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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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“The success of NISQ devices in solving small-scale electronic structure problems is substantiated by theoretical results showing that quantum computers can solve correlated electronic structure problems in polynomial time [1, 13], e.”
BackgroundInfluentialProspects for simulating a qudit-based model of ( 1 + 1 ) D scalar QED
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“The Trotterized time evolution operator from Eq.”
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“Quantum simulators [5] are special purpose quantum computers which are used as digital [6] or analogue [7] devices, for example, using ultracold atoms in optical lattices [8,9], trapped ions [10], photons [11] or superconducting circuits on a chip [12].”
BackgroundResolving correlated states of benzyne with an error-mitigated contracted quantum eigensolver
Smart, S. E., Boyn, J.-N., & Mazziotti, D. A. (2022) · Physical Review A · doi:10.1103/physreva.105.022405 · Cited by 46
“[6] Seth Lloyd, “Universal Quantum Simulators,” Science 273, 1073– (1996).”
Stable Quantum Computation of Unstable Classical Chaos
Georgeot, B., & Shepelyansky, D. L. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.5393 · Cited by 45
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“detail by Lloyd [130] and Zalka [180], and later by many other authors (e.”
BackgroundQuantum Random Access Memory for Dummies
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“Examples include Grover’s method for exploring unsorted databases [16], Shor’s algorithm for factoring large integers [12], and the quantum simulation algorithms [28].”
MethodVersatile microwave-driven trapped ion spin system for quantum information processing
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“54(2) for the input states |111〉 and |+++〉, respectively.”
BackgroundQudit-Basis Universal Quantum Computation Using χ(2) Interactions
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“This representation was first used for quantum simulation by Lloyd [16], and all VQE algorithms to date make use of this Hamiltonian representation.”
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Eigenvector Approximation Leading to Exponential Speedup of Quantum Eigenvalue Calculation
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Quantum chemistry simulation on quantum computers: theories and experiments
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QASMBench: A Low-level QASM Benchmark Suite for NISQ Evaluation and SimulationPreprint
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MethodMechanisms of Arsenic Exposure-Induced Hypertension and Atherosclerosis: an Updated Overview
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“…quantum computers [8–19] have the potential to solve problems that are intractable for classical computers, including applications in factoring [20, 21], quantum simulation [22] of quantum chemistry [23– 26] and materials [27], quantum machine learning [28] and topological data analysis [29, 30].”
BackgroundDemonstrating Bayesian quantum phase estimation with quantum error detection
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“For concreteness, we let the operator, U k , in the QPE circuit an approximation to e − iHkt with Hamiltonian (1) and t ∈ R by the Lie-Trotter first-order product formula [51], Here, the integer s is the number of discretized time steps.”
MethodOn the efficiency of quantum algorithms for Hamiltonian simulation
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“Lloyd [2] showed that local Hamiltonians can be simulated efficiently on a quantum computer.”
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Black-box Hamiltonian simulation and unitary implementation
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“An explicit procedure for simulating local Hamiltonians on a quantum computer was given by Lloyd [6].”
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“Shannon (1941) provided a theoretical model, the General Purpose Analogue Computer (GPAC), which is a mathematical description of the differential analyser. The GPAC consists of a set of nonlinear boxes, connected by their inputs and outputs. Four basic operations are sufficient, shown in figure 3. There are a few rul…”
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Exciton-Polariton Quantum Simulators
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“any quantum many-body problems [2] by nature in an effi- cient and economical way. This approach is dubbed quantum simulation. This seed of idea is evolved to a universal quantum simulator by S. Llyod [3], which mimics Exciton-Polariton Quantum Simulators 3 a quantum system of interest through coherent operations on th…”
BackgroundRandomizing multi-product formulas for Hamiltonian simulation
Faehrmann, P. K., Steudtner, M., Kueng, R., Kieferová, M., & Eisert, J. (2022) · Quantum · doi:10.22331/q-2022-09-19-806 · Cited by 49
“Benchmarking them on five different Hamiltonians, all of which are physically well motivated and each interesting in its own right, we have found that this advantage can be expected already at comparably large simulation times.”
InfluentialRobust and Efficient Hamiltonian Learning
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BackgroundQuantum simulations of one dimensional quantum systemsPreprint
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“One of the best known problems that a quantum computer would tackle more efficiently than a classical one is quantum simulation (QS) [13, 20, 26].”
BackgroundQuantum simulations of relativistic quantum physics in circuit QED
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“37 If we consider, for simplicity, spin-1/2 lattice models composed of n spins, it is easy to see that an exact simulation becomes unfeasible as soon as n ∼ 50. double-precision Storing a quantum state of 50 qubits with double-precision To perform arbitrary discrete-time evolution, we would need to…”
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Quantum computing methods for electronic states of the water molecule
Bian, T., Murphy, D., Xia, R., Daskin, A., & Kais, S. (2019) · Molecular Physics · doi:10.1080/00268976.2019.1580392 · Cited by 44
“However, based on the phase estimation algorithm [8, 9], the molecular ground state energies can be calculated with gate depth O(poly(n)) [10–12].”
MethodDestructive Error Interference in Product-Formula Lattice Simulation
Tran, M. C., Chu, S.-K., Su, Y., Childs, A. M., & Gorshkov, A. V. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.220502 · Cited by 39
Digital Simulation of Topological Matter on Programmable Quantum Processors
Mei, F., Guo, Q., Yu, Y.-F., Xiao, L., Zhu, S.-L., & Jia, S. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.160503 · Cited by 40
“In regard to topology, digitally simulating a topological Hamiltonian has been reported in single-qubit parameter space [65].”
BackgroundInfluentialQuantum Simulation of Three-Body Interactions in Weakly Driven Quantum Systems
Petiziol, F., Sameti, M., Carretta, S., Wimberger, S., & Mintert, F. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.250504 · Cited by 40
Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure
Tranter, A., Love, P., Mintert, F., Wiebe, N., & Coveney, P. V. (2019) · UCL Discovery (University College London) · Cited by 39
Constant-depth circuits for dynamic simulations of materials on quantum computers
Oftelie, L. B., Beeumen, R. V., Younis, E., Smith, E., Iancu, C., & de Jong, W. A. (2022) · Materials Theory · doi:10.1186/s41313-022-00043-x · Cited by 39
“…simulation, Dynamic simulation Introduction Quantum computers are intrinsically fit for efficiently simulating quantum systems (Feynman 1982; Lloyd 1996; Abrams and Lloyd 1997; Zalka 1998), making the simulation of quantum materials a leading “killer application” for this novel technology.”
BackgroundVariational quantum eigensolver for dynamic correlation functions
Chen, H., Nusspickel, M., Tilly, J., & Booth, G. H. (2021) · Physical Review A · doi:10.1103/physreva.104.032405 · Cited by 42
Topological Two-Dimensional Floquet Lattice on a Single Superconducting Qubit
Malz, D., & Smith, A. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.163602 · Cited by 45
“In principle, the time-evolution of any many-body quantum systems can be simulated by applying a Trotterization, which turns the continuous time evolution into a local quantum circuit [5].”
MethodProgress toward favorable landscapes in quantum combinatorial optimization
Lee, J., Magann, A. B., RABITZ, H. A., & Arenz, C. (2021) · Physical Review A · doi:10.1103/physreva.104.032401 · Cited by 48
“Quantum computers promise to offer computational advantages over classical computers for certain high-value tasks [1–3].”
BackgroundLloyd, S. (2012) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2011.0331 · Cited by 39
“Quantum computers can simulate the known laws of physics efficiently [24].”
BackgroundSelf-citationPreparation of Many-Body States for Quantum Simulation
Ward, N. J., Kassal, I., & Aspuru‐Guzik, A. (2009) · Digital Access to Scholarship at Harvard (DASH) (Harvard University) · Cited by 39
Quantum Lattice-Gas Models for the Many-Body Schrödinger Equation
Boghosian, B. M., & Taylor, W. (1997) · International Journal of Modern Physics C · doi:10.1142/s0129183197000606 · Cited by 48
Future Potential of Quantum Computing and Simulations in Biological Science
Pal, S., Bhattacharya, M., Dash, S., Lee, S., & Chakraborty, C. (2023) · Molecular Biotechnology · doi:10.1007/s12033-023-00863-3 · Cited by 41
“It is noteworthy to mention that we can program quantum computers to simulate localized quantum systems [75].”
Hybrid Quantum Image Classification and Federated Learning for Hepatic Steatosis Diagnosis
Lusnig, L., Sagingalieva, A., Surmach, M., Protasevich, T., Michiu, O., McLoughlin, J., Mansell, C., Petris, G. D., Bonazza, D., Zanconati, F., et al. (2024) · Diagnostics · doi:10.3390/diagnostics14050558 · Cited by 48
Model-Checking Linear-Time Properties of Quantum Systems
Ying, M., Li, Y., Yu, N., & Feng, Y. (2014) · ACM Transactions on Computational Logic · doi:10.1145/2629680 · Cited by 38
Stojanović, V. M., Mihajlo Vanević, A., Demler, E., & Tian, L. (2014) · Physical Review B · doi:10.1103/physrevb.89.144508 · Cited by 38
An efficient magic state approach to small angle rotations
Campbell, E. T., & O’Gorman, J. (2016) · Quantum Science and Technology · doi:10.1088/2058-9565/1/1/015007 · Cited by 36
Convex optimization of programmable quantum computers
Banchi, L., Pereira, J. L., Lloyd, S., & Pirandola, S. (2020) · npj Quantum Information · doi:10.1038/s41534-020-0268-2 · Cited by 39
“Another deep design of quantum processor is based on PQCs [9, 31].”
BackgroundMethodSelf-citationDigital quantum simulation of molecular dynamics and control
Magann, A. B., Grace, M., RABITZ, H. A., & Sarovar, M. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.023165 · Cited by 42
Quantum phase estimation for a class of generalized eigenvalue problems
Parker, J. B., & Joseph, I. (2020) · Physical Review A · doi:10.1103/physreva.102.022422 · Cited by 38
“Quantum computing has been recognized for its potential to solve currently intractable physics problems, such as quantum many-body problems [1].”
BackgroundHamiltonian Simulation by Uniform Spectral AmplificationPreprint
Low, G. H., & Chuang, I. L. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1707.05391 · Cited by 63
“…of exploiting structure from that of finding best simulation algorithms is highlighted by celebrated Hamiltonian simulation techniques such Lie-Product formulas [2], quantum walks [10], and truncated-Taylor series [5], each radically different and specialized to some class of structured matrices.”
BackgroundMethodPerformance of two different quantum annealing correction codes
Mishra, A., Albash, T., & Lidar, D. A. (2015) · Quantum Information Processing · doi:10.1007/s11128-015-1201-z · Cited by 34
“[42] introduced a new [4, 1, 4]0 code that uses the same physical resources as the [3, 1, 3]1 code, without a dedicated penalty qubit.”
BackgroundMethodInfluentialConstructive quantum Shannon decomposition from Cartan involutions
Drury, B. C., & Love, P. J. (2008) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/41/39/395305 · Cited by 37
“Subsequently efficient quantum algorithms for performing simulations of physical systems were developed [5, 6, 7, 8, 9, 10, 11], vindicating Feynman’s prediction and further motivating theoretical and experimental work towards realizing quantum computation.”
MethodDirect Measurement of Topological Numbers with Spins in Diamond
Kong, F., Ju, C., Liu, Y., Lei, C., Wang, M., Kong, X., Wang, P., Huang, P., Li, Z., Shi, F., et al. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.060503 · Cited by 37
Permutation-Invariant Constant-Excitation Quantum Codes for Amplitude Damping
Ouyang, Y., & Chao, R. (2019) · IEEE Transactions on Information Theory · doi:10.1109/tit.2019.2956142 · Cited by 35
“THE ability to manipulate quantum information promises to speed up algorithms such as factoring [1], [2], simulate physical systems more efficiently [3], and unlock the ability to perform cryptographic schemes with unprecedented security [4], [5].”
BackgroundUnsupervised Classification of Quantum Data
Sentís, G., Monràs, A., Muñoz-Tapia, R., Calsamiglia, J., & Bagán, E. (2019) · Physical Review X · doi:10.1103/physrevx.9.041029 · Cited by 35
“In origin, the advantages of quantum computing were exemplary showcased through instances of problems that are hard to solve in a classical computer, such as integer factorization [1], unstructured search [2], discrete optimization [3, 4], and simulation of many-body Hamiltonian dynamics [5].”
BackgroundQuantum simulation of light-front parton correlators
Echevarría, M. G., Egusquiza, I. L., Rico, E., & Schnell, G. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.104.014512 · Cited by 46
“[45] S.”
BackgroundInfluentialRohde, P. P. (2021) · Cambridge University Press eBooks · doi:10.1017/9781108868815 · Cited by 38
Long-time simulations for fixed input states on quantum hardware
Gibbs, J., Gili, K., Holmes, Z., Commeau, B., Arrasmith, A., Cincio, Ł., Coles, P. J., & Sornborger, A. T. (2022) · npj Quantum Information · doi:10.1038/s41534-022-00625-0 · Cited by 84
“Additional details on this adaptive learning method are provided in Supplementary Note 6.”
BackgroundMethodInfluentialQuantum information processing by nuclear magnetic resonance spectroscopy
Havel, T. F., Cory, D. G., Lloyd, S., Boulant, N., Fortunato, E. M., Pravia, M. A., Teklemariam, G., Weinstein, Y. S., Bhattacharyya, A., & Hou, J. (2002) · American Journal of Physics · doi:10.1119/1.1446857 · Cited by 35
Self-citationIntroduction to NMR Quantum Information ProcessingPreprint
Laflamme, R., Knill, E. H., Cory, D. G., Fortunato, E. M., Havel, T. F., Miquel, C., Martinez, R. M., Negrevergne, C., Ortíz, G., Pravia, M. A., et al. (2002) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0207172 · Cited by 55
“Noise still limits the number of useful operations, but non-trivi al physics simulations are believed to be possible with less than 100 qubits [40].”
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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