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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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Laserless trapped-ion quantum simulations without spontaneous scattering using microtrap arrays
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Pal, S., Bhattacharya, M., Lee, S.-S., & Chakraborty, C. (2024) · Molecular Biotechnology · doi:10.1007/s12033-023-00765-4 · Cited by 103
Quantum simulation of the Abelian-Higgs lattice gauge theory with ultracold atoms
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Real-time chiral dynamics from a digital quantum simulation
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“[2] S.”
BackgroundHamiltonian simulation in the low-energy subspace
Şahinoğlu, B., & Somma, R. D. (2021) · npj Quantum Information · doi:10.1038/s41534-021-00451-w · Cited by 85
“(2) discussed above are of the same order.”
BackgroundQuantum-enhanced Markov chain Monte Carlo
Layden, D., Mazzola, G., Mishmash, R. V., Motta, M., Wocjan, P., Kim, J.-S., & Sheldon, S. (2023) · Nature · doi:10.1038/s41586-023-06095-4 · Cited by 89
“We approximated U = e − iHt on this device through a randomly-compiled second-order Trotter-Suzuki product formula [24, 40, 41] with up to 48 layers of pulse-efficient 2-qubit gates [42] acting on up to 5 pairs of qubits in parallel [11], and set Q ( s | s ) /Q ( s | s ) = 1 in the acceptance…”
MethodClassification of Multipartite Entanglement of All Finite Dimensionality
Gour, G., & Wallach, N. R. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.060502 · Cited by 83
Quantum Artificial Life in an IBM Quantum Computer
Alvarez-Rodriguez, U., Sanz, M., Lamata, L., & Solano, E. (2018) · Scientific Reports · doi:10.1038/s41598-018-33125-3 · Cited by 90
Alipour, S., Chenu, A., Rezakhani, A. T., & del Campo, A. (2020) · Quantum · doi:10.22331/q-2020-09-28-336 · Cited by 90
Yalouz, S., Senjean, B., Günther, J., Buda, F., O’Brien, T. E., & Visscher, L. (2020) · Quantum Science and Technology · doi:10.1088/2058-9565/abd334 · Cited by 88
Fermionic quantum processing with programmable neutral atom arrays
González-Cuadra, D., Bluvstein, D., Kalinowski, M., Kaubruegger, R., Maskara, N., Naldesi, P., Zache, T. V., Kaufman, A. M., Lukin, M. D., Pichler, H., et al. (2023) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2304294120 · Cited by 104
“In the context of quantum simulation (QS) of manybody systems [5], we are interested in particle-number conserving unitaries acting on this register [67], which can be constructed using the gate set”
MethodLight-Shift-Induced Quantum Gates for Ions in Thermal Motion
Jonathan, D., & Plenio, M. B. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.127901 · Cited by 79
Holevo's bound from a general quantum fluctuation theorem
Kafri, D., & Deffner, S. (2012) · Physical Review A · doi:10.1103/physreva.86.044302 · Cited by 77
Hamiltonian simulation with optimal sample complexity
Kimmel, S., Lin, C. Y.-Y., Low, G. H., Ozols, M., & Yoder, T. J. (2017) · npj Quantum Information · doi:10.1038/s41534-017-0013-7 · Cited by 85
“Lloyd provided the first formal results on simulation, considering Hamiltonians that consist of sums of non-commuting terms.(1) Other lines of research have focused on simulating sparse Hamiltonians, with a long sequence of work recently culminating in an optimal algorithm(2) (see ref.”
BackgroundThe Universe as Quantum Computer
Lloyd, S. (2012) · WORLD SCIENTIFIC eBooks · doi:10.1142/9789814374309_0029 · Cited by 85
“In 1996, Lloyd developed a quantum algorithm for implementing such universal quantum simulators [21].”
Self-citationJiang, Z., Kalev, A., Mruczkiewicz, W., & Neven, H. (2020) · Quantum · doi:10.22331/q-2020-06-04-276 · Cited by 110
“, high temperature superconductivity) [1–6].”
Hamiltonian simulation algorithms for near-term quantum hardware
Clinton, L., Bausch, J., & Cubitt, T. S. (2021) · Nature Communications · doi:10.1038/s41467-021-25196-0 · Cited by 95
“This includes the simple first-order formula [13]”
BackgroundInfluentialBokhan, D., Mastiukova, A. S., Boev, A. S., Trubnikov, D. N., & Fedorov, A. K. (2022) · Frontiers in Physics · doi:10.3389/fphy.2022.1069985 · Cited by 89
“Examples of the problems, for whose quantum speedups are expected to be exponential, are prime factorization [4] and simulating quantum systems [5], for example, modelling complex molecules and chemical reactions [6].”
BackgroundChilds, A. M., Deotto, E., Farhi, E., Goldstone, J., Gutmann, S., & Landahl, A. J. (2002) · Physical Review A · doi:10.1103/physreva.66.032314 · Cited by 78
Experimental Implementation of the Quantum Baker’s Map
Weinstein, Y. S., Lloyd, S., Emerson, J., & Cory, D. G. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.157902 · Cited by 82
“If one can simulate quantum chaos on a quantum computer, by contrast, the computational complexity rises only as a small polynomial in the number of degrees of freedom and in the accuracy [10] [11] [12].”
BackgroundSelf-citationRelativistic quantum mechanics with trapped ions
Lamata, L., Casanova, J., Gerritsma, R., Roos, C. F., García-Ripoll, J. J., & Solano, E. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/9/095003 · Cited by 80
Low-Overhead Fault-Tolerant Quantum Error Correction with the Surface-GKP Code
Noh, K., Chamberland, C., & Brandão, F. G. S. L. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.010315 · Cited by 99
“Despite various opportunities offered by noisy intermediate-scale quantum (NISQ) devices [1], faulttolerant quantum-error-correction techniques [2] are essential for executing quantum algorithms intractable by classical computers such as integer factorization [3] and the simulation of real-time dynamics of large quant…”
BackgroundGujju, Y., Matsuo, A., & Raymond, R. (2024) · Physical Review Applied · doi:10.1103/physrevapplied.21.067001 · Cited by 104
Rent’s rule and extensibility in quantum computing
Franke, D. P., Clarke, J. S., Vandersypen, L. M. K., & Veldhorst, M. (2019) · Microprocessors and Microsystems · doi:10.1016/j.micpro.2019.02.006 · Cited by 88
Oracles for Gauss's law on digital quantum computers
Stryker, J. R. (2019) · Physical Review A · doi:10.1103/physreva.99.042301 · Cited by 76
Classical variational simulation of the Quantum Approximate Optimization Algorithm
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Bayesian deep learning on a quantum computer
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“The simulation of sparse Hamiltonians is more efficient when using quantum computers (Lloyd 1996; Childs 2010; Berry and Childs 2012).”
MethodSimulating quantum materials with digital quantum computers
Oftelie, L. B., Urbánek, M., Metcalf, M., Carter, J. T., Kemper, A. F., & de Jong, W. A. (2021) · Quantum Science and Technology · doi:10.1088/2058-9565/ac1ca6 · Cited by 83
Variational benchmarks for quantum many-body problems
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“Notably, the dynamics of quantum many-body systems can be ef-ficiently simulated by a digital quantum computer when the initial states are easy to prepare [14].”
BackgroundSwitchable Interaction in Molecular Double Qubits
Ferrando–Soria, J., Magee, S. A., Chiesa, A., Carretta, S., Santini, P. M., Vitórica‐Yrezábal, Í. J., Tuna, F., Whitehead, G. F. S., Sproules, S. A., Lancaster, K. M., et al. (2016) · Chem · doi:10.1016/j.chempr.2016.10.001 · Cited by 77
“64. Cotton, F.A., and Norman, J.G., Jr. (1972). Structural characterization of a basic trinuclear ruthenium acetate.”
BackgroundMethodUsing quantum computers for quantum simulation
Brown, K. L., Munro, W. J., & Kendon, V. M. (2015) · Cited by 79
Quantum information processing in continuous time
Childs, A. M., & Farhi, E. (2004) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 92
Deeply inelastic scattering structure functions on a hybrid quantum computer
Mueller, N., Tarasov, A., & Raju Venugopalan, B. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.102.016007 · Cited by 93
Scaling and Diabatic Effects in Quantum Annealing with a D-Wave Device
Weinberg, P., Tylutki, M., Rönkkö, J., Westerholm, J., Åström, J. A., Manninen, P., Törmä, P., & Sandvik, A. W. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.090502 · Cited by 79
Motta, M., Gujarati, T. P., Rice, J. E., Kumar, A., Masteran, C., Latone, J. A., Lee, E., Valeev, E. F., & Takeshita, T. Y. (2020) · Physical Chemistry Chemical Physics · doi:10.1039/d0cp04106h · Cited by 81
Exponential Speedup with a Single Bit of Quantum Information: Measuring the Average Fidelity Decay
Poulin, D., Blume-Kohout, R., Laflamme, R., & Ollivier, H. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.177906 · Cited by 79
Introduction to Quantum AlgorithmsPreprint
Shor, P. W. (2000) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0005003 · Cited by 81
“Some work has been done on simulating Hamiltonians on quantum computers [1, 29, 45], but I do not believe this question has been completely addressed yet.”
Quantum Simulation of the Majorana Equation and Unphysical Operations
Casanova, J., Sabín, C., León, J., Egusquiza, I. L., Gerritsma, R., Roos, C. F., García-Ripoll, J. J., & Solano, E. (2011) · Physical Review X · doi:10.1103/physrevx.1.021018 · Cited by 77
“While a quantum computer could in principle implement a universal quantum simulator [2], only particular systems have been simulated up to now using dedicated quantum simulators [3].”
MethodSelf-mitigating Trotter circuits for SU(2) lattice gauge theory on a quantum computer
Rahman, S. A., Lewis, R., Mendicelli, E., & Powell, S. J. M. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.074502 · Cited by 126
“As is well known, a Trotter formula [51] divides the total time t into small intervals dt, and expresses the time evolution operator e−iHt as an operator product that approximates the evolution with one dt step after another.”
BackgroundQuantum algorithms for quantum dynamics
Miessen, A., Ollitrault, P. J., Tacchino, F., & Tavernelli, I. (2022) · Nature Computational Science · doi:10.1038/s43588-022-00374-2 · Cited by 90
“Since Lloyd’s first proposal of a universal quantum algorithm for quantum dynamics 2 , the field of digital quantum simulators has seen immense progress.”
BackgroundMethodSupply chain logistics with quantum and classical annealing algorithms
Weinberg, S. J., Sanches, F., Ide, T., Kamiya, K., & Correll, R. (2023) · Scientific Reports · doi:10.1038/s41598-023-31765-8 · Cited by 90
“However, to handle much larger problems of thousands of binary variables requires the use of the hybrid solver–quantum annealer and (3) H(s) = (1− s)Hinit(s)+ sHfinal,”
MethodDigital Quantum Simulation of the Holstein Model in Trapped Ions
Mezzacapo, A., Casanova, J., Lamata, L., & Solano, E. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.200501 · Cited by 75
Exponential Gain in Quantum Computing of Quantum Chaos and Localization
Georgeot, B., & Shepelyansky, D. L. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.2890 · Cited by 78
Chamberland, C., & Noh, K. (2020) · npj Quantum Information · doi:10.1038/s41534-020-00319-5 · Cited by 97
Improving Hamiltonian encodings with the Gray code
Matteo, O. D., McCoy, A. E., Gysbers, P., Miyagi, T., Woloshyn, R. M., & Navrátil, P. (2021) · Physical Review A · doi:10.1103/physreva.103.042405 · Cited by 77
“Phase estimation circuits have depth beyond what is feasible for a NISQ machine, and require the implementation of a unitary simulating the time evolution of the system, often termed Hamiltonian simulation [2].”
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The physics of information technology
(2001) · Choice Reviews Online · doi:10.5860/choice.38-5598 · Cited by 79
Prospects of quantum computing for molecular sciences
Liu, H., Low, G. H., Steiger, D. S., Häner, T., Reiher, M., & Troyer, M. (2022) · Materials Theory · doi:10.1186/s41313-021-00039-z · Cited by 73
Confinement and entanglement dynamics on a digital quantum computer
Vovrosh, J., & Knolle, J. (2021) · Scientific Reports · doi:10.1038/s41598-021-90849-5 · Cited by 81
Recent Progress in Quantum Simulation Using Superconducting Circuits
Paraoanu, G. S. (2014) · Journal of Low Temperature Physics · doi:10.1007/s10909-014-1175-8 · Cited by 79
“A universal quantum computer would be able to efficiently simulate the dynamics of quantum systems, provided that the Hamiltonian is built up from local interactions [3].”
BackgroundInfluentialQuantum algorithm for obtaining the energy spectrum of molecular systems
Wang, H., Kais, S., Aspuru‐Guzik, A., & Hoffmann, M. R. (2008) · Digital Access to Scholarship at Harvard (DASH) (Harvard University) · Cited by 75
Quantum synchronization on the IBM Q system
Koppenhöfer, M., Bruder, C., & Roulet, A. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.023026 · Cited by 81
“With this mapping in place, we perform a digital quantum simulation [24, 25] of the synchronization dynamics on the publicly available few-qubit quantum processors at the IBM Q System [26].”
MethodTunable Resonant and Nonresonant Interactions between a Phase Qubit and L C Resonator
Allman, M. S., Whittaker, J. D., Castellanos-Beltran, M. A., Cicak, K., da Silva, F. T. F., DeFeo, M. P., Lecocq, F., Sirois, A. J., Teufel, J. D., Aumentado, J., et al. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.123601 · Cited by 71
Tensor lattice field theory for renormalization and quantum computing
Meurice, Y., Sakai, R., & Unmuth-Yockey, J. (2022) · Reviews of Modern Physics · doi:10.1103/revmodphys.94.025005 · Cited by 86
Digital quantum simulation with Rydberg atoms
Weimer, H., Müller, M., Büchler, H. P., & Lesanovsky, I. (2011) · Quantum Information Processing · doi:10.1007/s11128-011-0303-5 · Cited by 70
“It has been shown that, provided a universal set of quantum gates is available, such digital quantum simulator can be used to simulate the dynamics of any many-body Hamiltonian with short-range interactions efficiently [33].”
BackgroundErratum: Embryonic lethality in mice homozygous for a processing-deficient allele of Notch1
Huppert, S. S., Le, A., Schroeter, E. H., Mumm, J. S., Saxena, M. T., Milner, L. A., & Kopan, R. (2000) · Nature · doi:10.1038/35046136 · Cited by 74
Mitigating algorithmic errors in a Hamiltonian simulation
Endo, S., Zhao, Q., Li, Y., Benjamin, S., & Yuan, X. (2019) · Physical Review A · doi:10.1103/physreva.99.012334 · Cited by 72
Simulation of Chemical Isomerization Reaction Dynamics on a NMR Quantum Simulator
Lu, D., Xu, N., Xu, R., Chen, H., Gong, J., Peng, X., & Du, J. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.020501 · Cited by 73
Quantum fast Poisson solver: the algorithm and complete and modular circuit design
Wang, S., Wang, Z., Li, W., Fan, L., Wei, Z., & Gu, Y. (2020) · Quantum Information Processing · doi:10.1007/s11128-020-02669-7 · Cited by 83
“There are general methods to simulate ei At [34, 35], but here we utilize the specific properties of matrix A to deal with it to reduce the complexity.”
MethodLow-depth quantum state preparation
Zhang, X., Yung, M., & Yuan, X. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.043200 · Cited by 84
Classically optimized Hamiltonian simulation
Keever, C. M., & Lubasch, M. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.023146 · Cited by 92
“Figure S6 shows the spectral-norm distance as a function of time for the same set of circuits n ∈ [5, 8, 10] and L ∈ [1, 2, 3, 4, 5, 6] and for the same Hamiltonian considered in Fig.”
BackgroundMethodTowards Adiabatic Quantum Computing Using Compressed Quantum Circuits
Keever, C. M., & Lubasch, M. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.020362 · Cited by 89
“On digital quantum computers, time evolution can be readily realized using Trotter product formulas [8], but long evolution times can lead to deep circuits.”
MethodMolecular nanomagnets with switchable coupling for quantum simulation
Chiesa, A., Whitehead, G. F. S., Carretta, S., Carthy, L., Timco, G. A., Teat, S. J., Amoretti, G., Pavarini, E., Winpenny, R. E. P., & Santini, P. M. (2014) · Scientific Reports · doi:10.1038/srep07423 · Cited by 73
“(3) Since the interactions of each ring with the central Ni(21) ion are much weaker than the intra-ring couplings, we can project Hmicro in the subspace in which the two rings are in the ground doublets T 5 1/2.”
BackgroundQuantum Algorithm Design: Techniques and Applications
Shao, C., Yang, L., & Li, H. (2019) · Journal of Systems Science and Complexity · doi:10.1007/s11424-019-9008-0 · Cited by 74
Goodchild, A., Raftery, M. J., Saunders, N. F. W., Guilhaus, M., & Cavicchioli, R. (2004) · Journal of Proteome Research · doi:10.1021/pr0498988 · Cited by 73
Fermionic Linear Optics and MatchgatesPreprint
Knill, E. H. (2001) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0108033 · Cited by 95
“The conjecture is supported by the ability to efficient ly factor large numbers [1] and simulate physics [2] using quantum computers, by proofs that quantum co puters are more powerful with respect to some black boxes [3], and by results showing expon ential improvements in communication complexity [4].”
Quantum-circuit design for efficient simulations of many-body quantum dynamics
Raeisi, S., Wiebe, N., & Sanders, B. C. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/10/103017 · Cited by 72
Quantum Algorithm for Calculating Molecular Vibronic Spectra
Sawaya, N. P. D., & Huh, J. (2019) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.9b01117 · Cited by 79
“Convincing numerical evidence suggests that Trotterization [39, 45] is likely to be the most viable option for early quantum devices [51].”
BackgroundMethodAccuracy and Resource Estimations for Quantum Chemistry on a Near-Term Quantum Computer
Kühn, M., Zanker, S., Deglmann, P., Marthaler, M., & Weiß, H. (2019) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.9b00236 · Cited by 71
Simulation of collective neutrino oscillations on a quantum computer
Hall, B., Roggero, A., Baroni, A., & Carlson, J. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.104.063009 · Cited by 86
“For conditions leading to strong entanglement instead, simulations on digital/analog quantum computers have the potential to tackle the full neutrino dynamics while still enjoying a polynomial computational cost in system size N [17].”
BackgroundProvably accurate simulation of gauge theories and bosonic systems
Tong, Y., Albert, V. V., McClean, J. R., Preskill, J. P., & Su, Y. (2022) · Quantum · doi:10.22331/q-2022-09-22-816 · Cited by 73
“Our algorithm combines the Haah-Hastings-Kothari-Low (HHKL) decomposition [28], which provides a nearly optimal approach for geometrically local Hamiltonians, with the interaction-picture simulation method [50], which gives further improved scaling with the truncation threshold.”
MethodInfluentialLearning Many-Body Hamiltonians with Heisenberg-Limited Scaling
Huang, H.-Y., Tong, Y., Fang, D., & Su, Y. (2023) · Physical Review Letters · doi:10.1103/physrevlett.130.200403 · Cited by 108
“On the other hand, the first-order and second-order Trotterization method [51, 52, 53] considers approximations given by .”
MethodEfficient Quantum Algorithm for Computing n -time Correlation Functions
Pedernales, J. S., Candia, R. D., Egusquiza, I. L., Casanova, J., & Solano, E. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.020505 · Cited by 77
Digital-Analog Quantum Simulation of Spin Models in Trapped Ions
Arrazola, Í., Pedernales, J. S., Lamata, L., & Solano, E. (2016) · Scientific Reports · doi:10.1038/srep30534 · Cited by 74
“< < H J H J , ( ) (2) XX i j i j i x j x XY i j i j i x j x i y j y”
Rapid Adiabatic Preparation of Injective Projected Entangled Pair States and Gibbs States
Ge, Y., Molnár, A., & Cirac, J. I. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.080503 · Cited by 81
Richerme, P., Senko, C., Smith, J., Lee, A., Korenblit, S. É., & Monroe, C. R. (2013) · Physical Review A · doi:10.1103/physreva.88.012334 · Cited by 66
EXPONENTIAL PROPAGATORS (INTEGRATORS) FOR THE TIME-DEPENDENT SCHRÖDINGER EQUATION
Bandrauk, A. D., & Lu, H. (2013) · Journal of Theoretical and Computational Chemistry · doi:10.1142/s0219633613400014 · Cited by 70
Demon-like algorithmic quantum cooling and its realization with quantum optics
Xu, J., Yung, M., Xu, X.-Y., Boixo, S., Zhou, Z.-W., Li, C., Aspuru‐Guzik, A., & Guo, G. (2014) · Nature Photonics · doi:10.1038/nphoton.2013.354 · Cited by 67
Liquid-state NMR simulations of quantum many-body problems
Negrevergne, C., Somma, R. D., Ortíz, G., Knill, E., & Laflamme, R. (2005) · Physical Review A · doi:10.1103/physreva.71.032344 · Cited by 71
Climbing mount scalable: Physical resource requirements for a scalable quantum computer
Blume-Kohout, R., Caves, C. M., & Deutsch, I. (2002) · Cited by 70
Kiesewetter, S., He, Q., Drummond, P. D., & Reid, M. D. (2014) · Physical Review A · doi:10.1103/physreva.90.043805 · Cited by 71
Protecting Conditional Quantum Gates by Robust Dynamical Decoupling
Piltz, C., Scharfenberger, B., Khromova, A., Varón, A. F., & Wunderlich, C. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.200501 · Cited by 69
Experimental Demonstration of Self-Guided Quantum Tomography
Chapman, R. J., Ferrie, C., & Peruzzo, A. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.040402 · Cited by 69
“Quantum technologies require high fidelity preparation, control and characterization of quantum states, for application in quantum metrology [1], quantum simulators [2], and quantum computers [3].”
BackgroundQuantum circuit optimization with deep reinforcement learningPreprint
Fösel, T., Niu, M. Y., Marquardt, F., & Li, L. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2103.07585 · Cited by 218
“The long-term goal of fault-tolerant large-scale quantum computing promises disruptive progress in multiple important areas of science and technology [1], such as decryption [2], database search [3], quantum simulation [4], and for optimization problems [5].”
BackgroundSimulating the dynamics of braiding of Majorana zero modes using an IBM quantum computer
Stenger, J., Bronn, N. T., Egger, D. J., & Pekker, D. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.033171 · Cited by 68
Concentration for Random Product Formulas
Chen, C.-F., Huang, H.-Y., Kueng, R., & Tropp, J. A. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.040305 · Cited by 94
“The earliest compilation procedures for quantum simulation were based on product formulas [9,10], also known as Trotterization, or splitting methods.”
Near-term quantum algorithms for linear systems of equations with regression loss functions
Huang, H.-Y., Bharti, K., & Rebentrost, P. (2021) · New Journal of Physics · doi:10.1088/1367-2630/ac325f · Cited by 193
Speed limits and locality in many-body quantum dynamics
Chen, C.-F., Lucas, A., & Yin, C. (2023) · Reports on Progress in Physics · doi:10.1088/1361-6633/acfaae · Cited by 104
Bounding the costs of quantum simulation of many-body physics in real space
Kivlichan, I., Wiebe, N., Babbush, R., & Aspuru-Guzik, A. (2016) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/aa77b8 · Cited by 82
Hsieh, C., & Cao, J. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5018726 · Cited by 68
Quantum Computing in Big Data Analytics: A Survey
Shaikh, T. A., & Ali, R. (2016) · IEEE International Conference on Computer and Information Technology (CIT) · doi:10.1109/cit.2016.79 · Cited by 70
Computational complexity in electronic structure
Whitfield, J. D., Love, P. J., & Aspuru-Guzik, A. (2013) · Phys. Chem. Chem. Phys. · doi:10.1039/c2cp42695a · Cited by 71
Re, L. D., Rost, B., Kemper, A. F., & Freericks, J. K. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.102.125112 · Cited by 68
Simulating two-dimensional lattice gauge theories on a qudit quantum computer
Meth, M., Zhang, J., Haase, J. F., Edmunds, C., Postler, L., Jena, A., Steiner, A., Dellantonio, L., Blatt, R., Zoller, P., et al. (2025) · Nature Physics · doi:10.1038/s41567-025-02797-w · Cited by 129
“…took a first step in this direction by using mixed-dimensional entangling gates for a digital quantum simulation (in the form of a Trotter protocol 65 ) for the model used in ‘Simulating gauge fields and matter’, that is a plaquette with open boundary conditions including gauge fields and…”
Minimally entangled state preparation of localized wave functions on quantum computers
Klco, N., & A, M. J. S. (2020) · Physical Review A · doi:10.1103/physreva.102.012612 · Cited by 67
Universal simulation of Markovian open quantum systems
Sweke, R., Sinayskiy, I., Bernard, D., & Petruccione, F. (2015) · Physical Review A · doi:10.1103/physreva.91.062308 · Cited by 68
Climbing Mount Scalable: Physical Resource Requirements for a Scalable Quantum Computer
Blume-Kohout, R., Caves, C. M., & Deutsch, I. H. (2002) · Foundations of Physics · doi:10.1023/a:1021471621587 · Cited by 84
Simulating the dynamics of time-dependent Hamiltonians with a truncated Dyson series
Kieferová, M., Scherer, A., & Berry, D. W. (2019) · Physical Review A · doi:10.1103/physreva.99.042314 · Cited by 66
“The first quantum simulation algorithm was proposed by Lloyd [5] in 1996.”
MethodInfluentialVanadyl spin qubit 2D arrays and their integration on superconducting resonators
Urtizberea, A., Natividad, E., Alonso, P. J., Pérez-Martínez, L., Andrés, M., Gascón, I., Gimeno, I., Luis, F., & Roubeau, O. (2019) · Materials Horizons · doi:10.1039/c9mh01594a · Cited by 64
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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