The theory of variational hybrid quantum-classical algorithms
Open accessAbstract
Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as 'the quantum variational eigensolver' was developed (Peruzzo et al 2014 Nat. Commun. 5 4213 ) with the philosophy that even minimal quantum resources could be made useful when used in conjunction with classical routines. In this work we extend the general theory of this algorithm and suggest algorithmic improvements for practical implementations. Specifically, we develop a variational adiabatic ansatz and explore unitary coupled cluster where we establish a connection from second order unitary coupled cluster to universal gate sets through a relaxation of exponential operator splitting. We introduce the concept of quantum variational error suppression that allows some errors to be suppressed naturally in this algorithm on a pre-threshold quantum device. Additionally, we analyze truncation and correlated sampling in Hamiltonian averaging as ways to reduce the cost of this procedure. Finally, we show how the use of modern derivative free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques.
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By considering general commutations and increasing the number of gates of the circuit quadratically with n, the scaling of the number of measurements can be reduced to n^3.
“To this end, it has been shown that by considering general commutations (and increasing the number of gates of the circuit quadratically with n ) the scaling of the number of measurements can be reduced to n 3 [213, 214, 216-219].”
From Variational quantum algorithms (2021) · cites this paper as [218]
Section 4.2.2, “Commuting groups and correlated sampling” (page not provided), says that grouping commuting operators can reduce the number of state preparations. It does not establish an n³ measurement scaling or say that achieving it requires a quadratic increase in circuit gates; it also cautions that correlations can affect measurement costs. (LLM, conf=0.86)
Experimental — accuracy not yet measuredThe Variational Hamiltonian Ansatz was developed to reduce the number of parameters and accelerate convergence.
“Motivated by adiabatic state preparation, the Variational Hamiltonian Ansatz (VHA) was developed to reduce the number of parameters and accelerate the convergence (McClean et al. , 2016; Wecker et al. , 2015).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as McClean et al., 2016
Section 3.2 (page unavailable) describes an ansatz motivated by adiabatic state preparation and says a simple linear path can use as few as one parameter. It does not say the ansatz was developed to reduce parameter count or accelerate convergence. Section 5 discusses faster convergence for particular optimization methods, not for this ansatz. (LLM, conf=0.85)
Experimental — accuracy not yet measuredThe electronic structure problem is one of the most prominent tasks within VQAs and was the pioneering task for VQE.
“The electronic structure problem is one of the most prominent tasks within VQAs (see for example the reviews (Cao et al. , 2019; McArdle et al. , 2020)) and was the pioneering task for VQE (McClean et al. , 2016; Peruzzo et al. , 2014).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as McClean et al. , 2016
Section 2.2 identifies quantum chemistry and the electronic structure problem as an application of particular recent interest for VQE. The Introduction dates VQE’s development to 2014, but does not say that electronic structure was its pioneering task; it describes the original implementation without specifying its task. The broader prominence claim is cited to other reviews, not specifically to this paper. (LLM, conf=0.78)
Experimental — accuracy not yet measuredPauli strings that commute qubit-wise can be measured at the same time.
“Pauli strings that commute qubit-wise, i.e. the Pauli operators on each qubit commute, can be measured at the same time (Kandala et al. , 2017; McClean et al. , 2016).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as McClean et al., 2016
VQE has been proposed to find the ground state of a Hamiltonian in a manner suited for NISQ devices.
“To this end, VQE (McClean et al. , 2016; Peruzzo et al. , 2014) has been proposed, to find the ground state of a Hamiltonian H in a manner that is suited for NISQ devices (Wecker et al. , 2015).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as McClean et al. , 2016
The Boson Sampling model does not have the property of computational equivalence to the gate model.
“In contrast, the Boson Sampling model of computation does not have this property 63 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [63]
Hybrid quantum-classical algorithms partition workload between classical and quantum computers and are important for NISQ hardware.
“An important class of algorithms for NISQ hardware are socalled hybrid quantum-classical algorithms that partition the computational workload between a classical and a quantum computer.[124,125]”
From Quantum Computing for Molecular Biology** (2023) · cites this paper as [124]
Many algorithms for near-term quantum computers are based on variational circuits.
“Many algorithms for near-term quantum computers are based on variational circuits [1-6]”
From Estimating the gradient and higher-order derivatives on quantum hardware (2021) · cites this paper as [4]
The quantum volume definition differs from prior definitions and loosely coincides with the complexity of classically simulating the model circuits.
“This definition differs from [13, 14] and loosely coincides with the complexity of classically simulating the model circuits.”
From Validating quantum computers using randomized model circuits (2019) · cites this paper as [14]
Hybrid quantum-classical algorithms provide ways to use noisy intermediate-scale quantum computers for practical applications.
“Hybrid quantum-classical algorithms, such as the variational quantum eigensolver 2,3 (VQE) and the quantum approximate optimization algorithm 4,5 (QAOA), provide ways to use NISQ computers for practical applications.”
From A generative modeling approach for benchmarking and training shallow quantum circuits (2019) · cites this paper as [3]
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Cites
<i>Quantum Computation and Quantum Information</i>
Nielsen, M. A., Chuang, I., & Grover, L. K. (2002) · American Journal of Physics · doi:10.1119/1.1463744 · Cited by 21,895 · see citing works
Braun, W. J., & Murdoch, D. J. (2021) · Cambridge University Press eBooks · doi:10.1017/9781108993456.011 · Cited by 14,099 · see citing works
(1999) · Cited by 12,854 · see citing works
Nocedal, J. M., & Wright, S. J. (2006) · Springer series in operations research/Springer series in operations research and financial engineering · doi:10.1007/978-0-387-40065-5 · Cited by 9,575 · see citing works
A fifth-order perturbation comparison of electron correlation theories
Raghavachari, K., Trucks, G. W., Pople, J. A., & Head‐Gordon, M. (1989) · Chemical Physics Letters · doi:10.1016/s0009-2614(89)87395-6 · Cited by 8,511 · see citing works
Quantum Computation and Quantum Information: 10th Anniversary Edition
Nielsen, M. A., & Chuang, I. L. (2012) · doi:10.1017/cbo9780511976667 · Cited by 8,436 · see citing works
Simulating physics with computers
Feynman, R. P. (1982) · International Journal of Theoretical Physics · doi:10.1007/bf02650179 · Cited by 7,691 · see citing works
A variational eigenvalue solver on a photonic quantum processor
Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.-H., Zhou, X.-Q., Love, P. J., Aspuru-Guzik, A., & O’Brien, J. L. (2014) · Nature Communications · doi:10.1038/ncomms5213 · Cited by 4,552 · see citing works
Self-citationThe Mathematical Theory of Optimal Processes
Bellman, R., Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., Mishchenko, E. F., Trirogoff, Κ. N., & Neustadt, L. W. (1965) · Econometrica · doi:10.2307/1911909 · Cited by 4,212 · see citing works
Coupled-cluster theory in quantum chemistry
Bartlett, R. J., & Musiał, M. (2007) · Reviews of Modern Physics · doi:10.1103/revmodphys.79.291 · Cited by 3,343 · see citing works
Čı́žek, J. (1966) · The Journal of Chemical Physics · doi:10.1063/1.1727484 · Cited by 3,105 · see citing works
�ber das Paulische �quivalenzverbot
Jordan, P., & Wigner, E. (1928) · Zeitschrift f�r Physik · doi:10.1007/bf01331938 · Cited by 2,597 · see citing works
Molecular Electronic‐Structure Theory
Helgaker, T., Jørgensen, P., & Olsen, J. (2000) · doi:10.1002/9781119019572 · Cited by 2,594 · see citing works
On the product of semi-groups of operators
Trotter, H. F. (1959) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-1959-0108732-6 · Cited by 2,282 · see citing works
A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
Farhi, E., Goldstone, J., Gutmann, S., Lapan, J., Lundgren, A., & Preda, D. (2001) · Science · doi:10.1126/science.1057726 · Cited by 2,056 · see citing works
Kalos, M. H., & Whitlock, P. A. (1986) · Wiley eBooks · doi:10.1002/9783527617395 · Cited by 1,550 · see citing works
Molecular electronic-structure theory
Ratner, M. A. (2000) · Cited by 1,506 · see citing works
Born, M., & Fock, V. (1928) · Zeitschrift f�r Physik · doi:10.1007/bf01343193 · Cited by 1,494 · see citing works
Simulated Quantum Computation of Molecular Energies
Aspuru-Guzik, A., Dutoi, A. D., Love, P. J., & Head-Gordon, M. (2005) · Science · doi:10.1126/science.1113479 · Cited by 1,418 · see citing works
Self-citationDerivative-free optimization: a review of algorithms and comparison of software implementations
Rios, L. M., & Sahinidis, N. V. (2013) · Journal of Global Optimization · doi:10.1007/s10898-012-9951-y · Cited by 1,276 · see citing works
Short-range correlations in nuclear wave functions
Coester, F., & Kümmel, H. G. (1960) · Nuclear Physics · doi:10.1016/0029-5582(60)90140-1 · Cited by 1,261 · see citing works
Many-Body Methods in Chemistry and Physics
Shavitt, I., & Bartlett, R. J. (2009) · Cambridge University Press eBooks · doi:10.1017/cbo9780511596834 · Cited by 1,257 · see citing works
Aspuru-Guzik, A., & Walther, P. (2012) · Nature Physics · doi:10.1038/nphys2253 · Cited by 952 · see citing works
Self-citationAbout the Pauli exclusion principle
Jordán, P., & Wigner, E. P. (1928) · Cited by 951 · see citing works
Quantum Algorithm Providing Exponential Speed Increase for Finding Eigenvalues and Eigenvectors
Abrams, D. S., & Lloyd, S. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.5162 · Cited by 817 · see citing works
Towards quantum chemistry on a quantum computer
Lanyon, B. P., Whitfield, J. D., Gillett, G. G., Goggin, M. E., Almeida, M. P., Kassal, I., Biamonte, J. D., Mohseni, M., Powell, B. J., Barbieri, M., et al. (2010) · Nature Chemistry · doi:10.1038/nchem.483 · Cited by 796 · see citing works
Self-citationSimulation of Many-Body Fermi Systems on a Universal Quantum Computer
Abrams, D. S., & Lloyd, S. (1997) · Physical Review Letters · doi:10.1103/physrevlett.79.2586 · Cited by 745 · see citing works
MONTE CARLO METHODS IN AB INITIO QUANTUM CHEMISTRY
Hammond, B. L., & Lester, W. A. J. (1994) · World Scientific lecture and course notes in chemistry · doi:10.1142/9789814317245 · Cited by 697 · see citing works
The Complexity of the Local Hamiltonian Problem
Kempe, J., Kitaev, A., & Regev, O. (2006) · SIAM Journal on Computing · doi:10.1137/s0097539704445226 · Cited by 648 · see citing works
Quantum search by local adiabatic evolution
Roland, J., & Cerf, N. J. (2002) · Physical Review A · doi:10.1103/physreva.65.042308 · Cited by 629 · see citing works
The Bravyi-Kitaev transformation for quantum computation of electronic structure
Seeley, J. T., Richard, M. J., & Love, P. J. (2012) · The Journal of Chemical Physics · doi:10.1063/1.4768229 · Cited by 585 · see citing works
Solving Schrödinger’s equation around a desired energy: Application to silicon quantum dots
Wang, L., & Zunger, A. (1994) · The Journal of Chemical Physics · doi:10.1063/1.466486 · Cited by 556 · see citing works
Quantum Computation as Geometry
Nielsen, M. A., Dowling, M. R., Gu, M., & Doherty, A. C. (2006) · Science · doi:10.1126/science.1121541 · Cited by 539 · see citing works
Quantum Computation by Adiabatic Evolution
Farhi, E., Goldstone, J., Gutmann, S., & Sipser, M. (2000) · arXiv · doi:10.48550/arxiv.quant-ph/0001106 · Cited by 536 · see citing works
Simulation of electronic structure Hamiltonians using quantum computers
Whitfield, J. D., Biamonte, J., & Aspuru-Guzik, A. (2011) · Molecular Physics · doi:10.1080/00268976.2011.552441 · Cited by 472 · see citing works
Self-citationAdiabatic Quantum Computation Is Equivalent to Standard Quantum Computation
Aharonov, D., van Dam, W., Kempe, J., Landau, Z., Lloyd, S., & Regev, O. (2008) · SIAM Review · doi:10.1137/080734479 · Cited by 395 · see citing works
Mazziotti, D. A. (1998) · Physical Review A · doi:10.1103/physreva.57.4219 · Cited by 391 · see citing works
Eigenvalue computation in the 20th century
Golub, G. H., & van der Vorst, H. A. (2000) · Journal of Computational and Applied Mathematics · doi:10.1016/s0377-0427(00)00413-1 · Cited by 388 · see citing works
Polynomial-time quantum algorithm for the simulation of chemical dynamics
Kassal, I., Jordan, S. P., Love, P. J., Mohseni, M., & Aspuru-Guzik, A. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0808245105 · Cited by 385 · see citing works
Self-citationSimulating physical phenomena by quantum networks
Somma, R. D., Ortíz, G., Gubernatis, J. E., Knill, E. H., & Laflamme, R. (2002) · Physical Review A · doi:10.1103/physreva.65.042323 · Cited by 364 · see citing works
Simulating Chemistry Using Quantum Computers
Kassal, I., Whitfield, J. D., Perdomo-Ortiz, A., Yung, M.-H., & Aspuru-Guzik, A. (2011) · Annual Review of Physical Chemistry · doi:10.1146/annurev-physchem-032210-103512 · Cited by 352 · see citing works
Self-citationMaximum-likelihood estimation of the density matrix
Banaszek, K., D’Ariano, G. M., Paris, M. G. A., & Sacchi, M. F. (1999) · Physical Review A · doi:10.1103/physreva.61.010304 · Cited by 342 · see citing works
Boson sampling for molecular vibronic spectra
Huh, J., Guerreschi, G. G., Peropadre, B., McClean, J. R., & Aspuru-Guzik, A. (2015) · Nature Photonics · doi:10.1038/nphoton.2015.153 · Cited by 341 · see citing works
Self-citationGate-count estimates for performing quantum chemistry on small quantum computers
Wecker, D., Bauer, B., Clark, B. K., Hastings, M. B., & Troyer, M. (2014) · Physical Review A · doi:10.1103/physreva.90.022305 · Cited by 296 · see citing works
Most Quantum States Are Too Entangled To Be Useful As Computational Resources
Gross, D., Flammia, S. T., & Eisert, J. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.190501 · Cited by 279 · see citing works
A new Monte Carlo technique: antithetic variates
Hammersley, J. M., & Morton, K. W. (1956) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100031455 · Cited by 269 · see citing works
Quantum Simulation of Time-Dependent Hamiltonians and the Convenient Illusion of Hilbert Space
Poulin, D., Qarry, A., Somma, R., & Verstraete, F. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.170501 · Cited by 265 · see citing works
New perspectives on unitary coupled‐cluster theory
Taube, A. G., & Bartlett, R. J. (2006) · International Journal of Quantum Chemistry · doi:10.1002/qua.21198 · Cited by 254 · see citing works
A multi-reference coupled-cluster method for molecular applications
Laidig, W. D., & Bartlett, R. J. (1984) · Chemical Physics Letters · doi:10.1016/0009-2614(84)85617-1 · Cited by 250 · see citing works
Recent Progress in Coupled Cluster Methods
Čárský, P., Paldus, J., & Pittner, J. (2010) · Challenges and advances in computational chemistry and physics · doi:10.1007/978-90-481-2885-3 · Cited by 246 · 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-citationSimulation of Electronic Structure Hamiltonians Using Quantum Computers
Whitfield, J. D., Biamonte, J., & Aspuru‐Guzik, A. (2011) · Digital Access to Scholarship at Harvard (DASH) (Harvard University) · Cited by 218 · see citing works
Self-citationWeinstein, D. H. (1934) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.20.9.529 · Cited by 212 · see citing works
Mazziotti, D. A. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.143002 · Cited by 205 · see citing works
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-citationAdiabatic Quantum Simulation of Quantum Chemistry
Babbush, R., Love, P. J., & Aspuru-Guzik, A. (2014) · Scientific Reports · doi:10.1038/srep06603 · Cited by 191 · see citing works
Self-citationGeneral Decomposition Theory of Ordered Exponentials.
Suzuki, M. (1993) · Proceedings of the Japan Academy Series B · doi:10.2183/pjab.69.161 · Cited by 181 · see citing works
Experimental Implementation of an Adiabatic Quantum Optimization Algorithm
Steffen, M., van Dam, W., Hogg, T., Breyta, G., & Chuang, I. L. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.067903 · Cited by 180 · see citing works
Quantum Information and Computation for Chemistry
Lidar, D. A. (2014) · Advances in chemical physics · doi:10.1002/9781118742631 · Cited by 177 · see citing works
An augmented coupled cluster method and its application to the first-row homonuclear diatomics
Raghavachari, K. (1985) · The Journal of Chemical Physics · doi:10.1063/1.448718 · Cited by 171 · see citing works
Quantum Simulation of Helium Hydride Cation in a Solid-State Spin Register
Wang, Y., Dolde, F., Biamonte, J., Babbush, R., Bergholm, V., Yang, S., Jakobi, I., Neumann, P., Aspuru‐Guzik, A., Whitfield, J. D., et al. (2015) · ACS Nano · doi:10.1021/acsnano.5b01651 · Cited by 147 · see citing works
Self-citationImproving quantum algorithms for quantum chemistry
Hastings, M. B., Wecker, D., Bauer, B., & Troyer, M. (2015) · Quantum Information and Computation · doi:10.26421/qic15.1-2-1 · Cited by 147 · see citing works
Multireference coupled-cluster theory: The easy way
Musiał, M., Perera, A., & Bartlett, R. J. (2011) · The Journal of Chemical Physics · doi:10.1063/1.3567115 · Cited by 146 · see citing works
The B ravyi– K itaev transformation: Properties and applications
Tranter, A., Sofia, S. E., Seeley, J. T., Kaicher, M., McClean, J. R., Babbush, R., Coveney, P. V., Mintert, F., Wilhelm, F. K., & Love, P. J. (2015) · International Journal of Quantum Chemistry · doi:10.1002/qua.24969 · Cited by 133 · see citing works
Self-citationExploiting Locality in Quantum Computation for Quantum Chemistry
McClean, J. R., Babbush, R., Love, P. J., & Aspuru-Guzik, A. (2014) · The Journal of Physical Chemistry Letters · doi:10.1021/jz501649m · Cited by 125 · see citing works
Self-citationCooling by Heating: Refrigeration Powered by Photons
Cleuren, B., Rutten, B., & den Broeck, C. V. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.120603 · Cited by 125 · see citing works
Schmalfuß, D., Darradi, R., Richter, J., et al. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.157201 · Cited by 124 · see citing works
Polynomially scaling spin dynamics simulation algorithm based on adaptive state-space restriction
Kuprov, I., Wagner-Rundell, N., & Hore, P. J. (2007) · Journal of Magnetic Resonance · doi:10.1016/j.jmr.2007.09.014 · Cited by 118 · see citing works
Efficient quantum circuits for diagonal unitaries without ancillas
Welch, J., Greenbaum, D., Mostame, S., & Aspuru-Guzik, A. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/3/033040 · Cited by 114 · see citing works
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-citationGötze, O., FARNELL, D. J. J., Bishop, R. F., Li, P. H. Y., & Richter, J. (2011) · Physical Review B · doi:10.1103/physrevb.84.224428 · Cited by 102 · see citing works
Adiabatic state preparation study of methylene
Veis, L., & Pittner, J. (2014) · The Journal of Chemical Physics · doi:10.1063/1.4880755 · Cited by 90 · see citing works
Prospective study on microscopic potential with Gogny interaction
Blanchon, G., Dupuis, M., & Arellano, H. F. (2015) · The European Physical Journal A · doi:10.1140/epja/i2015-15165-1 · Cited by 89 · see citing works
Quantum algorithm for obtaining the energy spectrum of molecular systems
Wang, H., Kais, S., Aspuru‐Guzik, A., & Hoffmann, M. R. (2008) · Digital Access to Scholarship at Harvard (DASH) (Harvard University) · Cited by 75 · see citing works
Self-citationFARNELL, D. J. J., Götze, O., Richter, J., Bishop, R. F., & Li, P. H. Y. (2014) · Physical Review B · doi:10.1103/physrevb.89.184407 · Cited by 73 · see citing works
Simulation of Chemical Isomerization Reaction Dynamics on a NMR Quantum Simulator
Lu, D., Xu, N., Xu, R., Chen, H., Gong, J., Peng, X., & Du, J. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.020501 · Cited by 73 · see citing works
Neven, H., Rose, G., & Macready, W. G. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0804.4457 · Cited by 67 · see citing works
Different Strategies for Optimization Using the Quantum Adiabatic AlgorithmPreprint
Crosson, E., Farhi, E., Lin, C. Y.-Y., Lin, H.-H., & Shor, P. W. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1401.7320 · Cited by 66 · see citing works
Quantum Adiabatic Evolution Algorithms with Different PathsPreprint
Farhi, E., Goldstone, J., & Gutmann, S. (2002) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0208135 · Cited by 65 · see citing works
Algorithmic Complexity and Entanglement of Quantum States
Mora, C. E., & Briegel, H. J. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.200503 · Cited by 59 · see citing works
On the Modified Ritz Variation Method
MacDonald, J. K. L. (1934) · Physical Review · doi:10.1103/physrev.46.828 · Cited by 57 · see citing works
Necessary condition for the quantum adiabatic approximation
Boixo, S., & Somma, R. D. (2010) · Physical Review A · doi:10.1103/physreva.81.032308 · Cited by 56 · see citing works
Preparing Projected Entangled Pair States on a Quantum Computer
Schwarz, M., Temme, K., & Verstraete, F. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.110502 · Cited by 50 · see citing works
Robustness of the adiabatic quantum search
Åberg, J., Kult, D., & Sjöqvist, E. (2005) · Physical Review A · doi:10.1103/physreva.71.060312 · Cited by 46 · see citing works
Quantum Algorithms for Quantum Chemistry based on the sparsity of the CI-matrixPreprint
Toloui, B., & Love, P. J. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1312.2579 · Cited by 40 · see citing works
Cooling through optimal control of quantum evolution
Rahmani, A., Kitagawa, T., Demler, E., & Chamon, C. (2013) · Physical Review A · doi:10.1103/physreva.87.043607 · Cited by 36 · see citing works
Efficient quantum circuits for diagonal unitaries without ancillas
Welch, J., Greenbaum, D., Mostame, S., & Aspuru‐Guzik, A. (2014) · Digital Access to Scholarship at Harvard (DASH) (Harvard University) · Cited by 35 · see citing works
Self-citationMonte Carlo Methods in Ab Initio Quantum Chemistry
Fiedler, K. (1995) · Zeitschrift für Physikalische Chemie · doi:10.1524/zpch.1995.192.part_2.221 · Cited by 34 · cited 1× · see citing works
“For an operator O and a general mixed state ρ , this is given by A variational principle on the variance exists as well, and has been used extensively for optimization in the context of quantum Monte Carlo [36].”
MethodCommunication: 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 · see citing works
Foley, J. J., & Mazziotti, D. A. (2012) · Physical Review A · doi:10.1103/physreva.86.012512 · Cited by 23 · see citing works
Energy-Moment Methods in Quantum Mechanics
Delos, J. B., & Blinder, S. M. (1967) · The Journal of Chemical Physics · doi:10.1063/1.1712298 · Cited by 17 · see citing works
State complexity and quantum computation
Cai, Y., Le, H. N., & Scarani, V. (2015) · Annalen der Physik · doi:10.1002/andp.201400199 · Cited by 16 · see citing works
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 16 · see citing works
Probing nonlinear adiabatic paths with a universal integrator
Hofmann, M., & Schaller, G. (2014) · Physical Review A · doi:10.1103/physreva.89.032308 · Cited by 7 · see citing works
The Trotter Step Size Required for Accurate Quantum Simulation of Quantum ChemistryPreprint
Poulin, D., Hastings, M. B., Wecker, D., et al. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1406.4920 · Cited by 5 · see citing works
Numerical Methods for Large Eigenvalue Problems (Youcef Saad)
Cullum, J. K. (1994) · SIAM Review · doi:10.1137/1036077 · Cited by 2 · see citing works
Unified views of quantum simulation algorithms for chemistryPreprint
Whitfield, J. D. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1502.03771 · Cited by 1 · see citing works
Babbush, R., Berry, D. W., Kivlichan, I. D., et al. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1506.01020 · Cited by 1 · see citing works
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Research works printed but not linked: 4
- Bravyi S, 2000, Ann. Phys., 298, 18
- Urban M, 1985, Chem. Phys., 83, 4041
- 10.1002/9783527626212 · DOI
- Holmström K, 2015, User’s Guide for TOMLAB
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Sorted by citations
Quantum Computing in the NISQ era and beyond
Preskill, J. (2018) · Quantum · doi:10.22331/q-2018-08-06-79 · Cited by 8,830 · see citing works
“y states of many-particle quantum systems (large molecules, for example). When applied to quantum problems this hybrid quantum-classical procedure goes by the name Variation Quantum Eigensolver (VQE) [23]. Will NISQ technology running QAOA or VQE be able to outperform classical algorithms that find approximate solution…”
MethodVariational quantum algorithms
Cerezo, M., Arrasmith, A., Babbush, R., Benjamin, S. C., Endo, S., Fujii, K., McClean, J. R., Mitarai, K., Yuan, X., Cincio, L., et al. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00348-9 · Cited by 3,385 · see citing works
“Indeed, this was the first method introduced [192].”
MethodSelf-citationHardware-efficient variational quantum eigensolver for small molecules and quantum magnets
Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J. M., & Gambetta, J. M. (2017) · Nature · doi:10.1038/nature23879 · Cited by 2,982 · see citing works
Machine learning and the physical sciences
Carleo, G., Cirac, J. I., Cranmer, K. S., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., & Zdeborová, L. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.045002 · Cited by 2,453 · see citing works
Barren plateaus in quantum neural network training landscapes
McClean, J. R., Boixo, S., Smelyanskiy, V. N., Babbush, R., & Neven, H. (2018) · Nature Communications · doi:10.1038/s41467-018-07090-4 · Cited by 2,329 · see citing works
Self-citationQuantum Machine Learning in Feature Hilbert Spaces
Schuld, M., & Killoran, N. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.040504 · Cited by 1,840 · see citing works
Noisy intermediate-scale quantum algorithms
Bharti, K., Cervera-Lierta, A., Kyaw, T. H., Haug, T., Alperin-Lea, S., Anand, A., Degroote, M., Heimonen, H., Kottmann, J. S., Menke, T., et al. (2022) · Reviews of Modern Physics · doi:10.1103/revmodphys.94.015004 · Cited by 1,726 · see citing works
Self-citationQuantum computational chemistry
McArdle, S., Endo, S., Aspuru-Guzik, A., Benjamin, S. C., & Yuan, X. (2020) · Reviews of Modern Physics · doi:10.1103/revmodphys.92.015003 · Cited by 1,621 · see citing works
Self-citationQuantum Chemistry in the Age of Quantum Computing
Cao, Y., Romero, J., Olson, J. P., Degroote, M., Johnson, P. D., Kieferová, M., Kivlichan, I. D., Menke, T., Peropadre, B., Sawaya, N. P. D., et al. (2019) · Chemical Reviews · doi:10.1021/acs.chemrev.8b00803 · Cited by 1,560 · see citing works
Self-citationError Mitigation for Short-Depth Quantum Circuits
Temme, K., Bravyi, S., & Gambetta, J. M. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.180509 · Cited by 1,379 · see citing works
Quantum Chemistry in the Age of Quantum Computing
Cao, Y., Romero, J., Olson, J., Degroote, M., Johnson, P., Kieferová, M., Kivlichan, I., Menke, T., Peropadre, B., Sawaya, N., et al. (n.d.) · OPUS - Open Publications of UTS Scholars (University of Technology Sydney) · Cited by 1,265 · see citing works
Self-citationMachine learning & artificial intelligence in the quantum domain: a review of recent progress
Dunjko, V., & Briegel, H. J. (2018) · Reports on Progress in Physics · doi:10.1088/1361-6633/aab406 · Cited by 1,132 · see citing works
Cost function dependent barren plateaus in shallow parametrized quantum circuits
Cerezo, M., Sone, A., Volkoff, T., Cincio, L., & Coles, P. J. (2021) · Nature Communications · doi:10.1038/s41467-021-21728-w · Cited by 1,047 · see citing works
Circuit-centric quantum classifiers
Schuld, M., Bocharov, A., Svore, K. M., & Wiebe, N. (2020) · Physical Review A · doi:10.1103/physreva.101.032308 · Cited by 1,057 · see citing works
The Variational Quantum Eigensolver: A review of methods and best practices
Tilly, J., Chen, H., Cao, S., Picozzi, D., Setia, K., Li, Y., Grant, E., Wossnig, L., Rungger, I., Booth, G. H., et al. (2022) · Physics Reports · doi:10.1016/j.physrep.2022.08.003 · Cited by 1,031 · see citing works
An adaptive variational algorithm for exact molecular simulations on a quantum computer
Grimsley, H. R., Economou, S. E., Barnes, E., & Mayhall, N. J. (2019) · Nature Communications · doi:10.1038/s41467-019-10988-2 · Cited by 1,033 · see citing works
Sim, S., Johnson, P. D., & Aspuru‐Guzik, A. (2019) · Advanced Quantum Technologies · doi:10.1002/qute.201900070 · Cited by 972 · see citing works
Self-citationError mitigation extends the computational reach of a noisy quantum processor
Kandala, A., Temme, K., Corcoles, A. D., Mezzacapo, A., Chow, J. M., & Gambetta, J. (2019) · Nature · doi:10.1038/s41586-019-1040-7 · Cited by 870 · see citing works
Quantum Algorithms for Quantum Chemistry and Quantum Materials Science
Bauer, B., Bravyi, S., Motta, M., & Chan, G. K.-L. (2020) · Chemical Reviews · doi:10.1021/acs.chemrev.9b00829 · Cited by 848 · see citing works
Scalable Quantum Simulation of Molecular Energies
O’Malley, P. J. J., Babbush, R., Kivlichan, I. D., Romero, J., McClean, J. R., Barends, R., Kelly, J., Roushan, P., Tranter, A., Ding, N., et al. (2016) · Physical Review X · doi:10.1103/physrevx.6.031007 · Cited by 1,059 · see citing works
Self-citationProgrammable Quantum Simulations of Spin Systems with Trapped Ions
Monroe, C., Campbell, W. C., Duan, L. M., Gong, Z. X., Gorshkov, A. V., Hess, P., Islam, R., Kim, K., Linke, N., Pagano, G., et al. (2019) · arXiv · doi:10.48550/arxiv.1912.07845 · Cited by 806
Programmable quantum simulations of spin systems with trapped ions
Monroe, C. R., Campbell, W. C., Duan, L.-M., Gong, Z., Gorshkov, A. V., Hess, P., Islam, R., Kim, K., Linke, N. M., Pagano, G., et al. (2021) · Reviews of Modern Physics · doi:10.1103/revmodphys.93.025001 · Cited by 807 · see citing works
Power of data in quantum machine learning
Huang, H.-Y., Broughton, M., Mohseni, M., Babbush, R., Boixo, S., Neven, H., & McClean, J. R. (2021) · Nature Communications · doi:10.1038/s41467-021-22539-9 · Cited by 896 · see citing works
Self-citationEffect of data encoding on the expressive power of variational quantum-machine-learning models
Schuld, M., Sweke, R., & Meyer, J. J. (2021) · Physical Review A · doi:10.1103/physreva.103.032430 · Cited by 739 · see citing works
Noise-induced barren plateaus in variational quantum algorithms
Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., & Coles, P. J. (2021) · Nature Communications · doi:10.1038/s41467-021-27045-6 · Cited by 773 · see citing works
Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz
Romero, J., Babbush, R., McClean, J. R., Hempel, C., Love, P. J., & Aspuru-Guzik, A. (2019) · Quantum Science and Technology · doi:10.1088/2058-9565/aad3e4 · Cited by 726 · see citing works
Self-citationMotta, M., Sun, C., Tan, A. T. K., O’Rourke, M. J., Ye, E., Minnich, A. J., Brandão, F. G. S. L., & Chan, G. K.-L. (2020) · Nature Physics · doi:10.1038/s41567-019-0704-4 · Cited by 709 · see citing works
Materials challenges and opportunities for quantum computing hardware
de Leon, N. P., Itoh, K. M., Kim, D., Mehta, K. K., Northup, T. E., Paik, H., Palmer, B. S., Samarth, N., Sangtawesin, S., & Steuerman, D. W. (2021) · Science · doi:10.1126/science.abb2823 · Cited by 710 · see citing works
Validating quantum computers using randomized model circuits
Cross, A. W., Bishop, L. S., Sheldon, S., Nation, P. D., & Gambetta, J. M. (2019) · Physical Review A · doi:10.1103/physreva.100.032328 · Cited by 704 · see citing works
Efficient Variational Quantum Simulator Incorporating Active Error Minimization
Li, Y., & Benjamin, S. C. (2017) · Physical Review X · doi:10.1103/physrevx.7.021050 · Cited by 686 · see citing works
Quantum optimization using variational algorithms on near-term quantum devices
Moll, N., Barkoutsos, P., Bishop, L. S., Chow, J. M., Cross, A., Egger, D. J., Filipp, S., Fuhrer, A., Gambetta, J. M., Ganzhorn, M., et al. (2018) · Quantum Science and Technology · doi:10.1088/2058-9565/aab822 · Cited by 744 · see citing works
A Survey on quantum computing technology
Gyongyosi, L., & Imre, S. (2019) · Computer Science Review · doi:10.1016/j.cosrev.2018.11.002 · Cited by 646 · see citing works
Cai, Z., Babbush, R., Benjamin, S. C., Endo, S., Huggins, W. J., Li, Y., McClean, J. R., & O’Brien, T. E. (2023) · Reviews of Modern Physics · doi:10.1103/revmodphys.95.045005 · Cited by 668 · see citing works
Self-citationQuantum Chemistry Calculations on a Trapped-Ion Quantum Simulator
Hempel, C., Maier, C., Romero, J., McClean, J., Monz, T., Shen, H., Jurcevic, P., Lanyon, B. P., Love, P., Babbush, R., et al. (2018) · Physical Review X · doi:10.1103/physrevx.8.031022 · Cited by 597 · see citing works
Self-citationSelf-verifying variational quantum simulation of lattice models
Kokail, C., Maier, C., van Bijnen, R., Brydges, T., Joshi, M. K., Jurcevic, P., Muschik, C. A., Silvi, P., Blatt, R., Roos, C. F., et al. (2019) · Nature · doi:10.1038/s41586-019-1177-4 · Cited by 594 · see citing works
Hybrid Quantum-Classical Algorithms and Quantum Error Mitigation
Endo, S., Cai, Z., Benjamin, S. C., & Yuan, X. (2021) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.90.032001 · Cited by 566 · see citing works
Connecting Ansatz Expressibility to Gradient Magnitudes and Barren Plateaus
Holmes, Z., Sharma, K., Cerezo, M., & Coles, P. J. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.010313 · Cited by 570 · see citing works
Variational ansatz-based quantum simulation of imaginary time evolution
McArdle, S., Jones, T., Endo, S., Li, Y., Benjamin, S. C., & Yuan, X. (2019) · npj Quantum Information · doi:10.1038/s41534-019-0187-2 · Cited by 557 · see citing works
Quantum computing with neutral atoms
Henriet, L., Beguin, L., Signoles, A., Lahaye, T., Browaeys, A., Reymond, G.-O., & Jurczak, C. (2020) · Quantum · doi:10.22331/q-2020-09-21-327 · Cited by 550 · see citing works
Demonstration of the trapped-ion quantum CCD computer architecture
Pino, J. M., Dreiling, J. M., Figgatt, C., Gaebler, J. P., Moses, S. A., Allman, M. S., Baldwin, C. H., Foss-Feig, M., Hayes, D., Mayer, K., et al. (2021) · Nature · doi:10.1038/s41586-021-03318-4 · Cited by 547 · see citing works
Practical Quantum Error Mitigation for Near-Future Applications
Endo, S., Benjamin, S. C., & Li, Y. (2018) · Physical Review X · doi:10.1103/physrevx.8.031027 · Cited by 562 · see citing works
Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states
McClean, J. R., Kimchi-Schwartz, M. E., Carter, J., & de Jong, W. A. (2017) · Physical Review A · doi:10.1103/physreva.95.042308 · Cited by 516 · see citing works
Self-citationQuantum autoencoders for efficient compression of quantum data
Romero, J., Olson, J. P., & Aspuru-Guzik, A. (2017) · Quantum Science and Technology · doi:10.1088/2058-9565/aa8072 · Cited by 559 · see citing works
Self-citationOpenFermion: the electronic structure package for quantum computers
McClean, J. R., Rubin, N. C., Sung, K. J., Kivlichan, I., Bonet-Monroig, X., Cao, Y., Dai, C., Fried, E., Gidney, C., Gimby, B., et al. (2020) · Quantum Science and Technology · doi:10.1088/2058-9565/ab8ebc · Cited by 525 · see citing works
Self-citationQuantum Generative Adversarial Networks for learning and loading random distributions
Zoufal, C., Lucchi, A., & Woerner, S. (2019) · npj Quantum Information · doi:10.1038/s41534-019-0223-2 · Cited by 480 · see citing works
Variational Quantum Computation of Excited States
Higgott, O., Wang, D., & Brierley, S. (2019) · Quantum · doi:10.22331/q-2019-07-01-156 · Cited by 463 · see citing works
Theory of variational quantum simulation
Yuan, X., Endo, S., Zhao, Q., Li, Y., & Benjamin, S. C. (2019) · Quantum · doi:10.22331/q-2019-10-07-191 · Cited by 458 · see citing works
Variational Quantum Circuits for Deep Reinforcement Learning
Chen, S. Y.-C., Yang, C.-H. H., Qi, J., Chen, P., Ma, X., & Goan, H. (2020) · IEEE Access · doi:10.1109/access.2020.3010470 · Cited by 452 · see citing works
Quantum-classical computation of Schwinger model dynamics using quantum computers
Klco, N., Dumitrescu, E., McCaskey, A., Morris, T., Pooser, R. C., Sanz, M., Solano, E., Lougovski, P., & A, M. J. S. (2018) · Physical Review A · doi:10.1103/physreva.98.032331 · Cited by 428 · see citing works
Generalized Unitary Coupled Cluster Wave functions for Quantum Computation
Lee, J., Huggins, W. J., Head-Gordon, M., & Whaley, K. B. (2019) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.8b01004 · Cited by 432 · see citing works
Transfer learning in hybrid classical-quantum neural networks
Mari, A., Bromley, T. R., Izaac, J., Schuld, M., & Killoran, N. (2020) · Quantum · doi:10.22331/q-2020-10-09-340 · Cited by 435 · see citing works
Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
Kivlichan, I. D., McClean, J., Wiebe, N., Gidney, C., Aspuru-Guzik, A., Chan, G. K.-L., & Babbush, R. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.110501 · Cited by 431 · see citing works
Self-citationTang, H. L., Shkolnikov, V. O., Barron, G. S., Grimsley, H. R., Mayhall, N. J., Barnes, E., & Economou, S. E. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.020310 · Cited by 408 · see citing works
A review on Quantum Approximate Optimization Algorithm and its variants
Blekos, K., Brand, D., Ceschini, A., Chou, C.-H., Li, R.-H., Pandya, K., & Summer, A. (2024) · Physics Reports · doi:10.1016/j.physrep.2024.03.002 · Cited by 444 · see citing works
Quantum Computing for Finance: State-of-the-Art and Future Prospects
Egger, D. J., Gambella, C., Marecek, J., McFaddin, S., Mevissen, M., Raymond, R., Simonetto, A., Woerner, S., & Yndurain, E. (2020) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2020.3030314 · Cited by 422 · see citing works
Continuous-variable quantum neural networks
Killoran, N., Bromley, T. R., Arrazola, J. M., Schuld, M., Quesada, N., & Lloyd, S. (2019) · Physical Review Research · doi:10.1103/physrevresearch.1.033063 · Cited by 418 · see citing works
Cloud Quantum Computing of an Atomic Nucleus
Dumitrescu, E. F., McCaskey, A. J., Hagen, G., Jansen, G. R., Morris, T. D., Papenbrock, T., Pooser, R. C., Dean, D. J., & Lougovski, P. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.210501 · Cited by 393 · see citing works
Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
Babbush, R., Gidney, C., Berry, D. W., Wiebe, N., McClean, J., Paler, A., Fowler, A., & Neven, H. (2018) · Physical Review X · doi:10.1103/physrevx.8.041015 · Cited by 383 · see citing works
Self-citationSuperconducting quantum computing: a review
Huang, H.-L., Wu, D., Fan, D., & Zhu, X. (2020) · Science China Information Sciences · doi:10.1007/s11432-020-2881-9 · Cited by 389 · see citing works
A generative modeling approach for benchmarking and training shallow quantum circuits
Benedetti, M., Garcia-Pintos, D., Perdomo, O., Leyton-Ortega, V., Nam, Y., & Perdomo-Ortiz, A. (2019) · npj Quantum Information · doi:10.1038/s41534-019-0157-8 · Cited by 379 · see citing works
Barkoutsos, P. K., Gonthier, J. F., Sokolov, I., Moll, N., Salis, G., Fuhrer, A., Ganzhorn, M., Egger, D. J., Troyer, M., Mezzacapo, A., et al. (2018) · Physical Review A · doi:10.1103/physreva.98.022322 · Cited by 363 · see citing works
Towards quantum machine learning with tensor networks
Huggins, W. J., Patil, P., Mitchell, B., Whaley, K. B., & Stoudenmire, E. M. (2018) · Quantum Science and Technology · doi:10.1088/2058-9565/aaea94 · Cited by 363 · see citing works
Quantum simulation and computing with Rydberg-interacting qubits
Morgado, M., & Whitlock, S. (2021) · AVS Quantum Science · doi:10.1116/5.0036562 · Cited by 370 · see citing works
Computation of Molecular Spectra on a Quantum Processor with an Error-Resilient Algorithm
Colless, J. I., Ramasesh, V. V., Dahlen, D., Blok, M. S., Kimchi-Schwartz, M. E., McClean, J. R., Carter, J., de Jong, W. A., & Siddiqi, I. (2018) · Physical Review X · doi:10.1103/physrevx.8.011021 · Cited by 460 · see citing works
Self-citationQuantum Generative Adversarial Networks for learning and loading random distributions
Zoufal, C., Lucchi, A., & Woerner, S. (2019) · Repository for Publications and Research Data (ETH Zurich) · doi:10.3929/ethz-b-000382432 · Cited by 390 · see citing works
Potential of quantum computing for drug discovery
Cao, Y., Romero, J., & Aspuru-Guzik, A. (2018) · IBM Journal of Research and Development · doi:10.1147/jrd.2018.2888987 · Cited by 357 · see citing works
Self-citationContinuous-variable quantum neural networks
Killoran, N., Bromley, T. R., Arrazola, J. M., Schuld, M., Quesada, N., & Lloyd, S. (2018) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 358 · see citing works
Variational quantum algorithms for nonlinear problems
Lubasch, M., Joo, J., Moinier, P., Kiffner, M., & Jaksch, D. (2020) · Physical Review A · doi:10.1103/physreva.101.010301 · Cited by 332 · see citing works
Strawberry Fields: A Software Platform for Photonic Quantum Computing
Killoran, N., Izaac, J., Quesada, N., Bergholm, V., Amy, M., & Weedbrook, C. (2019) · Quantum · doi:10.22331/q-2019-03-11-129 · Cited by 327 · see citing works
Robust data encodings for quantum classifiers
LaRose, R., & Coyle, B. (2020) · Physical Review A · doi:10.1103/physreva.102.032420 · Cited by 332 · see citing works
Quantum Simulation for High-Energy Physics
Bauer, C., Davoudi, Z., Balantekin, A. B., Tanmoy Bhattacharya, A., Carena, M. S., de Jong, W. A., Draper, P., El-Khadra, A. X., Gemelke, N., Hanada, M., et al. (2023) · PRX Quantum · doi:10.1103/prxquantum.4.027001 · Cited by 356 · see citing works
Layerwise learning for quantum neural networks
Skolik, A., McClean, J. R., Mohseni, M., van der Smagt, P., & Leib, M. (2021) · Quantum Machine Intelligence · doi:10.1007/s42484-020-00036-4 · Cited by 324 · see citing works
Self-citationExperimental Quantum Generative Adversarial Networks for Image Generation
Huang, H.-L., Du, Y., Gong, M., Zhao, Y., Wu, Y., Wang, C., Li, S., Liang, F., Lin, J., Xu, Y., et al. (2021) · Physical Review Applied · doi:10.1103/physrevapplied.16.024051 · Cited by 314 · see citing works
Quantum Computation of Electronic Transitions Using a Variational Quantum Eigensolver
Parrish, R. M., Hohenstein, E. G., McMahon, P. L., & Martínez, T. J. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.230401 · Cited by 282 · see citing works
Hybrid Quantum-Classical Approach to Quantum Optimal Control
Li, J., Yang, X., Peng, X., & Sun, C.-P. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.150503 · Cited by 278 · see citing works
Simulating Large Quantum Circuits on a Small Quantum Computer
Peng, T., Harrow, A. W., Ozols, M., & Wu, X. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.150504 · Cited by 264 · see citing works
Gard, B. T., Zhu, L., Barron, G. S., Mayhall, N. J., Economou, S. E., & Barnes, E. (2020) · npj Quantum Information · doi:10.1038/s41534-019-0240-1 · Cited by 266 · see citing works
Measurement optimization in the variational quantum eigensolver using a minimum clique cover
Verteletskyi, V., Yen, T.-C., & Izmaylov, A. F. (2020) · The Journal of Chemical Physics · doi:10.1063/1.5141458 · Cited by 269 · see citing works
Low-Depth Quantum Simulation of Materials
Babbush, R., Wiebe, N., McClean, J., McClain, J., Neven, H., & Chan, G. K.-L. (2018) · Physical Review X · doi:10.1103/physrevx.8.011044 · Cited by 335 · see citing works
Self-citationHybrid quantum-classical convolutional neural networks
Liu, J., Lim, K. H., Wood, K. L., Huang, W., Guo, C., & Huang, H.-L. (2021) · Science China Physics, Mechanics & Astronomy · doi:10.1007/s11433-021-1734-3 · Cited by 289 · see citing works
Variational quantum algorithms for discovering Hamiltonian spectra
Jones, T., Endo, S., McArdle, S., Yuan, X., & Benjamin, S. C. (2019) · Physical Review A · doi:10.1103/physreva.99.062304 · Cited by 256 · see citing works
Quantum Computer Systems for Scientific Discovery
Alexeev, Y., Bacon, D., Brown, K. R., Calderbank, R., Carr, L. D., Chong, F. T., DeMarco, B., Englund, D. R., Farhi, E., Fefferman, B., et al. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.017001 · Cited by 311 · see citing works
Efficient and noise resilient measurements for quantum chemistry on near-term quantum computers
Huggins, W. J., McClean, J. R., Rubin, N. C., Jiang, Z., Wiebe, N., Whaley, K. B., & Babbush, R. (2021) · npj Quantum Information · doi:10.1038/s41534-020-00341-7 · Cited by 256 · see citing works
Self-citationQuantum Long Short-Term Memory
Chen, S. Y.-C., Yoo, S., & Fang, Y.-L. L. (2022) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp43922.2022.9747369 · Cited by 260 · see citing works
A versatile single-photon-based quantum computing platform
Maring, N., Fyrillas, A., Pont, M., Ivanov, E., Stepanov, P., Margaria, N., Hease, W., Pishchagin, A., Lemaître, A., Sagnes, I., et al. (2024) · Nature Photonics · doi:10.1038/s41566-024-01403-4 · Cited by 268 · see citing works
“We train a quantum neural network 48 on Ascella for a supervised learning classification task.”
Low-cost error mitigation by symmetry verification
Bonet-Monroig, X., Sagastizabal, R., Singh, M., & O'Brien, T. E. (2018) · Physical Review A · doi:10.1103/physreva.98.062339 · Cited by 250 · see citing works
Amplitude estimation without phase estimation
Suzuki, Y., Uno, S., Raymond, R., Tanaka, T., Onodera, T., & Yamamoto, N. (2020) · Quantum Information Processing · doi:10.1007/s11128-019-2565-2 · Cited by 249 · see citing works
Error-Mitigated Digital Quantum Simulation
McArdle, S., Yuan, X., & Benjamin, S. C. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.180501 · Cited by 238 · see citing works
Quantum Algorithm Implementations for Beginners
Jayakumar, A., Adedoyin, A. A., Ambrosiano, J. J., Anisimov, P. M., Casper, W., Chennupati, G., Coffrin, C., Djidjev, H. N., Gunter, D., Karra, S., et al. (2022) · ACM Transactions on Quantum Computing · doi:10.1145/3517340 · Cited by 299 · see citing works
Variational Quantum Simulation of General Processes
Endo, S., Sun, J., Li, Y., Benjamin, S. C., & Yuan, X. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.010501 · Cited by 237 · see citing works
Quantum Computer Systems for Scientific Discovery
Alexeev, Y., Bacon, D., Brown, K. R., Calderbank, R., Carr, L. D., Chong, F. T., DeMarco, B., Englund, D., Farhi, E., Fefferman, B., et al. (2021) · DSpace@MIT (Massachusetts Institute of Technology) · doi:10.6082/h7fqg-6vt65 · Cited by 257 · see citing works
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
A Practical Quantum Instruction Set ArchitecturePreprint
Smith, R. S., Curtis, M. J., & Zeng, W. J. (2016) · arXiv (Cornell University) · doi:10.4230/lipics.fsttcs.2021.51 · Cited by 315 · see citing works
Variational fast forwarding for quantum simulation beyond the coherence time
Cîrstoiu, C., Holmes, Z., Iosue, J., Cincio, L., Coles, P. J., & Sornborger, A. (2020) · npj Quantum Information · doi:10.1038/s41534-020-00302-0 · Cited by 232 · see citing works
“In order to approach the issue of initializing the parameters θ and γ, we often use a perturbative method [15, 36] in which we pre-train these parameters for a slightly different Hamiltonian.”
MethodProvably efficient machine learning for quantum many-body problems
Huang, H.-Y., Kueng, R., Torlai, G., Albert, V. V., & Preskill, J. P. (2022) · Science · doi:10.1126/science.abk3333 · Cited by 233 · see citing works
Simulating the vibrational quantum dynamics of molecules using photonics
Sparrow, C., Martín-López, E., Maraviglia, N., Neville, A., Harrold, C., Carolan, J., Joglekar, Y. N., Hashimoto, T., Matsuda, N., O’Brien, J. L., et al. (2018) · Nature · doi:10.1038/s41586-018-0152-9 · Cited by 230 · see citing works
Exact parameterization of fermionic wave functions via unitary coupled cluster theory
Evangelista, F. A., Chan, G. K.-L., & Scuseria, G. E. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5133059 · Cited by 225 · see citing works
A quantum deep convolutional neural network for image recognition
Li, Y., Zhou, R.-G., Xu, R., Luo, J., & Hu, W. (2020) · Quantum Science and Technology · doi:10.1088/2058-9565/ab9f93 · Cited by 225 · see citing works
VQE method: a short survey and recent developments
Fedorov, D. A., Peng, B., Govind, N., & Alexeev, Y. (2022) · Materials Theory · doi:10.1186/s41313-021-00032-6 · Cited by 224 · see citing works
A quantum computing view on unitary coupled cluster theory
Anand, A., Schleich, P., Alperin-Lea, S., Jensen, P. W. K., Sim, S., Díaz‐Tinoco, M., Kottmann, J. S., Degroote, M., Izmaylov, A. F., & Aspuru‐Guzik, A. (2022) · Chemical Society Reviews · doi:10.1039/d1cs00932j · Cited by 224 · see citing works
Self-citation
- Authors
- McClean, J. R., Romero, J., Babbush, R., & Aspuru-Guzik, A.
- Affiliations
- Lawrence Berkeley National Laboratory (US)
- Harvard University (US)
- Google (United States) (US)
- Corresponding author
- McClean, Jarrod R
- Venue
- New Journal of Physics
- Publisher
- IOP Publishing
- Published
- 2016-02-04
- Volume
- 18
- Issue
- 2
- Pages
- 023023
- ISSN
- 1367-2630 (ISSN-L)
- OpenAlex
- W2257937122
- Semantic Scholar
- c78988d6c8b3d0a0385164b372f202cdeb4a5849
- Cited by
- 2,227
- References
- 93
- Citations by year
- 2026: 219 · 2025: 353 · 2024: 306 · 2023: 321 · 2022: 310 · 2021: 337 · 2020: 203 · 2019: 99 · 2018: 50 · 2017: 18 · 2016: 9
- FWCI
- 48.22
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- New Journal of Physics (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- Digital Access to Scholarship at Harvard (DASH) (Harvard University) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Army Research Office (W911NF-15-1-0256)
- Air Force Office of Scientific Research (FA9550-12-1-0046)
- Office of Naval Research Global (N00014-16-1-2008)
- Defense Security Science Engineering Fellowship (N00014-16-1-2008)
- Lawrence Berkeley National Laboratory (Luis W. Alvarez Fellowship in Compu)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- hybrid quantum-classical algorithms, unitary coupled cluster, universal gate set, truncation, correlated sampling, derivative-free optimization
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