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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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Nobel Lecture: Superposition, entanglement, and raising Schrödinger’s cat
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“Indeed, the superconducting circuit models discussed here are an example of quantum simulators (Lloyd, 1996; Buluta and Nori, 2009): controllable quantum systems engineered to reproduce the physical properties of another, seemingly different, quantum system.”
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“Indeed, in this case, the Hamiltonian evolution can be accurately and efficiently simulated by a universal quantum computer [17].”
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FAULT-TOLERANT QUANTUM COMPUTATION
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High‐Dimensional Quantum Communication: Benefits, Progress, and Future Challenges
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“in quantum computing [1–5], communication [6–9] and simulation [10–14].”
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“A complementary approach is digital quantum computing, where logic gates combine to form quantum circuit algorithms [7].”
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“ecause quantum systems can be e- ciently encoded or represented by another quantum system and real time evolution of the Schrodinger equation can be eciently realised via a unitary quantum circuit [21,22]. However, implementing a universal quantum computer requires the coherent and accurate control of millions of qubi…”
Background10-Qubit Entanglement and Parallel Logic Operations with a Superconducting Circuit
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“It is believed that a scalable functioning quantum computer may help solve computational problems in such areas as scientific discovery, materials research, chemistry, and drug design, to name a few [2, 3, 4, 5].”
BackgroundQuantum-classical computation of Schwinger model dynamics using quantum computers
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Simulating lattice gauge theories within quantum technologies
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“Following Feynman’s pioneering work [2], it has been shown that universal quantum computers [3, 4] could in principle simulate general many-body systems [5] as well as quantum fields [6], serving as digital quantum simulators.”
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“More generally, a Hamiltonian can be simulated efficiently provided it is sparse and efficiently row-computable.”
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“In fact, historically, one of the key motivations to develop quantum computers is to simulate the dynamics of many-body quantum systems [24], and quantum simulation of many-body dynamics has been theoretically shown to be efficient with practical algorithms proposed [25].”
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“For this case it is reassuring to know that Lloyd has shown (Lloyd 1996) that any quantum system can be simulated on a quantum computer in something roughly proportional to real time.”
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“Fourteen years later, Lloyd formalized the concept of a universal quantum simulator [3] and demonstrated an extension for treating systems of interacting electrons in second quantization [4].”
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“The idea of mapping the dynamics of a quantum system of interest onto the dynamics of a controllable quantum system was proposed in 1982 by Feynman (43) and developed in 1996 by Lloyd (84).”
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Self-citationTrading Classical and Quantum Computational Resources
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“This early insight has since been refined to encompass more universal and versatile constructions of simulation [2,3].”
BackgroundThe future of quantum computing with superconducting qubits
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“Known examples of tasks with an exponential quantum speedup include simulation of quantum many-body systems 19 , number theoretic problems such as integer factoring 5 , solving certain types of linear systems 20 , estimation of Betti numbers used in topological data analysis 21–23 , and computing…”
Variational quantum algorithms for nonlinear problems
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“[9, 10], this adder circuit requires fewer ancilla qubits and gates.”
BackgroundQuantum Simulation for High-Energy Physics
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“However, 20 years later, we have witnessed so many advances that successful quantum computations, and other applications of quantum information processing such as quantum simulation [15, 16] and long-distance quantum communication [17], appear reachable within our lifetime, even if many discoveries and technological i…”
BackgroundEngineered Open Systems and Quantum Simulations with Atoms and Ions
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“It has been shown that a digital quantum simulator can implement the unitary time evolution operator U(t) generated by H(t) efficiently for any local quantum system (Lloyd, 1996; Abrams and Lloyd, 1997; Ortiz et al., 2001), i.e., where the individual terms Hα are quasi-local.”
BackgroundMethodInfluentialQuantum secure direct communication and deterministic secure quantum communication
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Can one trust quantum simulators?
Hauke, P., Cucchietti, F. M., Tagliacozzo, L., Deutsch, I., & Lewenstein, M. (2012) · Reports on Progress in Physics · doi:10.1088/0034-4885/75/8/082401 · Cited by 315
Temme, K., Osborne, T. J., Vollbrecht, K. G., Poulin, D., & Verstraete, F. (2011) · Nature · doi:10.1038/nature09770 · Cited by 305
Quantum Machine Learning: What Quantum Computing Means to Data Mining
Wittek, P. (2014) · Cited by 319
Quantum computation vs. firewalls
Harlow, D., & Hayden, P. (2013) · Journal of High Energy Physics · doi:10.1007/jhep06(2013)085 · Cited by 310
Shadbolt, P. J., Verde, M. R., Peruzzo, A., Politi, A., Laing, A., Lobino, M., Matthews, J. C. F., Thompson, M. G., & O'Brien, J. L. (2012) · Nature Photonics · doi:10.1038/nphoton.2011.283 · Cited by 297
“R(2) = 1− ∑ i(Si − Ti) 2 ∑ i(Si − S)(2) (4)”
Qulacs: a fast and versatile quantum circuit simulator for research purpose
Suzuki, Y., Kawase, Y., Masumura, Y., Hiraga, Y., Nakadai, M., Chen, J., Nakanishi, K. M., Mitarai, K., Imai, R., Tamiya, S., et al. (2021) · Quantum · doi:10.22331/q-2021-10-06-559 · Cited by 357
“The other application is a quantum simulator [36].”
BackgroundMethodQuantum implementation of the unitary coupled cluster for simulating molecular electronic structure
Shen, Y., Zhang, X., Zhang, S., Zhang, J.-N., Yung, M.-H., & Kim, K. (2015) · Physical Review A · doi:10.1103/physreva.95.020501 · Cited by 262
Qubit Coupled Cluster Method: A Systematic Approach to Quantum Chemistry on a Quantum Computer
Ryabinkin, I. G., Yen, T.-C., Genin, S. N., & Izmaylov, A. F. (2018) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.8b00932 · Cited by 287
Open-system dynamics of entanglement:a key issues review
Aolita, L., de Melo, F., & Davidovich, L. (2015) · Reports on Progress in Physics · doi:10.1088/0034-4885/78/4/042001 · Cited by 328
Implementation of the Quantum Fourier Transform
Weinstein, Y. S., Pravia, M. A., Fortunato, E. M., Lloyd, S., & Cory, D. G. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.1889 · Cited by 300
“For example, quantum computers, if constructed, could factor large numbers more rapidly [1], search data basis more quickly [2], and simulate quantum systems more efficiently [3] than is possible using current classical algorithms [4] [5] [6] [7] [8] [9] [10] [11].”
BackgroundSelf-citationA large-scale quantum simulator on a diamond surface at room temperature
Cai, J., Retzker, A., Jelezko, F., & Plenio, M. B. (2013) · Nature Physics · doi:10.1038/nphys2519 · Cited by 289
“Richard Feynman’s idea [10] of quantum simulation provides a powerful solution to this problem: one could gain deep insight into complex states of matter by experimentally simulating them with another well-controlled quantum system [11].”
BackgroundQuantum computation and quantum information
Nagy, M., & Akl, S. G. (2005) · International Journal of Parallel Emergent and Distributed Systems · doi:10.1080/17445760500355678 · Cited by 320
“Feynman's idea was refined by Lloyd, who showed in 1996 that the logical operations available on a quantum computer could be marshaled to simulate the behavior of virtually any quantum system whose dynamics is determined by local interactions [ 129 ].”
Leone, L., Oliviero, S. F. E., & Hamma, A. (2022) · Physical Review Letters · doi:10.1103/physrevlett.128.050402 · Cited by 393
Utility of Accurate Mass Tags for Proteome-Wide Protein Identification
Conrads, T. P., Anderson, G., Veenstra, T. D., Paša‐Tolić, L., & Smith, R. D. (2000) · Analytical Chemistry · doi:10.1021/ac0002386 · Cited by 281
Hybrid Quantum-Classical Approach to Quantum Optimal Control
Li, J., Yang, X., Peng, X., & Sun, C.-P. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.150503 · Cited by 278
Polynomial-Time T-Depth Optimization of Clifford+T Circuits Via Matroid Partitioning
Amy, M., Maslov, D. A., & Mosca, M. (2014) · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · doi:10.1109/tcad.2014.2341953 · Cited by 319
“Quantum computers have the potential to efficiently solve important computational problems, including integer factorization [29] and quantum simulation [18], for which there are no known efficient classical algorithms.”
BackgroundSimulation of Topological Field Theories¶by Quantum Computers
Freedman, M. H., Kitaev, A., & Wang, Z. (2002) · Communications in Mathematical Physics · doi:10.1007/s002200200635 · Cited by 299
High-order quantum algorithm for solving linear differential equations
Berry, D. W. (2014) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/47/10/105301 · Cited by 277
“Therefore the amplitude would not drop below the amplitude on the eigenspace corresponding to the largest eigenvalue.”
BackgroundSpin-Spin Interaction and Spin Squeezing in an Optical Lattice
Sørensen, A. S., & Mølmer, K. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.2274 · Cited by 273
NMR implementation of a molecular hydrogen quantum simulation with adiabatic state preparation.
Du, J., Xu, N., Peng, X., Wang, P.-F., Wu, S., & Lu, D.-W. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.030502 · Cited by 205
Lattice gauge theory simulations in the quantum information era
Dalmonte, M., & Montangero, S. (2016) · Contemporary Physics · doi:10.1080/00107514.2016.1151199 · Cited by 311
“In addition to the analogue quantum simulation strategy outlined above, it is possible to devise specific protocols to engineer gauge theories on quantum computers, or digital quantum simulators [112].”
MethodQuantum Simulation of Time-Dependent Hamiltonians and the Convenient Illusion of Hilbert Space
Poulin, D., Qarry, A., Somma, R., & Verstraete, F. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.170501 · Cited by 265
“…many-body Hamiltonian, with the constraint that 1) the Hamiltonian is local in the sense that it is the sum of terms each acting on at most k bodies for some constant k independent of N , and 2) the duration of the evolution scales at most as a polynomial in the number of particles in the system.”
BackgroundMachnes, S., Sander, U., Glaser, S. J., de Fouquieres, P., Gruslys, A., Schirmer, S. G., & Schulte‐Herbrüggen, T. (2011) · Physical Review A · doi:10.1103/physreva.84.022305 · Cited by 266
Simulating Large Quantum Circuits on a Small Quantum Computer
Peng, T., Harrow, A. W., Ozols, M., & Wu, X. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.150504 · Cited by 324
Experimental investigations of dipole–dipole interactions between a few Rydberg atoms
Browaeys, A., Barredo, D., & Lahaye, T. (2016) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/49/15/152001 · Cited by 254
“A seemingly more realistic goal is to realize quantum simulators [24, 25], in particular analog ones, i.”
BackgroundQuantum Computer Systems for Scientific Discovery
Alexeev, Y., Bacon, D., Brown, K. R., Calderbank, R., Carr, L. D., Chong, F. T., DeMarco, B., Englund, D. R., Farhi, E., Fefferman, B., et al. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.017001 · Cited by 339
“Another class of quantum algorithms are quantum simulations [9,30,31], which use a quantum computer to simulate models of a candidate physical system of interest, such as molecules, materials, or quantum field theories whose models are intractable using classical computers.”
BackgroundMethodSelf-citationOpen-system dynamics of entanglement:a key issues review
Aolita, L., de Melo, F., & Davidovich, L. (2015) · Refubium (Universitätsbibliothek der Freien Universität Berlin) · doi:10.17169/refubium-20820 · Cited by 258
Digital Quantum Simulation of Spin Models with Circuit Quantum Electrodynamics
Salathé, Y., Mondal, M., Oppliger, M., Heinsoo, J., Kurpiers, P., Potočnik, A., Mezzacapo, A., Heras, U. L., Lamata, L., Solano, E., et al. (2015) · Physical Review X · doi:10.1103/physrevx.5.021027 · Cited by 256
“Quantum simulations using well-controllable quantum systems to simulate the properties of another less tractable one [1,2] are expected to be able to predict the properties”
BackgroundMethodA modular design of molecular qubits to implement universal quantum gates
Ferrando–Soria, J., Pineda, E. M., Chiesa, A., Fernández, A., Magee, S. A., Carretta, S., Santini, P. M., Vitórica‐Yrezábal, Í. J., Tuna, F., Timco, G. A., et al. (2016) · Nature Communications · doi:10.1038/ncomms11377 · Cited by 250
“This perturbative picture is confirmed by the results of detailed calculations for compound 9 using the full Hamiltonian (2) (Fig.”
BackgroundMethodResultInfluentialCoherent Many-Body Spin Dynamics in a Long-Range Interacting Ising Chain
Zeiher, J., Choi, J.-Y., Rubio-Abadal, A., Pohl, T., van Bijnen, R., Bloch, I., & Groß, C. (2017) · Physical Review X · doi:10.1103/physrevx.7.041063 · Cited by 264
“This renders the observation of quantum revivals in a many-body system one of the most demanding tests to demonstrate its coherent evolution, which itself is indispensable, for example, for efficient adiabatic quantum computation [1,2].”
BackgroundNonlinear Quantum Mechanics Implies Polynomial-Time Solution for NP -Complete and # P Problems
Abrams, D. S., & Lloyd, S. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.3992 · Cited by 269
Self-citationExperimental quantum Hamiltonian learning
Wang, J., Paesani, S., Santagati, R., Knauer, S., Gentile, A. A., Wiebe, N., Petruzzella, M., O’Brien, J. L., Rarity, J., Laing, A., et al. (2017) · Nature Physics · doi:10.1038/nphys4074 · Cited by 260
“However, predicting behaviour in the exponentially large configuration space of quantum systems is known to be intractable to classical computing machines [18, 19].”
BackgroundError-Mitigated Digital Quantum Simulation
McArdle, S., Yuan, X., & Benjamin, S. C. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.180501 · Cited by 253
Real-Time Time-Dependent Electronic Structure Theory
Li, X., Govind, N., Isborn, C. M., DePrince, A. E., & Lopata, K. A. (2020) · Chemical Reviews · doi:10.1021/acs.chemrev.0c00223 · Cited by 247
Hybrid Quantum-Classical Approach to Correlated Materials
Bauer, B., Wecker, D., Millis, A. J., Hastings, M. B., & Troyer, M. (2016) · Physical Review X · doi:10.1103/physrevx.6.031045 · Cited by 277
“While it has been known for a long time [8, 41] that many quantum problems can be simulated on quantum computers with polynomial scaling, such scaling in the asymptotic regime is insufficient to make an algorithm practical, especially if the power of the polynomial is high and constants are large – as is the case for…”
BackgroundQuantum Computer Systems for Scientific Discovery
Alexeev, Y., Bacon, D., Brown, K. R., Calderbank, R., Carr, L. D., Chong, F. T., DeMarco, B., Englund, D., Farhi, E., Fefferman, B., et al. (2021) · DSpace@MIT (Massachusetts Institute of Technology) · doi:10.6082/h7fqg-6vt65 · Cited by 257
Self-citation
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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