The DOI matches its Crossref record; 54 of the 54 references it cites were found in a registry or an index.
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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“Indeed, quantum computers can efficiently simulate unitary evolutions of quantum many-body systems with local interactions [5, 11], because they can inherently deal with exponentially large Hilbert spaces.”
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“The task of creating such a universal quantum simulator was first conceptualized by Lloyd [34], and the past few years have witnessed significant progresses in the development of new quantum algorithms as well as the improvement of theoretical error bounds of existing quantum algorithms for time-independent Hamiltonia…”
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Demonstration of Adiabatic Variational Quantum Computing with a Superconducting Quantum Coprocessor
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“In contrast, quantum computing avoids the sign-problem by directly operating with quantum states and thus may provide a profound speedup [15, 16].”
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“If quantum computers ever become available, they would at least be able to handle the quantum dynamics, once the initial conditions are set(Lloyd, 1996).”
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“One popular class of QNNs has been Trotter-based [2, 5].”
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Error-mitigated simulation of quantum many-body scars on quantum computers with pulse-level control
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“In particular, simulating the time evolution of a quantum many-body system with local interactions on a quantum computer requires a number of local quantum gates scaling polynomially with the number N of qubits and linearly with the total simulation time T [1].”
BackgroundRecent progress on coherent computation based on quantum squeezing
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“Quantum computers should be able to simulate quantum systems more efficiently than classical computers [22, 23], but achieving large-scale quantum computers is still challenging at this stage.”
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“The time evolution is obtained from a Trotter decomposition [30] that we optimize for minimal gate depth.”
MethodExponential Quantum Speedup in Simulating Coupled Classical Oscillators
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Digital quantum simulation of the statistical mechanics of a frustrated magnet
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“Furthermore, although this algorithms can at most yield a quadratic speedup for simulating the most general thermal states [18], the subclass of the CETS which can be created efficiently on a quantum computer can serve as a “heat bath” [19] for the simulation of the dynamics of open quantum systems, which could give a…”
BackgroundSelf-guaranteed measurement-based quantum computation
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Progress towards creating optically addressable molecular qubits
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OpenQL: A Portable Quantum Programming Framework for Quantum Accelerators
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“de example 3 and then applying decomposition. 2)Unitary Gate Decomposition It has been demonstrated that a universal quantum computer can simulate any Turing machine [40] and any local quantum system [41]. A set of gates is called universal if they can be used to constitute a quantum circuit that can approximate any u…”
Identification and Characterization of the Sulfolobus solfataricus P2 Proteome
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Dynamics of Rényi entanglement entropy in diffusive qudit systems
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Quantum circuit cutting with maximum-likelihood tomography
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Hybrid quantum-classical machine learning for generative chemistry and drug design
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BackgroundOn the Stochastic Control of Quantum Ensembles
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Analog superconducting quantum simulator for Holstein polarons
Mei, F., Stojanović, V. M., Siddiqi, I. A., & Tian, L. (2013) · Physical Review B · doi:10.1103/physrevb.88.224502 · Cited by 58
A quantum approach to homomorphic encryption
Tan, S. H., Kettlewell, J. A., Ouyang, Y., Chen, L., & Fitzsimons, J. F. (2016) · White Rose Research Online (University of Leeds, The University of Sheffield, University of York) · Cited by 57
Analytic approaches to periodically driven closed quantum systems: methods and applications
Sen, A., Sen, D., & Sengupta, K. (2021) · Journal of Physics Condensed Matter · doi:10.1088/1361-648x/ac1b61 · Cited by 65
On applications of quantum computing to plasma simulations
Dodin, I. Y., & Startsev, E. A. (2021) · Physics of Plasmas · doi:10.1063/5.0056974 · Cited by 57
“[2], the recent works [3, 4], and the many papers cited therein.)”
BackgroundAn introduction to Boson-sampling
Gard, B., Motes, K., Olson, J., Rohde, P., & Dowling, J. (2015) · UTS ePRESS (University of Technology Sydney) · Cited by 56
Quantum Simulation of Partial Differential Equations via Schrödingerization
Jin, S., Liu, N., & Yu, Y. (2024) · Physical Review Letters · doi:10.1103/physrevlett.133.230602 · Cited by 128
“The most well-known include the preparation of quantum ground states [2, 3] and Gibbs states [4], which benefit from non-unitary dynamics, and are particularly important in areas like quantum chemistry [5] and optimisation.”
Confinement in a $${{\mathbb{Z}}}_{2}$$ lattice gauge theory on a quantum computer
Mildenberger, J., Mruczkiewicz, W., Halimeh, J. C., Zhang, J., & Hauke, P. (2025) · Nature Physics · doi:10.1038/s41567-024-02723-6 · Cited by 77
“(2) as one might expect from worst-case bounds [66].”
Solovay-Kitaev Decomposition Strategy for Single-Qubit Channels
Wang, D.-S., Berry, D. W., de Oliveira, M. C., & Sanders, B. C. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.130504 · Cited by 57
Efficient quantum simulation of fermionic and bosonic models in trapped ions
Lamata, L., Mezzacapo, A., Casanova, J., & Solano, E. (2014) · EPJ Quantum Technology · doi:10.1140/epjqt9 · Cited by 55
Subspace variational quantum simulator
Heya, K., Nakanishi, K. M., Mitarai, K., Yan, Z., Zuo, K., Suzuki, Y., Sugiyama, T., Tamate, S., Tabuchi, Y., Fujii, K., et al. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.023078 · Cited by 76
Sun, G., Voigt, J. H., Filippov, I. V., Márquez, V. E., & Nicklaus, M. C. (2004) · Journal of Chemical Information and Computer Sciences · doi:10.1021/ci049881+ · Cited by 56
Veis, L., Višňák, J., Nishizawa, H., Nakai, H., & Pittner, J. (2016) · International Journal of Quantum Chemistry · doi:10.1002/qua.25176 · Cited by 55
Quantum simulation of quantum field theories as quantum chemistry
Liu, J., & Xin, Y. (2020) · Journal of High Energy Physics · doi:10.1007/jhep12(2020)011 · Cited by 54
“rs of H i. Complicated higher-order terms in the expansion will involve more sophisticated commutators, but those contributions above the leading term ∏ ieiH i could be bounded (see the original work [90] and a very good recent discussion [91]). However, for specic problems in conformal truncation, it is hard to naive…”
A Leap among Quantum Computing and Quantum Neural Networks: A Survey
Massoli, F. V., Vadicamo, L., Amato, G. M., & Falchi, F. (2022) · ACM Computing Surveys · doi:10.1145/3529756 · Cited by 78
“Theoretical aspects of ML using quantum computers are also discussed in Reference [15].”
BackgroundMethodInfluentialSimulating key properties of lithium-ion batteries with a fault-tolerant quantum computer
Delgado, A., Casares, P. A. M., dos Reis, R., Zini, M. S., Campos, R., Hernández, N. C., Voigt, A.-C., Lowe, A., Jahangiri, S., Martin-Delgado, M. A., et al. (2022) · Physical Review A · doi:10.1103/physreva.106.032428 · Cited by 71
Boundaries of quantum supremacy via random circuit sampling
Zlokapa, A., Villalonga, B., Boixo, S., & Lidar, D. A. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00703-x · Cited by 66
“[25] Seth Lloyd, “Universal quantum simulators,” Science 273, 1073–1078 (1996).”
Preparation of excited states for nuclear dynamics on a quantum computer
Roggero, A., Gu, C., Baroni, A., & Papenbrock, T. (2020) · Physical Review C · doi:10.1103/physrevc.102.064624 · Cited by 58
“Thus, it is an important task to reduce the number of two-qubit gates in quantum circuits, for instance by keeping Hamiltonians and operators of interest as local as possible [23].”
BackgroundMarzuoli, A., & Rasetti, M. (2005) · Annals of Physics · doi:10.1016/j.aop.2005.01.005 · Cited by 54
Preparation of many-body states for quantum simulation
Ward, N. J., Kassal, I., & Aspuru-Guzik, A. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3115177 · Cited by 54
Biamonte, J., Bergholm, V., Whitfield, J. D., Fitzsimons, J., & Aspuru‐Guzik, A. (2011) · AIP Advances · doi:10.1063/1.3598408 · Cited by 56
Primitive quantum gates for an SU(2) discrete subgroup: Binary tetrahedral
Gustafson, E., Lamm, H., Lovelace, F., & Musk, D. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.114501 · Cited by 71
Efficient fully-coherent quantum signal processing algorithms for real-time dynamics simulation
Martyn, J. M., Liu, Y., Chin, Z. E., & Chuang, I. L. (2023) · The Journal of Chemical Physics · doi:10.1063/5.0124385 · Cited by 65
Demonstration of three- and four-body interactions between trapped-ion spins
Katz, O., Feng, L., Risinger, A., Monroe, C. R., & Cetina, M. (2023) · Nature Physics · doi:10.1038/s41567-023-02102-7 · Cited by 65
A Perspective on Protein Structure Prediction Using Quantum Computers
Doğa, H., Raubenolt, B. A., Cumbo, F., Joshi, J., DiFilippo, F. P., Qin, J., Blankenberg, D. J., & Shehab, O. (2024) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.4c00067 · Cited by 67
“A more recent work [18] proposed a pure quantum method that leverages Grover’s search algorithm with an adder-only oracle to find the lowest energy conformation of a given protein structure.”
InfluentialQuantum Walk Computing: Theory, Implementation, and Application
Qiang, X., Ma, S., & Song, H. (2024) · Intelligent Computing · doi:10.34133/icomputing.0097 · Cited by 75
Necessary and sufficient conditions for local manipulation of multipartite pure quantum states
Gour, G., & Wallach, N. R. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/7/073013 · Cited by 53
Quantum computer simulator based on the circuit model of quantum computation
Karafyllidis, I. G. (2005) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/tcsi.2005.851999 · Cited by 54
“Quantum computers are far more efficient that their classical counterparts in factoring large numbers [3], searching databases [4]–[6], and simulating physical systems [7].”
BackgroundSpectroscopy of Three-Particle Entanglement in a Macroscopic Superconducting Circuit
Xu, H., Strauch, F. W., Dutta, S. K., Johnson, P. R., Ramos, R., Berkley, A. J., Paik, H., Anderson, J. R., Dragt, A. J., Lobb, C. J., et al. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.027003 · Cited by 54
Circuit optimization of Hamiltonian simulation by simultaneous diagonalization of Pauli clusters
van den Berg, E., & Temme, K. (2020) · Quantum · doi:10.22331/q-2020-09-12-322 · Cited by 68
Experimental exploration of five-qubit quantum error-correcting code with superconducting qubits
Gong, M., Yuan, X., Wang, S., Wu, Y., Zhao, Y., Zha, C., Li, S., Zhang, Z., Zhao, Q., Liu, Y., et al. (2021) · National Science Review · doi:10.1093/nsr/nwab011 · Cited by 75
“Quantum computers can tackle classically intractable problems [1] and efficiently simulate many-body quantum systems [2].”
Efficient quantum computation of molecular forces and other energy gradients
O’Brien, T. E., Streif, M., Rubin, N. C., Santagati, R., Su, Y., Huggins, W. J., Goings, J. J., Moll, N., Kyoseva, E. S., Degroote, M., et al. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.043210 · Cited by 71
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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