doi:10.22331/q-2022-01-18-622 · Cited by 29
“While Case 1 appears in standard constructions for quantum circuits for simulating chemistry [4], Case 2 does not typically arise in existing quantum circuit constructions and so we provide optimized networks for implementing it, shown in Figure 2.”
BackgroundAdaptive Bayesian quantum algorithm for phase estimation
Smith, J. G., Barnes, C. H. W., & Arvidsson-Shukur, D. R. M. (2024) · Physical Review A · doi:10.1103/physreva.109.042412 · Cited by 29
Communication: Spin-free quantum computational simulations and symmetry adapted states
Whitfield, J. D. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4812566 · Cited by 23
Self-citationResource estimate for quantum many-body ground-state preparation on a quantum computer
Lemieux, J., Duclos-Cianci, G., Sénéchal, D., & Poulin, D. (2021) · Physical Review A · doi:10.1103/physreva.103.052408 · Cited by 27
“Nonetheless, heuristic methods have been proposed [4, 9, 25, 42, 47] that could be efficient for specific physical systems, and exponential-time algorithms [34, 46] could be sufficiently fast for intermediate-size problems.”
MethodKhan, I. T., Tudorovskaya, M., Kirsopp, J. J. M., Ramo, D. M., Warrier, P. W., Papanastasiou, D. K., & Singh, R. (2023) · The Journal of Chemical Physics · doi:10.1063/5.0144680 · Cited by 25
Two Algorithms for Excited-State Quantum Solvers: Theory and Application to EOM-UCCSD
Kim, Y., & Krylov, A. I. (2023) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.3c02480 · Cited by 25
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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