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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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Simulating large-size quantum spin chains on cloud-based superconducting quantum computers
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“In particular, Feynman suggested using quantum computers to simulate other quantum systems instead of using classical computers, giving rise to the notion of a universal quantum simulator [4].”
MethodA Trotter-Suzuki approximation for Lie groups with applications to Hamiltonian simulation
Somma, R. D. (2016) · Journal of Mathematical Physics · doi:10.1063/1.4952761 · Cited by 33
Closing Gaps of a Quantum Advantage with Short-Time Hamiltonian Dynamics
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Quantum simulation of nuclear inelastic scattering
Du, W., Vary, J. P., Zhao, X., & Wei, Z. (2021) · Physical Review A · doi:10.1103/physreva.104.012611 · Cited by 47
Bibliometric Survey of Quantum Machine Learning
Pande, M. B., & Mulay, P. (2020) · Science & Technology Libraries · doi:10.1080/0194262x.2020.1776193 · Cited by 39
“…quantum simulation, quantum chemistry, quantum communications, quantum internet, quantum cryptography, and quantum machine learning amongst others (Grover 1996; Bennett and Brassard 1987; Bennett 1992; Cirac and Zoller 1995; Jones and Mosca 1998; Lloyd 1996; Harrow, Hassidim, and Lloyd 2009).”
BackgroundSelected topics of quantum computing for nuclear physics*
Zhang, D.-B., Xing, H., Yan, H., Wang, E., & Zhu, S.-L. (2020) · Chinese Physics B · doi:10.1088/1674-1056/abd761 · Cited by 38
Initialization of quantum simulators by sympathetic cooling
Raghunandan, M., Wolf, F., Ospelkaus, C., Schmidt, P. O., & Weimer, H. (2020) · Institutional Repository of Leibniz Universität Hannover (Leibniz Universität Hannover) · doi:10.15488/9420 · Cited by 36
Digital quantum simulation of Floquet topological phases with a solid-state quantum simulator
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“AQS, digital quantum simulation (DQS) [11, 12, 40– 43] encodes the state of the quantum system onto ar X iv :2 01 2.”
BackgroundSopena, A., Gordon, M. H., García-Martín, D., Sierra, G., & López, E. (2022) · Quantum · doi:10.22331/q-2022-09-08-796 · Cited by 38
“One of the most widely-recognized applications of quantum computing is the efficient simulation of many-body quantum systems [1].”
BackgroundSimulating quantum operations with mixed environments
Terhal, B. M., Chuang, I. L., Divincenzo, D. P., Grassl, M., & Smolin, J. A. (1999) · Physical Review A · doi:10.1103/physreva.60.881 · Cited by 36
Testing integrability with a single bit of quantum information
Poulin, D., Laflamme, R., Milburn, G. J., & Paz, J. P. (2003) · Physical Review A · doi:10.1103/physreva.68.022302 · Cited by 39
Obada, A. ‐. F., Hessian, H. A., Mohamed, A. A., & Homid, A. H. (2013) · Quantum Information Processing · doi:10.1007/s11128-013-0664-z · Cited by 35
“For instance, quantum computers when constructed can factor large numbers more rapidly [3], search data basis more quickly [4], and simulate quantum systems more efficiently [5] than the classical ones.”
BackgroundGocho, S., Nakamura, H., Kanno, S., Gao, Q., Kobayashi, T., Inagaki, T., & Hatanaka, M. (2023) · npj Computational Materials · doi:10.1038/s41524-023-00965-1 · Cited by 41
Quantum Many-Body Systems in Thermal Equilibrium
Alhambra, A. M. (2023) · PRX Quantum · doi:10.1103/prxquantum.4.040201 · Cited by 55
“These Trotter errors are most commonly analyzed in the context of digital quantum simulation [39], for which it is often convenient to go to higher orders in the decomposition.”
BackgroundMagnetic Molecules as Building Blocks for Quantum Technologies
Pineda, E. M., & Wernsdorfer, W. (2024) · Advanced Quantum Technologies · doi:10.1002/qute.202300367 · Cited by 35
Quantum memories and error correction
Wootton, J. R. (2012) · Journal of Modern Optics · doi:10.1080/09500340.2012.737937 · Cited by 36
Quantum magnetism of spin-ladder compounds with trapped-ion crystals
Bermúdez, A., de Almeida, J. O., Ott, K., Kaufmann, H., Ulm, S., Poschinger, U., Schmidt‐Kaler, F., Retzker, A., & Plenio, M. B. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/9/093042 · Cited by 35
Quantum Monte Carlo study of long-range transverse-field Ising models on the triangular lattice
Humeniuk, S. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.93.104412 · Cited by 36
Kasture, S., Lenzini, F., Haylock, B., Boes, A., Mitchell, A., Streed, E. W., & Lobino, M. (2016) · Journal of Optics · doi:10.1088/2040-8978/18/10/104007 · Cited by 35
Towards simulation of the dynamics of materials on quantum computers
Oftelie, L. B., Liu, K., Krishnamoorthy, A., Linker, T., Geng, Y., Shebib, D., Fukushima, S., Shimojo, F., Kalia, R. K., Nakano, A., et al. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.101.184305 · Cited by 36
Digital quantum simulation of non-equilibrium quantum many-body systems
Fauseweh, B., & Zhu, J. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-03079-z · Cited by 42
“With quantum complexity theory, it is possible to prove that the simulation of quantum systems scales only polynomial on a general purpose quantum computer [5].”
BackgroundGutzwiller hybrid quantum-classical computing approach for correlated materials
Yao, Y., Zhang, F., Wang, C., Ho, K., & Orth, P. P. (2021) · Iowa State University Digital Repository (Iowa State University) · Cited by 35
Embedding classical dynamics in a quantum computer
Giannakis, D., Ourmazd, A., Pfeffer, P., Schumacher, J., & Sławińska, J. (2022) · Physical Review A · doi:10.1103/physreva.105.052404 · Cited by 40
Quantum readout error mitigation via deep learning
Kim, J., Oh, B., Chong, Y., Hwang, E. H., & Park, D. K. (2022) · New Journal of Physics · doi:10.1088/1367-2630/ac7b3d · Cited by 39
Shadow Tomography from Emergent State Designs in Analog Quantum Simulators
McGinley, M., & Fava, M. (2023) · Physical Review Letters · doi:10.1103/physrevlett.131.160601 · Cited by 41
“In a universal quantum computer, where logical gates can be selectively applied to a few qubits at a time, one can in principle mimic the dynamics of any Hamiltonian [3]; however at present such devices are limited by their size and noisiness [4].”
BackgroundQuantum computing for fusion energy science applications
Joseph, I., Shi, Y. C., Porter, M. D., Castelli, A. R., Geyko, V., Graziani, F. R., Libby, S. B., & DuBois, J. L. (2023) · Physics of Plasmas · doi:10.1063/5.0123765 · Cited by 42
“108 Then, one can use operator splitting techniques, such as the Trotter-Suzuki decomposition and Lie group decomposition formulas, 143 to approximate the unitary corresponding to the full Hamiltonian as a product of terms with sufficiently small time steps.”
MethodExperimental Quantum Simulation of Entanglement in Many-Body Systems
Zhang, J., Wei, T.-C., & Laflamme, R. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.010501 · Cited by 35
High Performance Single-Error-Correcting Quantum Codes for Amplitude Damping
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“Quantum computers may also be useful for simulating quantum systems [2], [3].”
BackgroundTowards a Coherent Theory of Physics and Mathematics
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Factorization of numbers with physical systems
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Level Reduction and the Quantum Threshold TheoremPreprint
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“, [11, 12, 13, 14, 15]), to understanding the physics of condensed-matter systems and computing ground-state energies of complex molecules (e.”
BackgroundQuantum Algorithms for Scientific Computing and Approximate OptimizationPreprint
Hadfield, S. (2018) · arXiv (Cornell University) · doi:10.7916/d8x650c9 · Cited by 76
“Later, Aharonov and Ta-Shma [5] generalized Lloyd’s results to sparse Hamiltonians.”
BackgroundBabbush, R., Huggins, W. J., Berry, D. W., Ung, S. F., Zhao, A., Reichman, D. R., Neven, H., Baczewski, A. D., & Lee, J. (2023) · Nature Communications · doi:10.1038/s41467-023-39024-0 · Cited by 32
“Quantum computers were first proposed as tools for dynamics by Feynman1 and later shown to be universal for that purpose by Lloyd et al.2.”
MethodPolla, S., Herasymenko, Y., & O’Brien, T. E. (2021) · Physical Review A · doi:10.1103/physreva.104.012414 · Cited by 36
“Simulating an entire bath would require an impractically large quantum register, however it has long been suggested that this may be mimicked by coupling to a single qubit which may be reset to its ground state with sufficient frequency [3].”
BackgroundToward simulating superstring/M-theory on a quantum computer
Gharibyan, H., Hanada, M., Honda, M., & Liu, J. (2021) · Journal of High Energy Physics · doi:10.1007/jhep07(2021)140 · Cited by 34
“[96–100].”
MethodVariational Quantum Simulation: A Case Study for Understanding Warm Starts
Puig, R., Drudis, M., Thanasilp, S., & Holmes, Z. (2025) · PRX Quantum · doi:10.1103/prxquantum.6.010317 · Cited by 59
“In practice, for each small evolution, one could further decompose it by using either Trotter approximation for real-time dynamics [44], or a similar procedure for imaginary-time dynamics [38].”
Simulation of single-qubit open quantum systems
Sweke, R., Sinayskiy, I., & Petruccione, F. (2014) · Physical Review A · doi:10.1103/physreva.90.022331 · Cited by 33
Unitarity, feedback, interactions—dynamics emergent from repeated measurements
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“This correspondence is directly applied in quantum simulations [9], quantum control [5], quantum computation [10, 11] – in all scenarios where a particular Hamiltonian for the system is desired, or when an existing system-environment interaction needs to be suppressed [12].”
BackgroundAb initio molecular dynamics on quantum computers
Fedorov, D. A., Otten, M., Gray, S. K., & Alexeev, Y. (2021) · The Journal of Chemical Physics · doi:10.1063/5.0046930 · Cited by 35
Quantum tomography using state-preparation unitaries
van Apeldoorn, J., Cornelissen, A., Gilyén, A., & Nannicini, G. (2023) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611977554.ch47 · Cited by 34
Two-Unitary Decomposition Algorithm and Open Quantum System Simulation
Suri, N., Barreto, J., Hadfield, S., Wiebe, N., Wudarski, F., & Marshall, J. (2023) · Quantum · doi:10.22331/q-2023-05-15-1002 · Cited by 37
“Since then an entire zoo of quantum algorithms for simulating quantum processes has emerged, some of them promise spectacular improvements over their classical alternatives, even exponential speedups [3, 4, 5, 6, 7, 8].”
BackgroundQuantum Differential Equation Solvers: Limitations and Fast-Forwarding
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Bio‐Inspired and Nanoscale Integrated Computing
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Experimental quantum channel simulation
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A Generic Compilation Strategy for the Unitary Coupled Cluster AnsatzPreprint
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“In order to generate a quantum circuit, we employ Trotterization, justified by Lloyd [39].”
MethodExperimental and theoretical challenges for the trapped electron quantum computer
Marzoli, I., Tombesi, P., Ciaramicoli, G., Werth, G., Bushev, P., Stahl, S., Schmidt-Kaler, F., Hellwig, M., Henkel, C., Marx, G., et al. (2009) · Journal of Physics B: Atomic, Molecular and Optical Physics · doi:10.1088/0953-4075/42/15/154010 · Cited by 33
“e to the same environment. In the low-frequency regime the wire mainly acts as a capacitive coupler. The coherent coupling is described by the Hamiltonian Hz,12 = ¯hΩ 12 a† z,1 az,2 +az,1 a † z,2 (7) Table 2. Coupling strength of the wire mediated interaction Ω12 in units ω/(2π) for different trap radii R0 and inter-tr…”
BackgroundChoi, S., Loaiza, I., & Izmaylov, A. F. (2023) · Quantum · doi:10.22331/q-2023-01-03-889 · Cited by 38
“A commonly employed technique for the time evolution is Trotterization [47, 48].”
MethodOne T Gate Makes Distribution Learning Hard
Hinsche, M., Ioannou, M., Nietner, A., Haferkamp, J., Quek, Y., Hangleiter, D., Seifert, J., Eisert, J., & Sweke, R. (2023) · Physical Review Letters · doi:10.1103/physrevlett.130.240602 · Cited by 61
Mitigating Barren Plateaus of Variational Quantum Eigensolvers
Liu, X., Liu, G., Zhang, H.-K., Huang, J., & Wang, X. (2024) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2024.3383050 · Cited by 55
“Quantum computers are expected to achieve quantum advantages [1] in solving valuable problems [2], [3], [4], [5].”
A flexible iron( ii ) complex in which zero-field splitting is resistant to structural variation
Zadrozny, J. M., Greer, S. M., Hill, S., & Freedman, D. E. (2015) · Chemical Science · doi:10.1039/c5sc02477c · Cited by 33
Experimental digital quantum simulation of temporal–spatial dynamics of interacting fermion system
Lu, Y., Feng, G., Li, Y., & Long, G. (2015) · 中国科学通报：英文版 · doi:10.1007/s11434-014-0712-9 · Cited by 32
“Since Feynman’s innovative proposal, there have been a number of significant works, including the general techniques of universal quantum simulation [2], the specific algorithms for various quantum simulation tasks such as the quantum many-body problem [3–10], quantum chemistry [11–17], and condensed matter physics [1…”
BackgroundProbing the Full Distribution of Many-Body Observables By Single-Qubit Interferometry
Xu, Z., & del Campo, A. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.160602 · Cited by 33
Efficient simulation of sparse Markovian quantum dynamics
Childs, A. M., & Li, T. (2017) · Quantum Information and Computation · doi:10.26421/qic17.11-12-1 · Cited by 65
Quantum computation of silicon electronic band structure
Cerasoli, F. T., Sherbert, K., Sławińska, J., & Nardelli, M. B. (2020) · Physical Chemistry Chemical Physics · doi:10.1039/d0cp04008h · Cited by 38
Efficient sampling of ground and low-energy Ising spin configurations with a coherent Ising machine
Ng, E., Onodera, T., Kako, S., McMahon, P. L., Mabuchi, H., & Yamamoto, Y. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.013009 · Cited by 35
“In the high-finesse limit, each discrete operation only implements an infinitesimal change ρ̂ 7→ ρ̂ + dρ̂ to the state ρ̂ and, as in the Trotterization of quantum dynamics [42, 43], the exact order in which the operations are composed within one roundtrip becomes unimportant, allowing us to analyze the operations in S…”
BackgroundReal-time quantum calculations of phase shifts using wave packet time delays
Gustafson, E., Zhu, Y., Dreher, P., Linke, N. M., & Meurice, Y. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.104.054507 · Cited by 44
Correlations and dynamical quantum phase transitions in an interacting topological insulator
Yu, W. C., Sacramento, P. D., Li, Y., & Lin, H. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.085104 · Cited by 36
Lumia, L., Torta, P., Mbeng, G. B., Santoro, G. E., Ercolessi, E., Burrello, M., & Wauters, M. M. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.020320 · Cited by 36
“Another strategic application is the simulation of interacting quantum many-body problems that are intrinsically hard to simulate with classical computers [20].”
BackgroundProbing resonating valence bonds on a programmable germanium quantum simulator
Wang, C.-A., Déprez, C., Tidjani, H., Lawrie, W. I. L., Hendrickx, N. W., Sammak, A., Scappucci, G., & Veldhorst, M. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00727-3 · Cited by 33
“[2], the authors evaluated the Zeeman energy noise in germanium ST qubits placed in a perpendicular magnetic field.”
BackgroundProgrammable N -Body Interactions with Trapped Ions
Katz, O., Cetina, M., & Monroe, C. R. (2023) · PRX Quantum · doi:10.1103/prxquantum.4.030311 · Cited by 39
Lloyd, S. (2003) · Springer eBooks · doi:10.1007/978-94-015-1258-9_5 · Cited by 33
Self-citationSpin qubits for quantum simulations
Peng, X., & Suter, D. (2009) · 物理学前沿：英文版 · doi:10.1007/s11467-009-0067-x · Cited by 33
Hamiltonian simulation with nearly optimal dependence on spectral norm
Low, G. H. (2019) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/3313276.3316386 · Cited by 35
“The first explicit quantum simulation algorithm by Lloyd [25] considered Hamiltonians described by a sum of nontrivial local interaction terms, which is relevant to many realistic systems.”
MethodQuantum computing classical physics
Meyer, D. (2002) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2001.0936 · Cited by 34
“Developments during the subsequent two decades have not only supported this observation [2–8], but have also demonstrated that quantum computers would—if they existed—solve certain classical problems like factoring more efficiently than is possible on classical computers running the best classical…”
Quantum Computing: Lecture NotesPreprint
de Wolf, R. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1907.09415 · Cited by 197
“This is the first-order Lie-Suzuki-Trotter approach to Hamiltonian simulation, due to Lloyd [100].”
MethodKang, M., Nuomin, H., Chowdhury, S. N., Yuly, J. L., Sun, K., Whitlow, J., Valdiviezo, J., Zhang, Z., Zhang, P., Beratan, D. N., et al. (2024) · Nature Reviews Chemistry · doi:10.1038/s41570-024-00595-1 · Cited by 40
“The evolution of the full system to time τ can be simulated using Trotterization, in which the time evolution of the Hamiltonian is simulated for a short time step τ / S , and the process is repeated S times 131 .”
Effect of loss on photon-pair generation in nonlinear waveguide arrays
Antonosyan, D. A., Solntsev, A. S., & Sukhorukov, A. A. (2014) · Physical Review A · doi:10.1103/physreva.90.043845 · Cited by 34
Efficient quantum circuits for Szegedy quantum walks
Loke, T., & Wang, J. B. (2017) · Annals of Physics · doi:10.1016/j.aop.2017.04.006 · Cited by 35
Castaldo, D., Rosa, M., & Corni, S. (2021) · Physical Review A · doi:10.1103/physreva.103.022613 · Cited by 32
“To compute the time evolution operator by making use of the Trotter-Suzuki (TS) approximation[29] we discretize the time axis in K time slots of width ∆ t = t j +1 − t j and approximate the integration as if the Hamiltonian were constant within the given time interval: We are now able to decompose…”
MethodVariational quantum eigensolver techniques for simulating carbon monoxide oxidation
Sapova, M. D., & Fedorov, A. K. (2022) · Communications Physics · doi:10.1038/s42005-022-00982-4 · Cited by 36
Quantum algorithms from fluctuation theorems: Thermal-state preparation
Holmes, Z., Muraleedharan, G., Somma, R. D., Subaşı, Y., & Şahinoğlu, B. (2022) · Quantum · doi:10.22331/q-2022-10-06-825 · Cited by 40
Quantum simulation with natural decoherence
Tseng, C.-H., Somaroo, S. S., Sharf, Y., Knill, E. H., Laflamme, R., Havel, T. F., & Cory, D. G. (2000) · Physical Review A · doi:10.1103/physreva.62.032309 · Cited by 32
Digital quantum simulators in a scalable architecture of hybrid spin-photon qubits
Chiesa, A., Santini, P. M., Gerace, D., Raftery, J. J., Houck, A., & Carretta, S. (2015) · Scientific Reports · doi:10.1038/srep16036 · Cited by 32
“[32] D. S. Abrams and S. Lloyd, Simulation of Many-Body Fermi Systems on a Universal Quantum Computer, Phys.”
BackgroundInfluentialNegative string tension of a higher-charge Schwinger model via digital quantum simulation
Honda, M., Itou, E., Kikuchi, Y., & Tanizaki, Y. (2022) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptac007 · Cited by 34
“This is the second-order Suzuki-Trotter approximation, and its error is estimated as O(Mδt2) for the whole operator for fixed T [73, 74].”
BackgroundCastaldo, D., Rosa, M., & Corni, S. (2020) · arXiv · doi:10.48550/arxiv.2007.00368 · Cited by 32
Geller, M. R., Martinis, J. M., Sornborger, A. T., Stancil, P. C., Pritchett, E., You, H., & Galiautdinov, A. (2015) · Physical Review A · doi:10.1103/physreva.91.062309 · Cited by 31
Fillion-Gourdeau, F., Herrmann, H. J., Mendoza, M., Palpacelli, S., & Succi, S. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.160602 · Cited by 31
Experimental simulation of the Unruh effect on an NMR quantum simulator
Jin, F., Chen, H., Rong, X., Zhou, H., Shi, M., Zhang, Q., Ju, C., Cai, Y.-F., Luo, S., Peng, X., et al. (2016) · Science China Physics Mechanics and Astronomy · doi:10.1007/s11433-016-5779-7 · Cited by 31
EXPONENTIAL IMPROVEMENT IN PRECISION FOR SIMULATING SPARSE HAMILTONIANS
Berry, D. W., Childs, A. M., Cleve, R., Kothari, R., & Somma, R. D. (2017) · Forum of Mathematics Sigma · doi:10.1017/fms.2017.2 · Cited by 39
Quantum Sampling Algorithms for Near-Term Devices
Wild, D. S., Sels, D., Pichler, H., Zanoci, C., & Lukin, M. D. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.100504 · Cited by 33
“Consequently, time evolution under these quantum Hamiltonians can be implemented using Hamiltonian simulation [47].”
MethodMany-body hierarchy of dissipative timescales in a quantum computer
Sommer, O. E., Piazza, F., & Luitz, D. J. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.023190 · Cited by 33
“[3] S.”
BackgroundQuantum computation of reactions on surfaces using local embedding
Gujarati, T. P., Motta, M., Friedhoff, T., Rice, J. E., Nguyen, N., Barkoutsos, P. K., Thompson, R. J., Smith, T., Kagele, M., Brei, M., et al. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00753-1 · Cited by 35
Quantum simulation of chiral phase transitions
Czajka, A. M., Kang, Z.-B., Ma, H., & Zhao, F. (2022) · Journal of High Energy Physics · doi:10.1007/jhep08(2022)209 · Cited by 42
Nonzero Momentum Requires Long-Range Entanglement
Gioia, L., & Wang, C. (2022) · Physical Review X · doi:10.1103/physrevx.12.031007 · Cited by 31
“The approach that we take utilizes the quantum circuit formalism, which is equivalent to the usual adiabatic Hamiltonian evolution formulation [1, 8] but conceptually cleaner.”
MethodQuantum pattern recognition on real quantum processing units
Das, S., Zhang, J., Martina, S., Suter, D., & Caruso, F. (2023) · Quantum Machine Intelligence · doi:10.1007/s42484-022-00093-x · Cited by 34
“Sreetama Das sreetama.das@unifi.it Extended author information available on the last page of the article. quantum simulation (Lloyd 1996; Peng et al. 2009; Peng and Suter 2010; Álvarez and Suter 2010; Peng et al. 2014; Chen et al. 2016; Li et al. 2017), Boson sampling (Aaronson and Arkhipov 2011;…”
BackgroundComputational complexity and the genetic algorithm
Rylander, B., & Foster, J. A. (2001) · Cited by 31
Bootstrap Tomography of the Pulses for Quantum Control
Dobrovitski, V. V., de Lange, G., Ristè, D., & Hanson, R. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.077601 · Cited by 31
Degenerate parametric oscillation in quantum membrane optomechanics
Benito, M., Muñoz, C. S., & Navarrete–Benlloch, C. (2016) · Physical Review A · doi:10.1103/physreva.93.023846 · Cited by 32
Causal fermions in discrete space-time
Farrelly, T., & Short, A. J. (2014) · Physical Review A · doi:10.1103/physreva.89.012302 · Cited by 32
“Simulation of quantum physics is likely to be the first practical application where a quantum computer could outpreform a classical one [1].”
BackgroundSingle-Crystal Study of a Low Spin Co(II) Molecular Qubit: Observation of Anisotropic Rabi Cycles
Xu, M., Liu, Z., Dong, B., Cui, H., Wang, Y., Su, J., Wang, Z., Song, Y., Chen, X., Jiang, S., et al. (2019) · Inorganic Chemistry · doi:10.1021/acs.inorgchem.8b02685 · Cited by 31
Quantum Lattice-Gas Models for the Many-Body Schrödinger Equation
Boghosian, B. M., & Taylor, W. (1997) · RePEc: Research Papers in Economics · Cited by 31
Gustafson, E., Dreher, P., Hang, Z., & Meurice, Y. (2021) · Quantum Science and Technology · doi:10.1088/2058-9565/ac1dff · Cited by 30
Integrable Digital Quantum Simulation: Generalized Gibbs Ensembles and Trotter Transitions
Vernier, E., Bertini, B., Giudici, G., & Piroli, L. (2023) · Physical Review Letters · doi:10.1103/physrevlett.130.260401 · Cited by 35
Variational quantum simulation of U(1) lattice gauge theories with qudit systems
Popov, P. P., Meth, M., Lewenstein, M., Hauke, P., Ringbauer, M., Zohar, E., & Kasper, V. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.013202 · Cited by 34
Fault-Tolerant Quantum Computation Using Large Spin-Cat Codes
Omanakuttan, S., Buchemmavari, V., Gross, J. A., Deutsch, I., & Marvian, M. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.020355 · Cited by 42
Combinatorial Optimization on Gate Model Quantum Computers: A Survey
Zahedinejad, E., & Zaribafiyan, A. (2017) · arXiv · doi:10.48550/arxiv.1708.05294 · Cited by 29
“Quantum computers [1, 2] are theoretically proven to solve certain families of computational problems faster than the best known classical algorithms [3, 4, 5].”
BackgroundLong-time simulations with high fidelity on quantum hardware
Gibbs, J., Gili, K., Holmes, Z., Commeau, B., Arrasmith, A., Cincio, L., Coles, P. J., & Sornborger, A. (2021) · arXiv · doi:10.48550/arxiv.2102.04313 · Cited by 28
“[3] Seth Lloyd, “Universal quantum simulators,” Science , 1073–1078 (1996).”
Method
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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