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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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Items 301–400 of 474
Zuniga-Hansen, N., Chi, Y.-C., & Byrd, M. (2012) · Physical Review A · doi:10.1103/physreva.86.042335 · Cited by 7
Decomposition Algorithm of an Arbitrary Pauli Exponential Through a Quantum Circuit
Mansky, M. B., Puigvert, V. R., Castillo, S. L., & Linnhoff–Popien, C. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00056 · Cited by 6
Chee, C. H., Leykam, D., Mak, A. M., & Angelakis, D. G. (2023) · Physical Review A · doi:10.1103/physreva.108.022416 · Cited by 8
“The CNOT ladder B µν in the gate decomposition of the Givens rotation ˆ U µν serves the purpose of encoding the parity of non-exciting qubits into the rotation gate and it consists of a cascade of CNOT gate [28, 40].”
BackgroundResultInfluentialFactorization of large tetra and penta prime numbers on IBM quantum processor
Dhaulakhandi, R., Behera, B. K., & Seo, F. J. (2024) · APL Quantum · doi:10.1063/5.0194993 · Cited by 6
Adiabatic ground-state preparation of fermionic many-body systems from a two-body perspective
van Vreumingen, D., & Schoutens, K. (2023) · Physical Review A · doi:10.1103/physreva.108.062603 · Cited by 6
On connectivity-dependent resource requirements for digital quantum simulation of d-level particles
Sawaya, N. P. D., Guerreschi, G. G., & Holmes, A. A. (2020) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce49297.2020.00031 · Cited by 9
“To approximate the exponential, one may implement [41], [42] the Suzuki-Trotter formula [43], [44]”
MethodQuantum Algorithms for Continuous Problems and Their Applications
Papageorgiou, A., & Traub, J. F. (2014) · Advances in chemical physics · doi:10.1002/9781118742631.ch06 · Cited by 6
“We remark that in [99] extra care is taken to group the terms”
BackgroundTriply-heavy/strange baryons with Cornell potential on a quantum computer
Arenaza, N. M., Gálvez-Viruet, J. J., & Llanes–Estrada, F. J. (2024) · The European Physical Journal A · doi:10.1140/epja/s10050-024-01430-3 · Cited by 7
Exact block encoding of imaginary time evolution with universal quantum neural networks
Rrapaj, E., & Rule, E. (2025) · Physical Review Research · doi:10.1103/physrevresearch.7.013306 · Cited by 7
“[68].”
Iterative quantum phase estimation with optimized sample complexity
van den Berg, E. (2020) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce49297.2020.00011 · Cited by 7
“The importance of quantum phase estimation is highlighted by the wide range of applications that rely on it, including Shor’s prime factorization algorithm [1], quantum chemistry [2], [3], [4], and quantum Metropolis sampling [5].”
MethodQuantum simulation costs for Suzuki-Trotter decomposition of quantum many-body lattice models
Myers, N. M., Scott, R., Park, K., & Scarola, V. W. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.023199 · Cited by 6
“In 1D this transformation takes the form of [9, 10],”
BackgroundMethodAccounting for errors in quantum algorithms via individual error reduction
Otten, M., & Gray, S. K. (2019) · npj Quantum Information · doi:10.1038/s41534-019-0125-3 · Cited by 50
“While methods like quantum phase estimation21 can give generally more accurate energies, VQE requires shorter circuits and has a natural robustness to noise.2,13,22 VQE is not limited to quantum chemistry; it has also been used to study problems in nuclear physics.23 When using VQE for quantum chemistry, the second qu…”
MethodVariational Quantum Algorithms via Measurement-Induced Passive Steering
Sanjaya, S., Volya, D., & Mishra, P. (2024) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce60285.2024.00063 · Cited by 4
“The first stage either initializes a reference state, which can be obtained from mean field calculations like the Hartree-Fock method [21] for problems like electronic structures or initializes ansatz parameters by guessing or by using past data.”
Computing electronic correlation energies using linear depth quantum circuits
Chee, C. H., Mak, A. M., Leykam, D., Barkoutsos, P. K., & Angelakis, D. G. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad1f3a · Cited by 5
“1(b), which is an 8-fold CNOT depth reduction over the traditional 16 sequential CNOT ladders [58].”
BackgroundFermionic quantum computation with Cooper pair splitters
Vilkelis, K., Manesco, A. L. R., Luna, J. D. T., Miles, S., Wimmer, M., & Akhmerov, A. (2024) · SciPost Physics · doi:10.21468/scipostphys.16.5.135 · Cited by 4
“However, the mapping from qubits to local fermionic modes (LFMs) is inefficient because it introduces additional overhead to the calculations [10, 11].”
Error mitigation in variational quantum eigensolvers using tailored probabilistic machine learning
Jiang, T., Rogers, J., Frank, M. S., Christiansen, O., Yao, Y., & Lanatà, N. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.033069 · Cited by 16
Graves, V., Sünderhauf, C., Blunt, N. S., Izsák, R., & Szöri, M. (2025) · ACS Physical Chemistry Au · doi:10.1021/acsphyschemau.5c00030 · Cited by 6
Višňák, J., & Veselý, P. (2017) · EPJ Web of Conferences · doi:10.1051/epjconf/201715401030 · Cited by 4
A Random Approach to Quantum Simulation
Berry, D. W. (2019) · Physics · doi:10.1103/physics.12.91 · Cited by 3
Composable Programming of Hybrid Workflows for Quantum Simulation
Nguyen, T., Oftelie, L. B., Lyakh, D. I., McCaskey, A., Leyton‐Ortega, V., Pooser, R. C., Elwasif, W. R., Humble, T. S., & de Jong, W. A. (2021) · IEEE International Conference on Software Architecture Companion (ICSA-C) · doi:10.1109/icsa-c52384.2021.00028 · Cited by 4
Topological obstructions to quantum computation with unitary oracles
Gavorová, Z., Seidel, M., & Touati, Y. (2024) · Physical Review A · doi:10.1103/physreva.109.032625 · Cited by 22
“Many candidate algorithms for quantum speedup [1–6] use Kitaev’s phase estimation algo-rithm [7].”
MethodNon-iterative disentangled unitary coupled-cluster based on lie-algebraic structure
Haidar, M., Adjoua, O., Badreddine, S., Peruzzo, A., & Piquemal, J. (2025) · Quantum Science and Technology · doi:10.1088/2058-9565/adb3c5 · Cited by 6
“The current landscape of quantum computers resides within the noisy intermediate-scale quantum (NISQ) era, which is constrained primarily by the number of qubits and by the circuit depth [10–13].”
A generalized circuit for the Hamiltonian dynamics through the truncated series
Daskin, A., & Kais, S. (2018) · Quantum Information Processing · doi:10.1007/s11128-018-2099-z · Cited by 4
Calculation of the moscovium ground‐state energy by quantum algorithms
Zaytsev, V. A., Groshev, M. E., Maltsev, I. A., Durova, A. V., & Шабаев, В. М. (2023) · International Journal of Quantum Chemistry · doi:10.1002/qua.27232 · Cited by 5
Quantum Computing Approach to Nonrelativistic and Relativistic Molecular Energy Calculations
Veis, L., & Pittner, J. (2014) · Advances in Chemical Physics · doi:10.1002/9781118742631.ch04 · Cited by 3
Programming Optical-Lattice Fermi-Hubbard Quantum Simulators
Tabares, C., Kokail, C., Zoller, P., González-Cuadra, D., & González-Tudela, A. (2025) · PRX Quantum · doi:10.1103/3nx4-bnyy · Cited by 12
Hakim, D. F., Prayitno, T. B., Choong, P. S., Sarwono, Y. P., & Kwek, L. C. (2026) · Physical Review A · doi:10.1103/jt1n-44dr · Cited by 3
Towards utility-scale electronic structure with sample-based quantum bootstrap embedding
Bierman, J., & Liu, Y. (2026) · Digital Discovery · doi:10.1039/d5dd00416k · Cited by 3
Optimized Quantum Program Execution Ordering to Mitigate Errors in Simulations of Quantum Systems
Tomesh, T., Gui, K., Gokhale, P., Shi, Y., Chong, F. T., Martonosi, M., & Suchara, M. (2021) · IEEE International Conference on Rebooting Computing (ICRC) · doi:10.1109/icrc53822.2021.00013 · Cited by 8
Xu, L., & Freericks, J. K. (2023) · Symmetry · doi:10.3390/sym15071429 · Cited by 4
Geometric Algebra Jordan–Wigner Transformation for Quantum Simulation
Veyrac, G., & Toffano, Z. (2024) · Entropy · doi:10.3390/e26050410 · Cited by 3
“Therefore, fermion creation and annihilation operators and qubit gates do not correspond to the same mathematical structure; this is the reason why a transformation is required to pass from one framework to the other [17].”
BackgroundMethodInfluentialNonunitary Coupled Cluster Enabled by Midcircuit Measurements on Quantum Computers
Fleury, A., Brown, J., Lloyd, E., Hernandez, M., & Kim, I. H. (2024) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.4c00837 · Cited by 3
Simplified projection on total spin zero for state preparation on quantum computers
Rule, E., Stetcu, I., & Carlson, J. (2024) · Physical Review C · doi:10.1103/physrevc.110.064003 · Cited by 3
“A ladder circuit that implements time evolution by a single Pauli string of complexity N c requires 2( N c − 1) cnot s [33] (and additional single-qubit gates that we neglect here).”
Tailoring Fault-Tolerance to Trotter Circuits
Chen, Z., & Rengaswamy, N. (2024) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce60285.2024.00025 · Cited by 3
“Since quantum simulation is a key motivation and application of quantum computers, we consider the problem of executing Trotter circuits fault-tolerantly with optimal depth [11], [12].”
Tarocco, F., Materia, D., Ratini, L., & Guidoni, L. (2025) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/adc4a1 · Cited by 5
“…promising application of quantum algorithms, especially sparkling considerable enthusiasm due to its potential applications in tackling in the realm of quantum chemistry [19–22], aiming to address the electronic structure of large molecules where electron correlation plays a crucial role.”
BackgroundPatil, S. R., Javadi-Abhari, A., Chiang, C.-F., Heckey, J., Martonosi, M., & Chong, F. T. (2014) · IEEE International Symposium on Workload Characterization · doi:10.1109/iiswc.2014.6983057 · Cited by 6
“QPE is a core building block computation for various quantum applications such as solving systems of linear equations [12], prime factorization [27], and finding answers to quantum many-body problems [31, 32].”
BackgroundMethodCharacterization of quantum workloads on SIMD architectures
Risque, R., & Jog, A. (2016) · IEEE International Symposium on Workload Characterization · doi:10.1109/iiswc.2016.7581264 · Cited by 3
“Provides means to simulate a chemical Hamiltonian on a quantum computer [15].”
MethodAnalyzing the spectral density of a perturbed analog quantum simulator using the Keldysh formalism
Zanker, S., Schwenk, I., Reiner, J.-M., Leppäkangas, J., & Marthaler, M. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.97.214301 · Cited by 3
A Comparison of Three Ways to Measure Time-Dependent Densities With Quantum Simulators
Yang, J., Brown, J. C., & Whitfield, J. D. (2021) · Frontiers in Physics · doi:10.3389/fphy.2021.546538 · Cited by 4
“Each individual term in the decomposition above can be simulated efficiently on a quantum computer [27].”
BackgroundSelf-citationQuantum algorithms for simulation of quantum chemistry problems by quantum computers: an appraisal
Sharma, S. (2022) · Foundations of Chemistry · doi:10.1007/s10698-022-09428-9 · Cited by 3
“…for solving chemical problems such as computation of electronic energies, estimation of correlation functions, determination of molecular properties, lattice protein folding and prediction of reaction rates as compared to a classical computer (Bettelli et al. 2003; Whitfield et al. 2011).”
Multistate transition dynamics by strong time-dependent perturbation in NISQ era
Wang, Y., & Krstić, P. (2023) · Journal of Physics Communications · doi:10.1088/2399-6528/ace67a · Cited by 8
Characterizing maximally many-body entangled fermionic states by using M -body density matrix
Giorgadze, I., Huang, H., Gaines, J., König, E. J., & Väyrynen, J. I. (2025) · Quantum · doi:10.22331/q-2025-06-24-1778 · Cited by 5
“(7).”
Dynamical implementation of canonical second quantization on a quantum computer
Gálvez-Viruet, J. J., & Llanes–Estrada, F. J. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.116018 · Cited by 3
MarQSim: Reconciling Determinism and Randomness in Compiler Optimization for Quantum Simulation
Cao, X., Zhou, J., Liu, Y., Shi, Y., & Li, G. (2025) · Proceedings of the ACM on Programming Languages · doi:10.1145/3729269 · Cited by 3
“Given a Hamiltonian with decomposition H = = 1 ℎ 𝑗 𝐻 𝑗 , the Trotter product formula [59] to approximately implement 𝑒 − 𝑖 H 𝑡 is: Note that the formula allows us to approximate the ideal Hamiltonian simulation by selecting sufficiently small time step Δ 𝑡 .”
Tailoring Fault-Tolerance to Quantum Algorithms
Chen, Z., & Rengaswamy, N. (2025) · IEEE Journal on Selected Areas in Information Theory · doi:10.1109/jsait.2025.3602446 · Cited by 4
“In quantum (Hamiltonian) simulation, a common strategy is to expand the Hamiltonian in the orthonormal basis of Hermitian Pauli operators E j to write H = (cid:2) j α j E j , where α j ∈ R [12].”
Chawla, P., Shetty, D., Tsemo, P. B., Sugisaki, K., Riu, J., Nogué, J., Mukherjee, D., & Prasannaa, V. S. (2025) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-025-06876-y · Cited by 4
Formulation and Emulation of Quantum-Inspired Dynamical Systems With Classical Analog Circuits
Cressman, A. J., Wattanapanitch, W., Chuang, I. L., & Sarpeshkar, R. (2022) · Neural Computation · doi:10.1162/neco_a_01481 · Cited by 3
Quantum Computing’s Classical Problem, Classical Computing’s Quantum Problem
Meter, R. V. (2014) · Foundations of Physics · doi:10.1007/s10701-014-9807-z · Cited by 3
Some error analysis for the quantum phase estimation algorithms
Li, X. (2022) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ac7f6c · Cited by 4
“In addition, it also has direct applications in quantum chemistry [3, 27].”
BackgroundCompiler 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 SIGPLAN Notices · doi:10.1145/2775054.2694357 · Cited by 3
Digital Quantum Simulation of Scalar Yukawa Coupling
Kaldenbach, T. N., Heller, M., Alber, G., & Stojanović, V. M. (2024) · Quantum Reports · doi:10.3390/quantum6030024 · Cited by 4
Multi-mode global driving of trapped ions for quantum circuit synthesis
Richerme, P. (2025) · Quantum Science and Technology · doi:10.1088/2058-9565/ade560 · Cited by 4
“For instance, many interesting systems in condensed matter physics, nuclear physics, and quantum chemistry contain multi-body interactions as crucial components of the system the Hamiltonian [49–53].”
Fault-Tolerant Quantum Simulation of Generalized Hubbard Models
Bay-Smidt, A. J., Klausen, F. R., Sünderhauf, C., Izsák, R., Solomon, G. C., & Blunt, N. S. (2025) · PRX Quantum · doi:10.1103/gr4t-b1w5 · Cited by 8
“Two recent papers by Kivlichan et al. [20] and Campbell [21] introduce efficient Trotterization schemes [22–24] to implement time evolution for the Hubbard model.”
Bistafa, C., Takahashi, N., Koyama, J., Sato, S., & Okuno, Y. (2025) · ACS Omega · doi:10.1021/acsomega.5c07817 · Cited by 4
Chemically motivated simulation problems are efficiently solvable on a quantum computer
Schleich, P., Kristensen, L. B., Campos-Gonzalez-Angulo, J. A., Aldossary, A., Avagliano, D., Bagherimehrab, M., Gorgulla, C., Fitzsimons, J., & Aspuru‐Guzik, A. (2025) · Digital Discovery · doi:10.1039/d5dd00377f · Cited by 12
Self-citationIryanti, I., Hue, J. H., Soesanto, Q. M. B., Hanna, M. Y., Rangkuti, C. N., Kwek, L. C., & Sarwono, Y. P. (2025) · Physica Scripta · doi:10.1088/1402-4896/ae2da6 · Cited by 2
Treespilation: architecture- and state-optimised fermion-to-qubit mappings
Miller, A., Glos, A., & Zimborás, Z. (2026) · npj Quantum Information · doi:10.1038/s41534-025-01170-2 · Cited by 2
“E Calculating this cost involves iterating over each T i in ∣ Ψ q”
Parametrized Quantum Circuit Learning for Quantum Chemical Applications
Jones, G. M., Prasad, V. K., Fekl, U., & Jacobsen, H. (2026) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.6c00376 · Cited by 4
Orbital expansion variational quantum eigensolver
Wu, Y., Huang, Z., Sun, J., Yuan, X., Wang, J. B., & Lv, D. (2023) · Quantum Science and Technology · doi:10.1088/2058-9565/acf9c7 · Cited by 2
Chen, M., Zhang, Y., Li, Y., Wang, Z., Li, J., & Li, X. (2022) · International Conference on Computer Aided Design · doi:10.1145/3508352.3549405 · Cited by 2
“a) Benchmarks: We totally collect 158 benchmarks which are selected from the previous work to evaluate QCIR following the method proposed by Whitfield [33], including: 1) quantum workloads from IBM Qiskit [15]’s Github; 2) 9 molecular Hamiltonian simulation workloads generated by ScaffCC [4].”
MethodReducing circuit depth with qubitwise diagonalization
Murairi, E. M., & Cervia, M. J. (2023) · Physical Review A · doi:10.1103/physreva.108.062414 · Cited by 3
Construction of Antisymmetric Variational Quantum States with Real Space Representation
Horiba, T., Shirai, S., & Hirai, H. (2024) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.4c00167 · Cited by 3
Revealing symmetries in quantum computing for many-body systems
van Leeuwen, R. (2024) · New Journal of Physics · doi:10.1088/1367-2630/ad8677 · Cited by 3
“…usually done by first writing the Hamiltonian in a second quantized form, i.e. as an operator in Fock space, and then use the Jordan–Wigner transformation [4–6] to translate the creation and annihilation operators into appropriate tensor products of Pauli matrices that can act on systems of qubits.”
InfluentialRocca, D., Loipersberger, M., Gonthier, J. F., Parrish, R. M., Hong, J., Kang, B., Park, C., & Lee, H.-W. (2024) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce60285.2024.00082 · Cited by 2
Learning density functionals from noisy quantum data
Koridon, E., Frohnert, F., Prehn, E., van Nieuwenburg, E., Tura, J., & Polla, S. (2025) · Machine Learning Science and Technology · doi:10.1088/2632-2153/adcb89 · Cited by 3
“Assuming we have a qubit-based quantum device and Jordan–Wigner Fermion-to-qubit encoding [35, 36], the real-space samples are simply obtained by measuring all qubits in the computational basis as ˆ n j ,σ = ( 1 (cid:0) Z j ,σ ) / 2 (where Z j ,σ is the Pauli Z-operator on the qubit that encodes…”
Order and chaos in Hamiltonian systems with quartic coupling
Ghamari, M. E., Kharbach, J., Chatar, W., Benkhali, M., Masrour, R., Rezzouk, A., & Jamil, M. O. (2022) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-022-03445-5 · Cited by 2
The geometry of parallelism: classical, probabilistic, and quantum effects
Lago, U. D., Faggian, C., Valiron, B., & Yoshimizu, A. (2016) · ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL) · doi:10.1145/3009837.3009859 · Cited by 2
“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].”
MethodOptimization of VQE-UCC Algorithm Based on Spin State Symmetry
Guo, Q., & Chen, P. (2021) · Frontiers in Physics · doi:10.3389/fphy.2021.735321 · Cited by 2
Exploring VQE for Ground State Energy Calculations of Small Molecules With Higher Bond Orders
Rutwik, S., Uttarkar, A., Setlur, A. S., Ashwath Babu, H., & Niranjan, V. (2024) · Global AI Summit - International Conference on Artificial Intelligence and Emerging Technology (AI Summit) · doi:10.1109/globalaisummit62156.2024.10947806 · Cited by 1
“Initially, for smaller molecules like Hydrogen, Neon, water, and so on, we used the QPUs provided by International Business Machines (IBM) Quantum [27] [28] [29].”
Adaptive Variational Quantum Simulations of Periodic Materials Using Qubit-Encoded Wave Functions
Li, X., Fan, Y., Liu, J., Li, Z., & Yang, J. (2025) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5c00412 · Cited by 1
Optimization of the Qubit Coupled Cluster Ansatz on Classical Computers
Ryabinkin, I. G., Jenab, S. M. H., & Genin, S. N. (2025) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5c00345 · Cited by 2
Iterative qubit coupled cluster using only clifford circuits
Brown, J. C., Coons, M. P., Lloyd, E., Fleury, A., Bieniasz, K., Senicourt, V., & Zaribafiyan, A. (2025) · Physica Scripta · doi:10.1088/1402-4896/ae0b08 · Cited by 1
A Review of Quantum Scientific Computing Algorithms Relevant to Computational Mechanics
Raisuddin, O. M., & De, S. (2025) · Archives of Computational Methods in Engineering · doi:10.1007/s11831-025-10321-9 · Cited by 2
“I ⊗ I ⊗ X ⊗ Y ⊗ Z ⊗ I ⊗ I , can be found in references [1] and [83].”
Analyzing Common Electronic Structure Theory Algorithms for Distributed Quantum Computing
Jones, G. M., & Jacobsen, H. (2025) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce65121.2025.10351 · Cited by 1
Adaptive random compiler for Hamiltonian simulation
Fan, Y.-Z., Wu, Y.-X., & Zhang, D.-B. (2025) · Physical Review A · doi:10.1103/4nmq-twj8 · Cited by 1
“In practice, this has led to meaningful improvements in both the accuracy and efficiency of simulations, particularly for electronic structure Hamiltonians [51–54] relevant to quantum chemistry.”
Quantum Machine Learning for Drug Discovery: Taxonomy, Research Challenges, and the Road Ahead
Duong, Y. H. P., Rizvi, S. M. A., McNiven, B. D. E., Nguyen, T. T., Shin, H., Dobre, O. A., & Duong, T. Q. (2025) · ACM Computing Surveys · doi:10.1145/3785660 · Cited by 3
“In the context of drug discovery, QPE plays a central role in algorithms for simulating molecular systems, enabling the calculation of electronic energy levels of drug molecules and protein active sites with high precision [180].”
Simulating fermions with a digital quantum computer
Chien, R. W., Chiew, M., Harrison, B., Necaise, J., Wang, W., Mudassar, M., McLauchlan, C., Henderson, T. M., Scuseria, G. E., Strelchuk, S., et al. (2026) · Nature Reviews Physics · doi:10.1038/s42254-025-00914-5 · Cited by 5
Self-citationAdvancing Full-Stack Acceleration for SchröDinger-Style Quantum Simulation
Liang, S., Lu, Y., Guo, C., Kelly, P. H. J., Luk, W., & Fan, H. (2026) · IEEE International Symposium on High-Performance Computer Architecture (HPCA) · doi:10.1109/hpca68181.2026.11408466 · Cited by 1
“…[4], Bernstein-Vazirani Algorithm (BV), Random Quantum Circuit (RQC) [3], Alternating Layered Ansatz (ALA) [8], Hardware Efficient Ansatz (HEA) [24], Integer Comparison Circuit (ICMP), and Hamiltonian Evolution Simulation via 4th and 6th order Trotterization (Trotter4 and Trotter6) [29], [43].”
Hamiltonian simulation of elastodynamics on a quantum computer via energy conservation mapping
Xu, Y., Zhao, K., Liu, H.-T., Huang, K., Liu, Z., Fan, H., & Hu, H. (2026) · Journal of the Mechanics and Physics of Solids · doi:10.1016/j.jmps.2026.106639 · Cited by 1
Kalam, A., Deb, P., Sakurai, A., Sahoo, B. K., Prasannaa, V. S., & Das, B. P. (2026) · Physical Review Research · doi:10.1103/kmb5-nkqz · Cited by 1
Sarkar, M., Roy, L., Gutal, A. P., Atul Kumar Dnyaan Prasad Global University, & Paranjothy, M. (2026) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.6c00363 · Cited by 4
Framework for Robust Quantum Speedups in Practical Correlated Electronic Structure and Dynamics
Anonymous, & Chan, G. K. (2026) · Physical Review Letters · doi:10.1103/v2ms-wmz1 · Cited by 7
“The amplitudes c ia,jb satisfy an effective Hamiltonian A BE [2] that naturally generalizes the single-exciton case, where the first line again represents single-particle Fock contributions for each electron and hole.”
Quantum Chemistry on a Photonic Chip
Shadbolt, P. (2015) · Springer theses · doi:10.1007/978-3-319-21518-1_5 · Cited by 1
A Quantum Variational Approach to Debugging Combinational Logic Circuits
Demetriou, P., Haupt, C. J., & Nixon, K. J. (2021) · IEEE Computer Society Annual Symposium on VLSI · doi:10.1109/isvlsi51109.2021.00083 · Cited by 1
“Whitfield et al. provide a brief discussion of Trotterisation [24] which has been extended to show the conceptual analogy for comparing Trotterisation to quantum annealing [25].”
BackgroundInfluentialGuaranteed-accuracy quantum annealing
Imoto, T., Seki, Y., Matsuzaki, Y., & Kawabata, S. (2022) · Physical Review A · doi:10.1103/physreva.106.042615 · Cited by 1
Singh, H., Mishra, S., & Majumder, S. (2023) · International Conference on Quantum Technologies, Communications, Computing, Hardware and Embedded Systems Security (iQ-CCHESS) · doi:10.1109/iq-cchess56596.2023.10391502 · Cited by 1
“… God Said”: Toward a Quantum Theology of Creation
Walton, R. D. (2024) · Open Theology · doi:10.1515/opth-2022-0244 · Cited by 1
Quantum circuit for high order perturbation theory corrections
Li, J., & Gao, X. (2024) · Scientific Reports · doi:10.1038/s41598-024-64854-3 · Cited by 1
“3 The circuit before | φ ′ V � is exactly the same quantum circuit that estimates ǫ n , as depicted in Fig.”
BackgroundEmulation of Density Matrix Dynamics With Classical Analog Circuits
Cressman, A. J., & Sarpeshkar, R. (2025) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2025.3552736 · Cited by 1
“Such cases have many practical applications, e.g., in quantum-inspired search at room temperature or in computational chemistry [8].”
Quantum Information Theory on Sparse Wave Functions and Applications for Quantum Chemistry
Materia, D., Ratini, L., & Guidoni, L. (2025) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.5c02137 · Cited by 3
“In the field of Quantum Chemistry, 6,7 this exchange has enabled for existing algorithms 8 − 12 to benefit from the inclusion of chemical concepts, exemplified by the UCCSD ansatz 13 − 17 for variational quantum chemistry algorithms.”
Accuracy and Compactness of DDs in the Quantum Realm
Zulehner, A., & Wille, R. (2020) · Springer eBooks · doi:10.1007/978-3-030-41753-6_8 · Cited by 1
QuaSiMo: A composable library to program hybrid workflows for quantum simulation
Nguyen, T., Oftelie, L. B., Lotshaw, P. C., Lyakh, D. I., McCaskey, A., Leyton‐Ortega, V., Pooser, R. C., Elwasif, W. R., Humble, T. S., & de Jong, W. A. (2021) · IET Quantum Communication · doi:10.1049/qtc2.12024 · Cited by 2
Balanced electron flow and the hydrogen bridge energy levels in Pt, Au, or Cu nanojunctions
Domagalska, I. A., Durajski, A. P., Gruszka, K. M., Wrona, I. A., Krok, K. A., Leoński, W., & Szczȩśniak, R. (2022) · Applied Nanoscience · doi:10.1007/s13204-022-02537-z · Cited by 1
“2020) and are of fundamental importance in the field of quantum computing (Whitfield et al. 2011; Setia and Whitfield 2018).”
BackgroundNumerical Simulations of Noisy Quantum Circuits for Computational Chemistry
Gowrishankar, M., Wright, J., Claudino, D., Lotshaw, P. C., Nguyen, T., McCaskey, A., & Humble, T. S. (2022) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce53715.2022.00128 · Cited by 2
Manenti, R., & Motta, M. (2023) · Oxford University Press eBooks · doi:10.1093/oso/9780198787488.005.0003 · Cited by 1
Nambury, S. B. (2026) · Research Square · doi:10.21203/rs.3.rs-9953338/v1 · Cited by 1
Türkpençe, D., & Gençten, A. (2013) · Journal of Quantum Information Science · doi:10.4236/jqis.2013.32012
“Recent studies about quantum simulations of quantum chemistry problems can be found elsewhere [18-23].”
BackgroundImpact of Quantum Information Technology on Future National Security Space
Bowes, B., Metodi, T. S., Gasster, S. D., Marcus, L., & Reed, S. A. (2011) · AIAA SPACE Conference & Exposition · doi:10.2514/6.2011-7303
Exploring a spectral filtering approach to electronic structure calculations
Kiessling, A. J., & Cina, J. A. (2020) · Molecular Physics · doi:10.1080/00268976.2020.1827178
QuPAA: Exploiting Parallel and Adaptive Architecture to Scale up Quantum Computing
Fu, Y., Sun, Y., & Li, T. (2020) · IEEE International Conference on Computer Design: VLSI in Computers and Processors (ICCD) · doi:10.1109/iccd50377.2020.00037
“These quantum algorithms are Binary Welded Tree (BWT) [19], Class Number (CN) [20], Ground State Estimation [21], Grover’s Search (GS) [8], Secure Hash Algorithm (SHA-1) [22], and Shor’s Algorithm (SHORS) [2].”
Method
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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