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Universal Quantum Simulators
Abstract
Feynman's 1982 conjecture, that quantum computers can be programmed to simulate any local quantum system, is shown to be correct.
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In the citing paper
“The algorithm runs in time polynomial in the size of the system being simulated (the number of qubits) and the desired evolution time, giving an exponential speedup over the best general classical algorithms known.”
From Quantum algorithms: an overview (2016) · cites this paper as [44]
In the citing paper
“A general-purpose quantum computer can indeed ef fi ciently simulate quantum mechanics in this sense for many physically realistic cases, such as systems with locality restrictions on their interactions. 44”
From Quantum algorithms: an overview (2016) · cites this paper as [44]
In the citing paper
“It is noteworthy that we can program quantum computers to simulate localized quantum systems [68].”
From Quantum Computing in the Next-Generation Computational Biology Landscape: From Protein Folding to Molecular Dynamics (2024) · cites this paper as [68]
In the citing paper
“With this universal approach, a wide range of quantum problems can be simulated to the desired accuracy with a polynomial increase in quantum resources only (Lloyd, 1996).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Lloyd, 1996
In the citing paper
“The belief in this quantum approach was indeed supported in the 90's by the first efficient quantum algorithms [316], which were rapidly followed by breakthrough discoveries applicable to quantum chemistry [3,624]”
From Photonic quantum information processing: a review (2019) · cites this paper as [3]
In the citing paper
“The quantum computational cost of these algorithms has continued to be reduced 47-50 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [50]
In the citing paper
“Later, it was also demonstrated that the Trotter errors depend on the maximum nuclear charge rather than the number of spin-orbitals 50 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [50]
In the citing paper
“In the general case, it would require a number of elementary gates of 2 20 ≃ 10 6 [2]. With our method, the number of gates can be as small as 10 per Trotter step, consisting of Mølmer-Sørensen gates (dark blue and green), local exp( iφ ′ σ y 2 ) gates (red), exp[ ± i ( π/ 4) ∑ i σ y i ] (yellow) and exp[ ± i ( π/ 4) ∑ i σ x i ] (cyan) gates (see Fig. 1b) [35].”
From Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions (2012) · cites this paper as [2]
In the citing paper
“We map products of fermionic operators onto nonlocal spin operators and decompose the resulting dynamics in efficient steps with Trotter methods, yielding an overall protocol that employs only polynomial resources.”
From Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions (2012) · cites this paper as [2]
In the citing paper
“Note that for bounded Hamiltonians, the Trotter expansion associated with the exponential of the polynomial sum of efficiently implementable nonlocal terms is also efficient [2, 29, 30], i.e., it only requires polynomial resources [35].”
From Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions (2012) · cites this paper as [2]
In the citing paper
“On a fault-tolerant computer, one may directly measure the full-CI energy by first preparing a wave function ansatz on the quantum hardware (as in VQE) and then applying the Quantum Phase Estimation algorithm, which projects a prepared state into an energy eigenstate of the Hamiltonian.[111,[132][133][134][135][136]”
From Quantum Computing for Molecular Biology** (2023) · cites this paper as [111]
In the citing paper
“A proposed solution is to use highly controlled laboratory quantum systems themselves to perform such simulations [1-3].”
From Quantum Simulation of the Klein Paradox with Trapped Ions (2011) · cites this paper as [2]
In the citing paper
“Simulating quantum mechanics using conventional computers rapidly becomes intractable as the physical systems to which it is applied grow larger.”
From Quantum Simulation of the Klein Paradox with Trapped Ions (2011) · cites this paper as [2]
In the citing paper
“Indeed, this fact is related to correlation and entanglement spreading according to the Lieb-Robinson theorem that states that, after a sufficiently large time, states can become strongly entangled ([91-96], see also [97]).”
From Can one trust quantum simulators? (2012) · cites this paper as [96]
In the citing paper
“or that the quantum dynamics is in general computationally hard [96, 97].”
From Can one trust quantum simulators? (2012) · cites this paper as [96]
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Quantum algorithm for linear regression
Wang, G. (2017) · Physical Review A · doi:10.1103/physreva.96.012335 · Cited by 145
Global entangling gates on arbitrary ion qubits
Lu, Y., Zhang, S., Zhang, K., Chen, W., Shen, Y., Zhang, J., Zhang, J.-N., & Kim, K. (2019) · Nature · doi:10.1038/s41586-019-1428-4 · Cited by 145
“[3] Seth Lloyd.”
BackgroundFarrell, R. C., Illa, M., Ciavarella, A. N., & A, M. J. S. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.020315 · Cited by 216
Ultracold molecules for quantum simulation: rotational coherences in CaF and RbCs
Blackmore, J. A., Caldwell, L., Gregory, P. D., Bridge, E. M., Sawant, R., Aldegunde, J., Mur-Petit, J., Jaksch, D., Hutson, J. M., Sauer, B. E., et al. (2018) · Quantum Science and Technology · doi:10.1088/2058-9565/aaee35 · Cited by 143
SupermarQ: A Scalable Quantum Benchmark Suite
Tomesh, T., Gokhale, P., Omole, V., Ravi, G. S., Smith, K. N., Viszlai, J., Wu, X.-C., Hardavellas, N., Martonosi, M., & Chong, F. T. (2022) · IEEE International Symposium on High-Performance Computer Architecture (HPCA) · doi:10.1109/hpca53966.2022.00050 · Cited by 184
Quantum search without entanglement
Lloyd, S. (1999) · Physical Review A · doi:10.1103/physreva.61.010301 · Cited by 146
Self-citationTwo-photon quantum walks in an elliptical direct-write waveguide array
Owens, J. O., Broome, M. A., Biggerstaff, D. N., Goggin, M. E., Fedrizzi, A., Linjordet, T., Ams, M., Marshall, G. D., Twamley, J., Withford, M. J., et al. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/7/075003 · Cited by 135
Digital Quantum Simulation of Open Quantum Systems Using Quantum Imaginary–Time Evolution
Kamakari, H., Sun, S.-N., Motta, M., & Minnich, A. J. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.010320 · Cited by 154
“The first term exp (−iH1τ) is unitary and can be implemented on a quantum simulator via Trotterization and standard quantum simulation techniques [2,45,46].”
MethodQuantum simulation of spin models on an arbitrary lattice with trapped ions
Korenblit, S. É., Kafri, D., Campbell, W. C., Islam, R., Edwards, E. E., Gong, Z.-X., Lin, G.-D., Duan, L.-M., Kim, J., Kim, K., et al. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/9/095024 · Cited by 138
Exponentially more precise quantum simulation of fermions in second quantization
Babbush, R., Berry, D. W., Kivlichan, I. D., Wei, A. Y., Love, P. J., & Aspuru-Guzik, A. (2016) · New Journal of Physics · doi:10.1088/1367-2630/18/3/033032 · Cited by 135
Digital lattice gauge theories
Zohar, E., Farace, A., Reznik, B., & Cirac, J. I. (2017) · Physical Review A · doi:10.1103/physreva.95.023604 · Cited by 130
Towards analog quantum simulations of lattice gauge theories with trapped ions
Davoudi, Z., Hafezi, M., Monroe, C. R., Pagano, G., Seif, A., & Shaw, A. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.023015 · Cited by 146
“quantum simulation and quantum computation [3–5], to tackle these problems.”
BackgroundThe 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
Quantum singular-value decomposition of nonsparse low-rank matrices
Rebentrost, P., Steffens, A., Marvian, I., & Lloyd, S. (2018) · Physical Review A · doi:10.1103/physreva.97.012327 · Cited by 132
Self-citationIntroduction to topological quantum computation with non-Abelian anyons
Field, B., & Simula, T. (2018) · Quantum Science and Technology · doi:10.1088/2058-9565/aacad2 · Cited by 139
“Using this exponentially large computation space, it is possible, at least in principle, for quantum computers to efficiently solve classically difficult problems such as prime factorisation of large numbers (Shor, 1994) or the simulation of complex quantum systems (Feynman, 1982; Lloyd, 1996).”
BackgroundProspects for quantum enhancement with diabatic quantum annealing
Crosson, E., & Lidar, D. A. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00313-6 · Cited by 153
Chen, S., Yu, W., Zeng, P., & Flammia, S. T. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.030348 · Cited by 162
Mazza, L., Bermudez, A., Goldman, N., Rizzi, M., Martin-Delgado, M. A., & Lewenstein, M. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/1/015007 · Cited by 136
Sun, S.-N., Motta, M., Tazhigulov, R. N., Tan, A. T. K., Chan, G. K.-L., & Minnich, A. J. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.010317 · Cited by 152
“Quantum computers have long been considered as a potential tool to simulate quantum many-body systems [1–3].”
BackgroundTrapped-Ion Quantum Simulator: Experimental Application to Nonlinear Interferometers
Leibfried, D. G., DeMarco, B., Meyer, V., Rowe, M., Ben-Kish, A., Britton, J., Itano, W. M., Jelenkovic, B. M., Langer, C., Rosenband, T., et al. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.247901 · Cited by 133
Demonstrating Anyonic Fractional Statistics with a Six-Qubit Quantum Simulator
Lu, C.-Y., Gao, W.-B., Gühne, O., Zhou, X.-Q., Chen, Z.-B., & Pan, J.-W. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.030502 · Cited by 132
Quantum machine learning in high energy physics
Guan, W., Perdue, G., Pesah, A. C., Schuld, M., Terashi, K., Vallecorsa, S., & Vlimant, J.-R. (2020) · Machine Learning Science and Technology · doi:10.1088/2632-2153/abc17d · Cited by 152
“The second path follows the idea of quantum simulations [97], an important use of quantum computers in simulating complex quantum systems to determine their”
BackgroundQuantum simulation of a three-body-interaction Hamiltonian on an NMR quantum computer
Tseng, C.-H., Somaroo, S. S., Sharf, Y., Knill, E. H., Laflamme, R., Havel, T. F., & Cory, D. G. (1999) · Physical Review A · doi:10.1103/physreva.61.012302 · Cited by 132
Individual Addressing of Trapped Ions and Coupling of Motional and Spin States Using rf Radiation
Johanning, M., Braun, A., Timoney, N., Elman, V., Neuhauser, W., & Wunderlich, C. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.073004 · Cited by 128
Adaptive Variational Quantum Dynamics Simulations
Yao, Y.-X., Gomes, N., Zhang, F., Wang, C.-Z., Ho, K.-M., Iadecola, T., & Orth, P. P. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.030307 · Cited by 152
A non-orthogonal variational quantum eigensolver
Huggins, W., Lee, J., Baek, U., O'Gorman, B., & Whaley, K. (2020) · eScholarship (California Digital Library) · Cited by 128
Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions
Nguyen, N. H., Tran, M. C., Zhu, Y., Green, A., Alderete, C. H., Davoudi, Z., & Linke, N. M. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.020324 · Cited by 162
“An exciting prospect for quantum computers is the simulation of complex physical systems [1, 2].”
BackgroundQuantum localization bounds Trotter errors in digital quantum simulation
Heyl, M., Hauke, P., & Zoller, P. (2019) · Science Advances · doi:10.1126/sciadv.aau8342 · Cited by 136
“1A) ( 3 ).”
A Case for Multi-Programming Quantum Computers
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“Quantum computers can solve problems deemed hard on conventional computers [7, 11, 20, 32, 37].”
BackgroundQuantum simulation of the transverse Ising model with trapped ions
Kim, K., Korenblit, S. É., Islam, R., Edwards, E. E., Chang, M.-S., Noh, C., Carmichael, H. J., Lin, G.-D., Duan, L.-M., Wang, C. ‐. J., et al. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/10/105003 · Cited by 134
Optical investigation of electrical spin injection into semiconductors
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Floquet prethermalization in dipolar spin chains
Peng, P., Yin, C., Huang, X., Ramanathan, C., & Cappellaro, P. (2021) · Nature Physics · doi:10.1038/s41567-020-01120-z · Cited by 128
Noisy intermediate-scale quantum computers
Cheng, B., Deng, X., Gu, X. Q., He, Y., Hu, G., Huang, P., Li, J., Lin, B., Lu, D., Lu, Y., et al. (2023) · Frontiers of Physics · doi:10.1007/s11467-022-1249-z · Cited by 147
Quantum computing: pro and con
Preskill, J. P. (1998) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.1998.0171 · Cited by 135
“Particularly notable is the problem of understanding the capacity of noisy quantum channels for sending either quantum or classical information (Lloyd 1996; Bennett et al. 1996; Shor & Smolin 1996; Schumacher & Nielsen 1996; Barnum et al. 1997; Bennett et al. 1997; Holevo 1996; Fuchs 1997).”
InfluentialSimulating open quantum systems: from many-body interactions to stabilizer pumping
Müller, M., Hammerer, K., Zhou, Y. L., Roos, C. F., & Zoller, P. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/8/085007 · Cited by 127
“Recently, quantum control of open many-body systems, which amounts to engineering both the Hamiltonian time evolution of the many-body system itself as well as its coupling to the environment [2, 21], has become a major research focus.”
BackgroundInfluentialJohnson, T. H., Clark, S. R., & Jaksch, D. (2014) · EPJ Quantum Technology · doi:10.1140/epjqt10 · Cited by 127
Quantum computation of scattering in scalar quantum field theories
Jordan, S. P., Lee, K. S. M., & Preskill, J. P. (2014) · Quantum Information and Computation · doi:10.26421/qic14.11-12-8 · Cited by 255
“Feynman’s original question about whether a universal quantum computer can efficiently simulate not only other models of quantum computation but also naturally occurring quantum systems has also been addressed: quantum circuits have been designed to simulate the evolution for time t of systems of n nonrelativistic par…”
MethodQuantum Information and Algorithms for Correlated Quantum Matter
Head-Marsden, K., Flick, J., Ciccarino, C. J., & Narang, P. (2020) · Chemical Reviews · doi:10.1021/acs.chemrev.0c00620 · Cited by 133
Multilevel distillation of magic states for quantum computing
Jones, C. (2013) · Physical Review A · doi:10.1103/physreva.87.042305 · Cited by 123
Suzuki, Y., Endo, S., Fujii, K., & Tokunaga, Y. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.010345 · Cited by 154
“The long-term FTQC allows executing conventional quantum algorithms such as Hamiltonian simulation algorithms [8].”
MethodUsing Quantum Computers for Quantum Simulation
Brown, K. L., Munro, W. J., & Kendon, V. M. (2010) · Entropy · doi:10.3390/e12112268 · Cited by 129
“Feynman’s seminal ideas [3] from 1982 were fleshed out by Lloyd in 1996, in his paper on universal quantum simulators [8].”
BackgroundMethodInfluentialTowards quantum simulating QCD
Wiese, U. ‐. (2014) · Nuclear Physics A · doi:10.1016/j.nuclphysa.2014.09.102 · Cited by 116
Characterization of Multipartite Entanglement for One Photon Shared Among Four Optical Modes
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Quantum Computing and Simulations for Energy Applications: Review and Perspective
Paudel, H. P., Syamlal, M., Crawford, S. E., Lee, Y., Shugayev, R., Lu, P., Ohodnicki, P. R., Mollot, D., & Duan, Y. (2022) · ACS Engineering Au · doi:10.1021/acsengineeringau.1c00033 · Cited by 153
Fault-tolerant quantum simulations of chemistry in first quantization
Su, Y., Berry, D. W., Wiebe, N., Rubin, N., & Babbush, R. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.040332 · Cited by 123
Possible existence of optical communication channels in the brain
Kumar, S., Boone, K., Tuszyński, J. A., Barclay, P. E., & Simon, C. (2016) · Scientific Reports · doi:10.1038/srep36508 · Cited by 124
Quantum Computing 40 Years Later
Preskill, J. P. (2023) · CRC Press eBooks · doi:10.1201/9781003358817-7 · Cited by 132
Linear Optics Simulation of Quantum Non-Markovian Dynamics
Chiuri, A., Greganti, C., Mazzola, L., Paternostro, M., & Mataloni, P. (2012) · Scientific Reports · doi:10.1038/srep00968 · Cited by 122
Material matters in superconducting qubits
Murray, C. E. (2021) · Materials Science and Engineering R Reports · doi:10.1016/j.mser.2021.100646 · Cited by 138
QuTiP 5: The Quantum Toolbox in Python
Lambert, N., Giguère, E., Menczel, P., Li, B., Hopf, P., Suárez, G., Labarias, M. A. G., Lishman, J., Gadhvi, R., Agarwal, R., et al. (2025) · Physics Reports · doi:10.1016/j.physrep.2025.10.001 · Cited by 123
Superconducting Circuit Companion—an Introduction with Worked Examples
Rasmussen, S. E., Christensen, K. S., Pedersen, S. P., Kristensen, L. B., Bækkegaard, T., Loft, N. J. S., & Zinner, N. T. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.040204 · Cited by 144
“Since Richard Feynman first proposed to use quantum simulators to simulate physics [1, 2], an increasing amount of attention has been given to quantum processor and quantum technology, something which is only expected to increase further in the coming years [3–5].”
BackgroundNon-Abelian SU(2) Lattice Gauge Theories in Superconducting Circuits
Mezzacapo, A., Rico, E., Sabín, C., Egusquiza, I. L., Lamata, L., & Solano, E. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.240502 · Cited by 123
Quantum State Engineering of a Hubbard System with Ultracold Fermions
Chiu, C., Ji, G., Mazurenko, A., Greif, D., & Greiner, M. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.243201 · Cited by 114
Efficient state preparation for a register of quantum bits
Soklakov, A. N., & Schack, R. (2006) · Physical Review A · doi:10.1103/physreva.73.012307 · Cited by 120
Quantum neuromorphic computing
Marković, D., & Grollier, J. (2020) · Applied Physics Letters · doi:10.1063/5.0020014 · Cited by 131
Simulating Ising spin glasses on a quantum computer
Lidar, D. A., & Biham, O. (1997) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.56.3661 · Cited by 124
Simulating quantum mechanics on a quantum computer
Boghosian, B. M., & Taylor, W. (1998) · Physica D: Nonlinear Phenomena · doi:10.1016/s0167-2789(98)00042-6 · Cited by 120
“Recently, it was argued by Lloyd [4] that for a fairly general class of quantum systems, particularly for discrete systems, it should be possible to achieve an exponential speedup when simulating quantum mechanical systems on a quantum computer.”
BackgroundMethodQuantum Simulation of Interacting Fermion Lattice Models in Trapped Ions
Casanova, J., Mezzacapo, A., Lamata, L., & Solano, E. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.190502 · Cited by 118
New Frontiers in Quantum Information With Atoms and Ions
Cirac, J. I., & Zoller, P. (2004) · Physics Today · doi:10.1063/1.1712500 · Cited by 115
Preparing Ground States of Quantum Many-Body Systems on a Quantum Computer
Poulin, D., & Wocjan, P. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.130503 · Cited by 115
Making hybrid [n]-rotaxanes as supramolecular arrays of molecular electron spin qubits
Fernández, A., Ferrando–Soria, J., Pineda, E. M., Tuna, F., Vitórica‐Yrezábal, Í. J., Knappke, C. E. I., Ujma, J., Muryn, C. A., Timco, G. A., Barran, P. E., et al. (2016) · Nature Communications · doi:10.1038/ncomms10240 · Cited by 117
“link hybrid organic–inorganic [2]- and [3]-rotaxanes into still larger [4]-, [5]- and”
BackgroundMethodInfluentialArtificial Intelligence and Advanced Materials
López, C. (2022) · Advanced Materials · doi:10.1002/adma.202208683 · Cited by 123
Calculating the thermal rate constant with exponential speedup on a quantum computer
Lidar, D. A., & Wang, H. (1999) · Physical Review E · doi:10.1103/physreve.59.2429 · Cited by 115
Measurement reduction in variational quantum algorithms
Zhao, A., Tranter, A., Kirby, W. M., Ung, S. F., Miyake, A., & Love, P. J. (2020) · Physical Review A · doi:10.1103/physreva.101.062322 · Cited by 121
Applications of near-term photonic quantum computers: software and algorithms
Bromley, T. R., Arrazola, J. M., Jahangiri, S., Izaac, J., Quesada, N., Gran, A. D., Schuld, M., Swinarton, J., Zabaneh, Z., & Killoran, N. (2020) · Quantum Science and Technology · doi:10.1088/2058-9565/ab8504 · Cited by 128
Smart, S. E., & Mazziotti, D. A. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.070504 · Cited by 121
A random walk approach to quantum algorithms
Kendon, V. M. (2006) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2006.1901 · Cited by 113
“However, this is not possible within the constraints of quantum dynamics, as shown by Meyer (1996).”
BackgroundCodeword Stabilized Quantum Codes
Cross, A. W., Smith, G., Smolin, J. A., & Zeng, B. (2009) · IEEE Transactions on Information Theory · doi:10.1109/tit.2008.2008136 · Cited by 121
“Q UANTUM computers hold the promise of the efficient solution of problems, such as factoring [1] and simulation of quantum systems [2]–[4] that are generally believed to be intractable on a classical computer.”
BackgroundSynthetic gauge fields and homodyne transmission in Jaynes–Cummings lattices
Nunnenkamp, A., Koch, J., & Girvin, S. M. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/9/095008 · Cited by 116
Digital Quantum Simulation of Spin Systems in Superconducting Circuits
Heras, U. L., Mezzacapo, A., Lamata, L., Filipp, S., Wallraff, A. J., & Solano, E. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.200501 · Cited by 116
Simple universal models capture all classical spin physics
Cuevas, G. D. L., & Cubitt, T. S. (2016) · Science · doi:10.1126/science.aab3326 · Cited by 115
QUANTUM WALKS ON GENERAL GRAPHS
Kendon, V. M. (2006) · International Journal of Quantum Information · doi:10.1142/s0219749906002195 · Cited by 109
Suppressing environmental noise in quantum computation through pulse control
Duan, L.-M., & Guo, G. (1999) · Physics Letters A · doi:10.1016/s0375-9601(99)00592-7 · Cited by 115
Hamiltonian Simulation Using Linear Combinations of Unitary Operations
Childs, A. M., & Wiebe, N. (2012) · Quantum Information and Computation · doi:10.26421/qic12.11-12 · Cited by 119
“The original approach to quantum simulation, based on product formulas, was proposed by Lloyd for time-independent local Hamiltonians [8].”
MethodOn entropy growth and the hardness of simulating time evolution
Schuch, N., Wolf, M. M., Vollbrecht, K. G. H., & Cirac, J. I. (2008) · New Journal of Physics · doi:10.1088/1367-2630/10/3/033032 · Cited by 113
Quantum interferometry with three-dimensional geometry
Spagnolo, N., Aparo, L., Vitelli, C., Crespi, A., Ramponi, R., Osellame, R., Mataloni, P., & Sciarrino, F. (2012) · Scientific Reports · doi:10.1038/srep00862 · Cited by 115
“Further perspectives may lead to the application of this multiport splitters in other contexts, such as quantum simulations [48], linear-optical co mputing [49] and nonlocality tests [50].”
Digital Quantum Simulation of Z2 Lattice Gauge Theories with Dynamical Fermionic Matter
Zohar, E., Farace, A., Reznik, B., & Cirac, J. I. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.070501 · Cited by 110
Emulating Solid-State Physics with a Hybrid System of Ultracold Ions and Atoms
Bissbort, U., Cocks, D., Negretti, A., Idziaszek, Z., Calarco, T., Schmidt‐Kaler, F., Hofstetter, W., & Gerritsma, R. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.080501 · Cited by 115
Quantum Computation and Quantum InformationPreprint
Wang, Y. (2016) · Cited by 128
Quantum 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
Experimental realization of quantum algorithm for solving linear systems of equations
Pan, J., Cao, Y., Yao, X., Li, Z., Ju, C., Chen, H., Peng, X., Kais, S., & Du, J. (2014) · Physical Review A · doi:10.1103/physreva.89.022313 · Cited by 110
“The proposition of quantum computer dates back to 1980s [1], but it was not until the late 80’s and early 90’s that quantum computers are shown to be more powerful than classical computers on various specialized problems [2–5].”
BackgroundMethodGrover Mixers for QAOA: Shifting Complexity from Mixer Design to State Preparation
Bartschi, A., & Eidenbenz, S. (2020) · 2020 IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce49297.2020.00020 · Cited by 122
“It follows as a benefit that GM-QAOA does not suffer from numerical errors that Hamiltonian simulation methods, such as Trotterization [10], Local Combination of Unitaries [11], or Quantum Walk based simulation [12], introduce.”
MethodInfluentialBravyi-Kitaev Superfast simulation of electronic structure on a quantum computer
Setia, K., & Whitfield, J. D. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5019371 · Cited by 118
Time-dependent Hamiltonian simulation with L 1 -norm scaling
Berry, D. W., Childs, A. M., Su, Y., Wang, X., & Wiebe, N. (2020) · Quantum · doi:10.22331/q-2020-04-20-254 · Cited by 133
“Then the problem can be greatly simplified and it has been thoroughly studied by previous works on quantum simulation [1, 4, 5, 7– 9, 13, 16, 18, 19, 29, 31–33, 35, 36].”
MethodAutomated distribution of quantum circuits via hypergraph partitioning
Andrés-Martínez, P., & Heunen, C. (2019) · Physical Review A · doi:10.1103/physreva.100.032308 · Cited by 112
“Quantum computation [1–3] employs the laws of quantum mechanics to design systems capable of outperforming classical computers in certain problems [4–6].”
BackgroundQuantum amplification and simulation of strong and ultrastrong coupling of light and matter
Qin, W., Kockum, A. F., Muñoz, C. S., Miranowicz, A., & Nori, F. (2024) · Physics Reports · doi:10.1016/j.physrep.2024.05.003 · Cited by 123
Interpretation of tomography and spectroscopy as dual forms of quantum computation
Miquel, C., Paz, J. P., Saraceno, M., Knill, E., Laflamme, R., & Negrevergne, C. (2002) · Nature · doi:10.1038/nature00801 · Cited by 110
“(which underlies a quantum computer's ability to perform efficient simulation”
BackgroundMagann, A. B., Arenz, C., Grace, M. D., Ho, T.-S., Kosut, R. L., McClean, J. R., Rabitz, H. A., & Sarovar, M. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.010101 · Cited by 116
“The development of large scale, fault-tolerant quantum computers would enable diverse and disruptive applications, such as the ability to break RSA encryption protocols using Shor’s factoring algorithm [1] and to efficiently simulate the dynamics of complex quantum systems [2].”
BackgroundKoopman–von Neumann approach to quantum simulation of nonlinear classical dynamics
Joseph, I. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.043102 · Cited by 108
Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule
Banchi, L., & Crooks, G. E. (2021) · Quantum · doi:10.22331/q-2021-01-25-386 · Cited by 129
“Such “simple” device is still capable of universal quantum computation, provided that the operators Ĥ0 and Ĥ1 are multi-qubit operators that generate the full Lie algebra [25].”
BackgroundQuantum Krylov subspace algorithms for ground- and excited-state energy estimation
Cortes, C. L., & Gray, S. K. (2022) · Physical Review A · doi:10.1103/physreva.105.022417 · Cited by 130
“While quantum computers provide a scalable route for solving this problem through the multi-ancilla-based quantum phase estimation algorithm, this approach will most likely require fault-tolerant quantum computing hardware [1–7].”
MethodQuantum Algorithm for Spectral Measurement with a Lower Gate Count
Poulin, D., Kitaev, A., Steiger, D. S., Hastings, M. B., & Troyer, M. (2018) · Physical Review Letters · doi:10.1103/physrevlett.121.010501 · Cited by 108
“While methods to produce the time-evolution operator have been known for decades [1, 2], the static problem is often a bottleneck of quantum simulations.”
MethodInfluentialQuantum simulation of strongly correlated condensed matter systems
Hofstetter, W., & Qin, T. (2017) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/1361-6455/aaa31b · Cited by 108
“These developments build on the pioneering ideas of Feynman [7, 8], who already envisioned a universal ‘digital’ quantum simulator, and others [9].”
BackgroundAlgorithms for Quantum Simulation at Finite Energies
Lu, S., Bañuls, M. C., & Cirac, J. I. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.020321 · Cited by 123
“The advent of quantum simulators [1, 2] opens many exciting opportunities to probe and understand fundamental problems in physics, ranging from condensed matter to high energy physics and quantum chemistry [3– 5].”
BackgroundEfficient quantum circuits for quantum computational chemistry
Yordanov, Y. S., Arvidsson-Shukur, D. R. M., & Barnes, C. H. W. (2020) · Physical Review A · doi:10.1103/physreva.102.062612 · Cited by 105
Simulation of quantum dynamics with quantum optical systems
Jané, E., Vidal, G., Dür, W., Zoller, P., & Cirac, J. I. (2002) · CaltechAUTHORS (California Institute of Technology) · Cited by 107
Polynomial-Time Simulation of Pairing Models on a Quantum Computer
Wu, L.-A., Byrd, M., & Lidar, D. A. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.057904 · Cited by 106
Barondeau, D. P., & Lindahl, P. A. (1997) · Journal of the American Chemical Society · doi:10.1021/ja963597k · Cited by 107
Path-polarization hyperentangled and cluster states of photons on a chip
Ciampini, M. A., Orieux, A., Paesani, S., Sciarrino, F., Corrielli, G., Crespi, A., Ramponi, R., Osellame, R., & Mataloni, P. (2016) · Light: Science & Applications · doi:10.1038/lsa.2016.64 · Cited by 105
Quantum simulation and phase diagram of the transverse-field Ising model with three atomic spins
Edwards, E. E., Korenblit, S. É., Kim, K., Islam, R., Chang, M.-S., Freericks, J. K., Lin, G.-D., Duan, L., & Monroe, C. R. (2010) · Physical Review B · doi:10.1103/physrevb.82.060412 · Cited by 106
Metadata
- Authors
- Lloyd, S.
- Affiliations
- Massachusetts Institute of Technology (US)
- Corresponding author
- Lloyd, Seth
- ORCID
- Lloyd, Seth
- Venue
- Science
- Published
- 1996-08-23
- Volume
- 273
- Issue
- 5278
- Pages
- 1073-1078
- ISSN
- 0036-8075 (ISSN-L)
- 1095-9203
- OpenAlex
- W2040792108
- Cited by
- 3,088
- References
- 54
- Citations by year
- 2026: 183 · 2025: 317 · 2024: 287 · 2023: 268 · 2022: 221 · 2021: 251 · 2020: 208 · 2019: 150 · 2018: 117 · 2017: 134 · 2016: 104 · 2015: 82 · 2014: 97 · 2013: 72 · 2012: 75
- FWCI
- 30.78
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Science (publishedVersion)
- PubMed (publishedVersion)
- 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 › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Keywords
- quantum simulation, quantum computing hardware, quantum computing
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