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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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Items 401–500 of 1,008
A two-qubit molecular architecture for electron-mediated nuclear quantum simulation
Atzori, M., Chiesa, A., Morra, E., Chiesa, M., Sorace, L., Carretta, S., & Sessoli, R. (2018) · Chemical Science · doi:10.1039/c8sc01695j · Cited by 106
Efficient classical simulation of noisy random quantum circuits in one dimension
Noh, K., Jiang, L., & Fefferman, B. (2020) · Quantum · doi:10.22331/q-2020-09-11-318 · Cited by 118
“α1,··· ,αn−1=0 A[1]I1 α1 A [2]I2 α1α2 · · ·A [n]In αn−1 .”
BackgroundInfluentialLin, L., & Tong, Y. (2020) · Quantum · doi:10.22331/q-2020-11-11-361 · Cited by 158
“A well-known quantum eigenstate filtering algorithm is phase estimation [40], which relies on Hamiltonian simulation [10, 11, 42, 43, 44, 45] and the quantum Fourier transform.”
MethodPetruzziello, L., & Illuminati, F. (2021) · Nature Communications · doi:10.1038/s41467-021-24711-7 · Cited by 120
Characterizing and Optimizing Qubit Coherence Based on SQUID Geometry
Braumüller, J., Ding, L., Vepsäläinen, A. P., Sung, Y., Kjærgaard, M., Menke, T., Winik, R., Kim, D. K., Niedzielski, B. M., Melville, A. J., et al. (2020) · Physical Review Applied · doi:10.1103/physrevapplied.13.054079 · Cited by 102
“[2] S.”
BackgroundDigital-analog quantum computation
Parra-Rodriguez, A., Lougovski, P., Lamata, L., Solano, E., & Sanz, M. (2020) · Physical Review A · doi:10.1103/physreva.101.022305 · Cited by 104
“In order to do it in a systematic manner, we will make use of a Trotter decomposition on top of the previous algo-rithm [30].”
BackgroundMethodQuantum simulation of chemistry with sublinear scaling in basis size
Babbush, R., Berry, D. W., McClean, J. R., & Neven, H. (2019) · npj Quantum Information · doi:10.1038/s41534-019-0199-y · Cited by 121
Fermion-to-qubit mappings with varying resource requirements for quantum simulation
Steudtner, M., & Wehner, S. (2018) · New Journal of Physics · doi:10.1088/1367-2630/aac54f · Cited by 113
Adaptive Variational Quantum Dynamics Simulations
Yao, Y., Gomes, N., Zhang, F., Wang, C., Ho, K., Iadecola, T., & Orth, P. P. (2021) · Iowa State University Digital Repository (Iowa State University) · Cited by 104
Quantum Machine Learning over Infinite Dimensions
Lau, H.-K., Pooser, R. C., Siopsis, G., & Weedbrook, C. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.080501 · Cited by 104
Principles of Quantum Computation and Information - Volume I: Basic Concepts
Benenti, G., Casati, G., & Strini, G. (2004) · WORLD SCIENTIFIC eBooks · doi:10.1142/9789812794796 · Cited by 106
A concentrated array of copper porphyrin candidate qubits
Yu, C.-J., Krzyaniak, M. D., Fataftah, M. S., Wasielewski, M. R., & Freedman, D. E. (2018) · Chemical Science · doi:10.1039/c8sc04435j · Cited by 104
Digital quantum simulation, Trotter errors, and quantum chaos of the kicked top
Sieberer, L. M., Olsacher, T., Elben, A., Heyl, M., Hauke, P., Haake, F., & Zoller, P. (2019) · npj Quantum Information · doi:10.1038/s41534-019-0192-5 · Cited by 121
“(3) corresponds to the lowest-order decomposition with m= 1, and a first improvement can be obtained by symmetrization”
BackgroundInfluentialUniversal simulation of Markovian quantum dynamics
Bacon, D., Childs, A. M., Chuang, I. L., Kempe, J., Leung, D., & Zhou, X. (2001) · Physical Review A · doi:10.1103/physreva.64.062302 · Cited by 104
Aharonov, D. (1999) · WORLD SCIENTIFIC eBooks · doi:10.1142/9789812815569_0007 · Cited by 131
Entangling dipole-dipole interactions for quantum logic with neutral atoms
Brennen, G. K., Deutsch, I., & Jessen, P. (2000) · Physical Review A · doi:10.1103/physreva.61.062309 · Cited by 101
Digital Quantum Rabi and Dicke Models in Superconducting Circuits
Mezzacapo, A., Las Heras, U., Pedernales, J. S., DiCarlo, L., Solano, E., & Lamata, L. (2014) · Scientific Reports · doi:10.1038/srep07482 · Cited by 111
“(2), via digital decomposition [21], by interleaving the simulated interactions.”
BackgroundEfficiently Computable Bounds for Magic State Distillation
Wang, X., Wilde, M. M., & Su, Y. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.090505 · Cited by 120
Chia, N.-H., Gilyén, A., Li, T., Lin, H.-H., Tang, E., & Wang, C. (2020) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/3357713.3384314 · Cited by 106
Solving Gauss's law on digital quantum computers with loop-string-hadron digitization
Raychowdhury, I., & Stryker, J. R. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.033039 · Cited by 101
“Quantum computation is expected to efficiently simulate quantum-mechanical many-body problems [1–3], as quantum computers can handle the exponential growth of information in entangled quantum systems that overwhelms classical computers.”
BackgroundCollision Models Can Efficiently Simulate Any Multipartite Markovian Quantum Dynamics
Cattaneo, M., Chiara, G. D., Maniscalco, S., Zambrini, R., & Giorgi, G. L. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.130403 · Cited by 100
“This is a standard assumption for quantum simulation on a cir-cuital quantum computer, introduced by Kliesch et al. for open systems [68, 80], and first imposed in the seminal paper by Lloyd on Hamiltonian quantum simulation [81].”
BackgroundMethodQuantum lattice-gas model for the many-particle Schrödinger equation in d dimensions
Boghosian, B. M., & Taylor, W. (1998) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.57.54 · Cited by 109
Architectures for Quantum Simulation Showing a Quantum Speedup
Bermejo-Vega, J., Hangleiter, D., Schwarz, M., Raussendorf, R., & Eisert, J. (2018) · Physical Review X · doi:10.1103/physrevx.8.021010 · Cited by 122
“The anticipated device of a universal quantum computer would solve problems for which no efficient classical algorithm is known, such as integer factorization [1] and simulating many-body Hamiltonian dynamics [2].”
BackgroundCalculating energy derivatives for quantum chemistry on a quantum computer
O’Brien, T. E., Senjean, B., Sagastizabal, R., Bonet-Monroig, X., Dutkiewicz, A., Buda, F., DiCarlo, L., & Visscher, L. (2019) · npj Quantum Information · doi:10.1038/s41534-019-0213-4 · Cited by 108
Many-Body Physics in the NISQ Era: Quantum Programming a Discrete Time Crystal
Ippoliti, M., Kechedzhi, K., Moessner, R., Sondhi, S. L., & Khemani, V. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.030346 · Cited by 105
“We emphasize here that we are not viewing these platforms as universal computational devices that can simulate any desired unitary evolution [2, 12, 13] or allow computational investigation of the properties of particular Hamiltonians and quantum states [14–16].”
BackgroundChen, S., Cotler, J. S., Huang, H.-Y., & Li, J. Z. (2023) · Nature Communications · doi:10.1038/s41467-023-41217-6 · Cited by 139
“Fault-tolerant quantum computing promises to offer speed-ups to various computational problems, including simulating quantum systems [1, 2, 3, 4, 5], factoring large numbers [6, 7], performing optimization [8, 9, 10, 11], and solving linear systems of equations [12].”
Black-box Hamiltonian simulation and unitary implementation
Childs, A. M., & Berry, D. W. (2012) · Quantum Information and Computation · doi:10.26421/qic12.1-2-4 · Cited by 107
Quantum computing for near-term applications in generative chemistry and drug discovery.
Pyrkov, A., Aliper, A., Bezrukov, D., Lin, Y.-C., Polykovskiy, D., Kamya, P., Ren, F., & Zhavoronkov, A. (2023) · Drug Discovery Today · doi:10.1016/j.drudis.2023.103675 · Cited by 100
Confirmation via Analogue Simulation: What Dumb Holes Could Tell Us about Gravity
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“18See (Lloyd 1996; Cirac and Zoller 2012; Greiner, Mandel, Esslinger, Hänsch, and Bloch 2002b; Ma, Dakic, Naylor, Zeilinger, and Walther 2011) for more details of both the concept and its applications.”
BackgroundLocality and Digital Quantum Simulation of Power-Law Interactions
Tran, M. C., Guo, A. Y., Su, Y., Garrison, J. R., Eldredge, Z., Foss‐Feig, M., Childs, A. M., & Gorshkov, A. V. (2019) · Physical Review X · doi:10.1103/physrevx.9.031006 · Cited by 109
“Using the best-known rigorous error bounds, simulations based on the first-order Suzuki-Trotter product formula [44] use OðT2n6=εÞ gates to simulate the evolution U0;T of a time-dependent Hamiltonian on n sites up to a fixed error ε.”
MethodHolographic quantum algorithms for simulating correlated spin systems
Foss-Feig, M., Hayes, D., Dreiling, J. M., Figgatt, C., Gaebler, J. P., Moses, S. A., Pino, J. M., & Potter, A. C. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.033002 · Cited by 100
“[12] Seth Lloyd, “Universal quantum simulators,” Science 273, 1073–1078 (1996).”
BackgroundCompact fermion to qubit mappings
Derby, C., Klassen, J., Bausch, J., & Cubitt, T. S. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.035118 · Cited by 100
“We wish to implement a time dynamics simulation of the system via Trotterization [4]; for instance, for a small time-step δ, we approximate e−iHF T T/δ∏ n=0 ∏ j e−iHjδ + O(δ).”
MethodBlack-box hamiltonian simulation and unitary implementationPreprint
Berry, D. W., & Childs, A. M. (2012) · doi:10.5555/2231036.2231040 · Cited by 122
Brown, K. R., Clark, R. J., & Chuang, I. L. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.050504 · Cited by 98
Trapped ions in optical lattices for probing oscillator chain models
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A scalable quantum computing platform using symmetric-top molecules
Yu, P., Cheuk, L. W., Kozyryev, I., & Doyle, J. M. (2019) · New Journal of Physics · doi:10.1088/1367-2630/ab428d · Cited by 98
Quantum information processing and metrology with trapped ions
Wineland, D. J., & Leibfried, D. G. (2011) · Laser Physics Letters · doi:10.1002/lapl.201010125 · Cited by 96
Universal quantum Hamiltonians
Cubitt, T. S., Montanaro, A., & Piddock, S. (2018) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1804949115 · Cited by 132
“Lloyd S (1996) Universal quantum simulators.”
MethodQX: A high-performance quantum computer simulation platform
Khammassi, N., Ashraf, I., Fu, X., Almudéver, C. G., & Bertels, K. (2017) · Design, Automation, and Test in Europe · doi:10.23919/date.2017.7927034 · Cited by 98
“It has been demonstrated that a universal quantum computer can simulate any Turing machine [23] and any local quantum system [24].”
BackgroundElectronic Structure Calculations and the Ising Hamiltonian
Xia, R., Bian, T., & Kais, S. (2017) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.7b10371 · Cited by 103
Digital quantum simulation of molecular vibrations
McArdle, S., Mayorov, A., Shan, X., Benjamin, S. C., & Yuan, X. (2019) · Chemical Science · doi:10.1039/c9sc01313j · Cited by 108
Quantum thermodynamics and open-systems modeling
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Quantum simulation of quantum field theory in the light-front formulation
Kreshchuk, M., Kirby, W. M., Goldstein, G. R., Beauchemin, P. H., & Love, P. J. (2022) · Physical Review A · doi:10.1103/physreva.105.032418 · Cited by 125
“A decade later the first general quantum algorithms appeared [2, 3, 4, 5, 6], with applications to quantum chemistry [7], condensed matter [8], and high energy physics [9].”
BackgroundEntanglement and work extraction in the central-spin quantum battery
Liu, J., Shi, H., Shi, Y., Wang, X.-H., & Yang, W. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.245418 · Cited by 98
Simulating Quantum Mechanics on a Quantum Computer
Boghosian, B. M., & Taylor, W. (1997) · Cited by 98
Quantum localization bounds Trotter errors in digital quantum simulation
Heyl, M., Hauke, P., & Zoller, P. (2019) · MPG.PuRe (Max Planck Society) · Cited by 97
A comprehensive review of quantum machine learning: from NISQ to fault tolerance
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“We begin by introducing Quantum Phase Estimation (QPE) [32, 81] in section 3.1, where we also delve into the Quantum Principal Component Analysis (QPCA) program [101].”
InfluentialQuantum Dot Systems: a versatile platform for quantum simulations
Barthelemy, P., & Vandersypen, L. M. K. (2013) · Annalen der Physik · doi:10.1002/andp.201300124 · Cited by 95
Qubit devices and the issue of quantum decoherence
Brandt, H. E. (1999) · Progress in Quantum Electronics · doi:10.1016/s0079-6727(99)00003-8 · Cited by 102
Operator locality in the quantum simulation of fermionic models
Havlíček, V., Troyer, M., & Whitfield, J. D. (2017) · Physical Review A · doi:10.1103/physreva.95.032332 · Cited by 92
“Among the various applications of quantum computing, quantum simulation has long stood out as a primary motivation [1, 2].”
BackgroundMethodUsing Concatenated Quantum Codes for Universal Fault-Tolerant Quantum Gates
Jochym-O’Connor, T., & Laflamme, R. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.010505 · Cited by 94
Quantum Supremacy for Simulating a Translation-Invariant Ising Spin Model
Gao, X., Wang, S.-T., & Duan, L. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.040502 · Cited by 96
Rimbach-Russ, M., & Burkard, G. (2017) · Journal of Physics Condensed Matter · doi:10.1088/1361-648x/aa761f · Cited by 97
“to be superior in simulating other quant um systems [29, 30],”
BackgroundA volumetric framework for quantum computer benchmarks
Blume-Kohout, R., & Young, K. C. (2020) · Quantum · doi:10.22331/q-2020-11-15-362 · Cited by 122
“Protocol: Trotterized Hamiltonian simulation [40].”
Single-Copies Estimation of Entanglement Negativity
Zhou, Y., Zeng, P., & Liu, Z. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.200502 · Cited by 93
Kim, I. H., Liu, Y.-H., Pallister, S., Pol, W., Roberts, S., & Lee, E. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.023019 · Cited by 116
“Quantum computers are capable of carrying out computational tasks that are intractable for classical computers, such as integer factorization [1], combinatorial optimization [2], simulation of interacting quantum manybody systems [3, 4], and quantum chemistry [5] to name a few.”
BackgroundA perspective on scaling up quantum computation with molecular spins
Carretta, S., Zueco, D., Chiesa, A., Gómez-León, Á., & Luis, F. (2021) · Applied Physics Letters · doi:10.1063/5.0053378 · Cited by 99
Simulation of quantum dynamics with quantum optical systems
Jané, E., Vidal, G., Dür, W., Zoller, P., & Cirac, J. I. (2003) · Quantum Information and Computation · doi:10.26421/qic3.1-2 · Cited by 145
A Full Quantum Eigensolver for Quantum Chemistry Simulations
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“The universal quantum simulation method [4] and the first quantum algorithm for simulating fermions [5] have laid down the fundamental block of quantum chemistry simulation.”
MethodPreparations for quantum simulations of quantum chromodynamics in 1+1 dimensions. I. Axial gauge
Farrell, R. C., Chernyshev, I. A., Powell, S. J. M., Zemlevskiy, N. A., Illa, M., & A, M. J. S. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.054512 · Cited by 97
Efficient Quantum Computing of Complex Dynamics
Benenti, G., Casati, G., Montangero, S., & Shepelyansky, D. L. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.227901 · Cited by 95
Digital-analog quantum simulations with superconducting circuits
Lamata, L., Parra-Rodriguez, A., Sanz, M., & Solano, E. (2018) · Advances in Physics X · doi:10.1080/23746149.2018.1457981 · Cited by 103
Quantum computing for neutrino-nucleus scattering
Roggero, A., Li, A. C. Y., Carlson, J., Gupta, R., & Perdue, G. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.101.074038 · Cited by 103
A survey on HHL algorithm: From theory to application in quantum machine learning
Duan, B., Yuan, J., Yu, C., Huang, J., & Hsieh, C. (2020) · Physics Letters A · doi:10.1016/j.physleta.2020.126595 · Cited by 99
García-Pérez, G., Rossi, M. A. C., Sokolov, B., Tacchino, F., Barkoutsos, P. K., Mazzola, G., Tavernelli, I., & Maniscalco, S. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.040342 · Cited by 105
“[4] Seth Lloyd, “Universal quantum simulators,” Science 273, 1073–1078 (1996).”
Quantum Computation Over Continuous Variables
Lloyd, S., & Braunstein, S. L. (1999) · Springer eBooks · doi:10.1007/978-94-015-1258-9_2 · Cited by 113
Self-citationMolecular Nanomagnets as Quantum Simulators
Santini, P. M., Carretta, S., Troiani, F., & Amoretti, G. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.230502 · Cited by 94
Quantum Simulation of Quantum Field Theories in Trapped Ions
Casanova, J., Lamata, L., Egusquiza, I. L., Gerritsma, R., Roos, C. F., García‐Ripoll, J. J., & Solano, E. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.260501 · Cited by 91
Quantum Computing for Molecular Biology**
Baiardi, A., Christandl, M., & Reiher, M. (2023) · ChemBioChem · doi:10.1002/cbic.202300120 · Cited by 93
Heilmann, R., Gräfe, M., Nolte, S., & Szameit, A. (2015) · 中国科学通报：英文版 · doi:10.1007/s11434-014-0688-5 · Cited by 93
Improved quantum algorithms for linear and nonlinear differential equations
Krovi, H. (2023) · Quantum · doi:10.22331/q-2023-02-02-913 · Cited by 148
“Simulating the Schr¨odinger equation or, in other words, Hamiltonian simulation can be done efficiently for several classes of Hamil-tonians and important techniques were developed in a long line of work [4–8].”
Zeng, B., Chen, X., Zhou, D.-L., & Wen, X.-G. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1508.02595 · Cited by 182
“e quantum circuit needs to have a depth which scales at least linearly with system size. On the other hand, the simulability of local unitary evolution by a local unitary quantum circuit was shown in [28]. [6] gives a general discussion of the local unitary equivalence condition, the relation between topological order…”
BackgroundEfficient quantum walk on a quantum processor
Qiang, X., Loke, T., Montanaro, A., Aungskunsiri, K., Zhou, X., O’Brien, J. L., Wang, J. B., & Matthews, J. C. F. (2016) · Nature Communications · doi:10.1038/ncomms11511 · Cited by 108
Metal–ligand covalency enables room temperature molecular qubit candidates
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Global optimization of quantum dynamics with AlphaZero deep exploration
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“[3] Lloyd, S.”
MethodReview: Quantum metrology and sensing with many-body systems
Montenegro, V., Mukhopadhyay, C., Yousefjani, R., Sarkar, S., Mishra, U., Paris, M. G. A., & Bayat, A. (2025) · Physics Reports · doi:10.1016/j.physrep.2025.05.005 · Cited by 145
“In a broad sense, quantum technologies are developed in three directions, namely quantum simulation and computation [2, 3], quantum communication [4, 5], and quantum sensing [6].”
Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits
Bonneau, D., Engin, E., Ohira, K., Suzuki, N., Yoshida, H., Iizuka, N., Ezaki, M., Natarajan, C. M., Tanner, M. G., Hadfield, R. H., et al. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/4/045003 · Cited by 79
“modes of computation [1, 2], simulation [3, 4] and communication [5], as well as enhanced measurements and sensing [6].”
BackgroundQuantum algorithm for nonhomogeneous linear partial differential equations
Arrazola, J. M., Kalajdzievski, T. Z., Weedbrook, C., & Lloyd, S. (2019) · Physical Review A · doi:10.1103/physreva.100.032306 · Cited by 98
Self-citationQuantum computing in power systems
Zhou, Y., Tang, Z., Nikmehr, N., Babahajiani, P., Feng, F., Wei, T.-C., Zheng, H., & Zhang, P. (2022) · iEnergy · doi:10.23919/ien.2022.0021 · Cited by 105
Testing the Structure of Multipartite Entanglement with Bell Inequalities
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Effect of loss on multiplexed single-photon sources
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Coherent imaging spectroscopy of a quantum many-body spin system
Senko, C., Smith, J., Richerme, P., Lee, A., Campbell, W. C., & Monroe, C. R. (2014) · Science · doi:10.1126/science.1251422 · Cited by 89
Symmetry principles in quantum systems theory
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Fermion-Fermion Scattering in Quantum Field Theory with Superconducting Circuits
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An introduction to quantum information processing: applications and realizations
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Learning high-accuracy error decoding for quantum processors
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“Beyond Shor’s well-known prime factoring algorithm [83] and Grover’s quadratic speedup for unstructured search [39], many potential applications in fields such as material science [59, 3, 4, 75], machine learning [8, 47, 46], and optimization [25, 86], have been proposed.”
Tunable spin–spin interactions and entanglement of ions in separate potential wells
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“1(2) kHz) and an optical sideband excitation at v0{ v (Rabi frequency, gVs 5 2p3 2.”
BackgroundMethodInfluentialAdiabatic state preparation study of methylene
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Current nuclear data needs for applications
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“In theory, universal quantum computers can achieve the same exponential scaling, with the up-shot that a quantum computer with thousands of qubits could simulate some nuclear reactions not possible even on future exascale classical supercomputers [58].”
BackgroundBiology and medicine in the landscape of quantum advantages
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“Quantum algorithms for quantum simulation Arguably, there are three broad quantum computational methods used when studying quantum physical systems: time propagation [37,74], quantum phase estimation (QPE) [294,295] and the variational quantum eigensolver (VQE) [136,163,296].”
BackgroundDynamical decoupling leads to improved scaling in noisy quantum metrology
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Petruzziello, L., & Illuminati, F. (2021) · RePEc: Research Papers in Economics · Cited by 86
Molecular nanomagnets: a viable path toward quantum information processing?
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Simulating quantum dynamics on a quantum computer
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Digital quantum simulation, Trotter errors, and quantum chaos of the kicked top
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Prediction and real-time compensation of qubit decoherence via machine learning
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Simulating Sparse Hamiltonians with Star Decompositions
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“These Hamiltonians are then recombined using the Lie–Trotter formula, which expresses the time evolution due to H as a product of time evolutions due to the Hj.”
MethodInfluentialQuantum Computation of Scattering in Scalar Quantum Field Theories
Jordan, S. P., Lee, K. S. M., & Preskill, J. P. (2014) · CaltechAUTHORS (California Institute of Technology) · Cited by 85
Babbush, R., Berry, D. W., Sanders, Y. R., Kivlichan, I., Scherer, A., Wei, A. Y., Love, P. J., & Aspuru‐Guzik, A. (2017) · Quantum Science and Technology · doi:10.1088/2058-9565/aa9463 · Cited by 85
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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