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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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Accelerated Variational Quantum Eigensolver
Wang, D., Higgott, O., & Brierley, S. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.140504 · Cited by 241
Variational Quantum Simulation of General Processes
Endo, S., Sun, J., Li, Y., Benjamin, S. C., & Yuan, X. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.010501 · Cited by 237
Quantum simulation with interacting photons
Hartmann, M. J. (2016) · Journal of Optics · doi:10.1088/2040-8978/18/10/104005 · Cited by 237
Experimental Realization of Noiseless Subsystems for Quantum Information Processing
Viola, L., Fortunato, E. M., Pravia, M. A., Knill, E. H., Laflamme, R., & Cory, D. G. (2001) · Science · doi:10.1126/science.1064460 · Cited by 228
Variational fast forwarding for quantum simulation beyond the coherence time
Cîrstoiu, C., Holmes, Z., Iosue, J., Cincio, L., Coles, P. J., & Sornborger, A. (2020) · npj Quantum Information · doi:10.1038/s41534-020-00302-0 · Cited by 232
Simulating the vibrational quantum dynamics of molecules using photonics
Sparrow, C., Martín-López, E., Maraviglia, N., Neville, A., Harrold, C., Carolan, J., Joglekar, Y. N., Hashimoto, T., Matsuda, N., O’Brien, J. L., et al. (2018) · Nature · doi:10.1038/s41586-018-0152-9 · Cited by 230
Quantum simulation of dynamical maps with trapped ions
Schindler, P., Müller, M., Nigg, D., Barreiro, J. T., Martinez, E. A., Hennrich, M., Monz, T., Diehl, S., Zoller, P., & Blatt, R. (2013) · Nature Physics · doi:10.1038/nphys2630 · Cited by 227
Simulating lattice gauge theories on a quantum computer
Byrnes, T., & Yamamoto, Y. (2006) · Physical Review A · doi:10.1103/physreva.73.022328 · Cited by 218
From transistor to trapped-ion computers for quantum chemistry
Yung, M.-H., Casanova, J., Mezzacapo, A., McClean, J., Lamata, L., Aspuru-Guzik, A., & Solano, E. (2014) · Scientific Reports · doi:10.1038/srep03589 · Cited by 221
“We can generate the UCC state by simulating a pseudo time evolution through Suzuki-Trotter expansion on the evolution operator eT−T † [21].”
MethodQuantum computation using electrons trapped by surface acoustic waves
Barnes, C. H. W., Shilton, J. M., & Robinson, A. M. (2000) · Physical review. B, Condensed matter · doi:10.1103/physrevb.62.8410 · Cited by 220
Generation and sampling of quantum states of light in a silicon chip
Paesani, S., Ding, Y., Santagati, R., Chakhmakhchyan, L., Vigliar, C., Rottwitt, K., Oxenløwe, L. K., Wang, J., Thompson, M. G., & Laing, A. (2019) · Nature Physics · doi:10.1038/s41567-019-0567-8 · Cited by 214
“The horizontal axis labels anti-bunched (one photon per detector) states in increasing order {(1, 2, 3, 4), (1, 2, 3, 5), .”
BackgroundHamiltonian Learning and Certification Using Quantum Resources
Wiebe, N., Granade, C., Ferrie, C., & Cory, D. G. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.190501 · Cited by 236
“Quantum information processing promises to dramatically advance physics and chemistry by providing efficient simulators for the Schr¨odinger or Dirac equations [1–3].”
BackgroundBerry, D. W., Childs, A. M., Ostrander, A., & Wang, G. (2017) · Communications in Mathematical Physics · doi:10.1007/s00220-017-3002-y · Cited by 218
“The first algorithms for this problem had complexity polynomial in 1/ [2,4,10,13].”
BackgroundAutomated optimization of large quantum circuits with continuous parameters
Nam, Y., Ross, N. J., Su, Y., Childs, A. M., & Maslov, D. (2018) · npj Quantum Information · doi:10.1038/s41534-018-0072-4 · Cited by 274
“We also consider circuits for the product formula approach to Hamiltonian simulation.(17,18) In all cases, we focus on circuit sizes likely to be useful in applications that outperform classical computation.”
MethodQubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization
Berry, D. W., Gidney, C., Motta, M., McClean, J. R., & Babbush, R. (2019) · Quantum · doi:10.22331/q-2019-12-02-208 · Cited by 222
Simulation of Electronic Structure Hamiltonians Using Quantum Computers
Whitfield, J. D., Biamonte, J., & Aspuru‐Guzik, A. (2011) · Digital Access to Scholarship at Harvard (DASH) (Harvard University) · Cited by 218
Quantum Computing for High-Energy Physics: State of the Art and Challenges
Meglio, A. D., Jansen, K., Tavernelli, I., Alexandrou, C., Arunachalam, S., Bauer, C., Borras, K., Carrazza, S., Crippa, A., Croft, V. A., et al. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.037001 · Cited by 359
“Among decomposition methods, product formulas represent the simplest and most widely adopted paradigm [69, 78, 259].”
BackgroundMethodThe prospects of quantum computing in computational molecular biology
Outeiral, C., Strahm, M., Shi, J., Morris, G. M., Benjamin, S. C., & Deane, C. M. (2021) · WIREs Computational Molecular Science · doi:10.1002/wcms.1481 · Cited by 232
“We will present the simplest technique, Trotterization, also known as the product formula approach [140]; for a full review see [26,27].”
BackgroundMethodExponential improvement in precision for simulating sparse Hamiltonians
Berry, D. W., Childs, A. M., Cleve, R., Kothari, R., & Somma, R. D. (2014) · Proceedings of the forty-sixth annual ACM symposium on Theory of computing · doi:10.1145/2591796.2591854 · Cited by 324
“Lloyd provided an explicit algorithm for simulating many realistic quantum systems, namely those whose Hamiltonian is a sum of interactions acting nontrivially on a small number of subsystems of limited dimension [24].”
BackgroundWitnessing eigenstates for quantum simulation of Hamiltonian spectra
Santagati, R., Wang, J., Gentile, A. A., Paesani, S., Wiebe, N., McClean, J. R., Morley-Short, S., Shadbolt, P. J., Bonneau, D., Silverstone, J. W., et al. (2018) · Science Advances · doi:10.1126/sciadv.aap9646 · Cited by 211
“However, quantum devices are expected to provide scalable solutions to some instances of interest (2, 3).”
BackgroundBöhi, P., Riedel, M. F., Hoffrogge, J., Reichel, J., Hänsch, T. W., & Treutlein, P. (2009) · Nature Physics · doi:10.1038/nphys1329 · Cited by 213
“Applications of ultracold neutral atoms in quantum information processing (QIP) [1, 2], quantum simulations [3, 4], and quantum-enhanced metrology [5, 6] rely on the coherent control of internal states, motional states, and collisional interactions [7].”
BackgroundEntanglement-Based Machine Learning on a Quantum Computer
Cai, X., Wu, D., Su, Z.-E., Chen, M.-C., Wang, X., Li, L., Liu, N.-L., Lu, C., & Pan, J.-W. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.110504 · Cited by 207
Quantum algorithm and circuit design solving the Poisson equation
Cao, Y., Papageorgiou, A., Petras, I., Traub, J., & Kais, S. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/1/013021 · Cited by 204
“Indeed in some cases the quantum algorithm is exponentially faster than the best classical algorithm known [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12].”
BackgroundTowards Practical Classical Processing for the Surface Code
Fowler, A. G., Whiteside, A. C., & Hollenberg, L. C. L. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.180501 · Cited by 203
Experimentally simulating the dynamics of quantum light and matter at deep-strong coupling
Langford, N. K., Sagastizabal, R., Kounalakis, M., Dickel, C., Bruno, A., Luthi, F., Thoen, D. J., Endo, A., & DiCarlo, L. (2017) · Nature Communications · doi:10.1038/s41467-017-01061-x · Cited by 203
Poulin, D., & Wocjan, P. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.220502 · Cited by 201
“Thermalization processes that occur in nature constitute of local interactions (all forces of nature are two-body), so can be efficiently simulated by a quantum computer, i.e., in a time proportional to the duration of the thermalization process [1, 3, 12, 20].”
BackgroundMaterial platforms for defect qubits and single-photon emitters
Zhang, G., Cheng, Y., Chou, J., & Gali, Á. (2020) · Applied Physics Reviews · doi:10.1063/5.0006075 · Cited by 220
Harnessing the Power of the Second Quantum Revolution
Deutsch, I. H. (2020) · PRX Quantum · doi:10.1103/prxquantum.1.020101 · Cited by 207
“Preskill laid out a number of examples where such an advantage might be seen, including optimization [85–87], quantum machine learning [88], and quantum simulation [47,75–83].”
BackgroundQuantum Simulation of the Klein Paradox with Trapped Ions
Gerritsma, R., Lanyon, B. P., Kirchmair, G., Zähringer, F., Hempel, C., Casanova, J., García-Ripoll, J. J., Solano, E., Blatt, R., & Roos, C. F. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.060503 · Cited by 204
Li, R. Y., Di Felice, R., Rohs, R., & Lidar, D. A. (2018) · npj Quantum Information · doi:10.1038/s41534-018-0060-8 · Cited by 202
“…has been the subject of intense scientific scrutiny for its potential to solve certain fundamental problems, such as factoring of integers [1] or simulation of quantum systems [2, 3], more efficiently than classical algorithms, by using unique quantum phenomena including entanglement and tunneling.”
BackgroundGeometry of quantum phase transitions
Carollo, A. C. M., Valenti, D., & Spagnolo, B. (2019) · Physics Reports · doi:10.1016/j.physrep.2019.11.002 · Cited by 212
“A second more versatile interpretation originates from the concept of digital simulators [381, 382, 373, 383, 384, 371, 385], where a set of arbitrary (local) Lindblad operators Λα can be explicitly implemented in terms of local, tailored interactions [373].”
BackgroundUsing Dark States to Charge and Stabilize Open Quantum Batteries
Quach, J. Q., & Munro, W. J. (2020) · Physical Review Applied · doi:10.1103/physrevapplied.14.024092 · Cited by 202
Lloyd, S., & Viola, L. (2001) · Physical Review A · doi:10.1103/physreva.65.010101 · Cited by 197
Self-citationDemonstration of a Scaling Advantage for a Quantum Annealer over Simulated Annealing
Albash, T., & Lidar, D. A. (2018) · Physical Review X · doi:10.1103/physrevx.8.031016 · Cited by 238
“[3] Seth Lloyd, “Universal quantum simulators,” Science”
Unbiasing fermionic quantum Monte Carlo with a quantum computer
Huggins, W. J., O’Gorman, B., Rubin, N. C., Reichman, D. R., Babbush, R., & Lee, J. (2022) · Nature · doi:10.1038/s41586-021-04351-z · Cited by 220
“5,6 While the ultimate ambition of this field is to construct a universal fault-tolerant quantum computer, 7 the experimental devices of today are limited to Noisy Intermediate-Scale Quantum (NISQ) computers.”
BackgroundCiavarella, A. N., Klco, N., & A, M. J. S. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.103.094501 · Cited by 195
Adiabatic Quantum Simulation of Quantum Chemistry
Babbush, R., Love, P. J., & Aspuru-Guzik, A. (2014) · Scientific Reports · doi:10.1038/srep06603 · Cited by 191
“[46] S.”
Long Coherence Times in Nuclear Spin-Free Vanadyl Qubits.
Yu, C.-J., Graham, M. J., Zadrozny, J. M., Niklas, J., Krzyaniak, M. D., Wasielewski, M., Poluektov, O., & Freedman, D. (2016) · Journal of the American Chemical Society · doi:10.1021/jacs.6b08467 · Cited by 156
Quantum Image Processing and Its Application to Edge Detection: Theory and Experiment
Yao, X., Wang, H., Liao, Z., Chen, M.-C., Pan, J., Li, J., Zhang, K., Lin, X., Wang, ., Luo, Z., et al. (2017) · Physical Review X · doi:10.1103/physrevx.7.031041 · Cited by 200
“…of classical computation and reaches higher computational speed for certain problems like factoring large numbers [24, 25] , searching an unsorted database [26], boson sampling [27–32], quantum simulation [33–40], solving linear systems of equations [41–45], and machine learning [46–48].”
BackgroundFaster quantum simulation by randomization
Childs, A. M., Ostrander, A., & Su, Y. (2019) · Quantum · doi:10.22331/q-2019-09-02-182 · Cited by 222
“In particular, the cost of simulation can be reduced when many pairs of summands commute [2, 17, 25].”
BackgroundInfluentialNear-optimal ground state preparation
Lin, L., & Tong, Y. (2020) · Quantum · doi:10.22331/q-2020-12-14-372 · Cited by 243
Jones, J. A. (2010) · Progress in Nuclear Magnetic Resonance Spectroscopy · doi:10.1016/j.pnmrs.2010.11.001 · Cited by 195
Review on novel methods for lattice gauge theories
Bañuls, M. C., & Cichy, K. (2019) · Reports on Progress in Physics · doi:10.1088/1361-6633/ab6311 · Cited by 221
Problem of equilibration and the computation of correlation functions on a quantum computer
Terhal, B. M., & Divincenzo, D. P. (2000) · Physical Review A · doi:10.1103/physreva.61.022301 · Cited by 204
Romero, J., & Aspuru‐Guzik, A. (2021) · Advanced Quantum Technologies · doi:10.1002/qute.202000003 · Cited by 186
Three-photon bosonic coalescence in an integrated tritter
Spagnolo, N., Vitelli, C., Aparo, L., Mataloni, P., Sciarrino, F., Crespi, A., Ramponi, R., & Osellame, R. (2013) · Nature Communications · doi:10.1038/ncomms2616 · Cited by 170
A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons
Stair, N. H., Huang, R., & Evangelista, F. A. (2020) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.9b01125 · Cited by 183
Effective spin quantum phases in systems of trapped ions
Deng, X., Porras, D., & Cirac, J. I. (2005) · Physical Review A · doi:10.1103/physreva.72.063407 · Cited by 187
Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems
Ma, X.-S., Dakic, B., Naylor, W., Zeilinger, A., & Walther, P. (2011) · Nature Physics · doi:10.1038/nphys1919 · Cited by 179
“An alternative approach utilizes the adiabatic theorem[34], where an initial Hamiltonian, whose ground state is easy to prepare, can be adiabatically evolved to a final Hamiltonian with a nontrivial ground state of interest[8, 9, 13, 26].”
MethodExperimental Bayesian Quantum Phase Estimation on a Silicon Photonic Chip
Paesani, S., Gentile, A. A., Santagati, R., Wang, J., Wiebe, N., Tew, D. P., O’Brien, J. L., & Thompson, M. G. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.100503 · Cited by 178
“Introduction—Quantum algorithms promise exponential advantages over their classical counterparts, allowing the possibility to accomplish tasks otherwise unachievable on a classical computer [1, 2].”
BackgroundNearly Optimal Lattice Simulation by Product Formulas
Childs, A. M., & Su, Y. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.050503 · Cited by 197
“The lattice Hamiltonians there have similar locality, so our analysis still applies.”
BackgroundInfluentialQuantum Simulations on a Quantum Computer
Somaroo, S., Tseng, C. H., Havel, T. F., Laflamme, R., & Cory, D. G. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.5381 · Cited by 180
Quantum machine learning for image classification
Senokosov, A., Sedykh, A., Sagingalieva, A., Kyriacou, B., & Melnikov, A. A. (2024) · Machine Learning Science and Technology · doi:10.1088/2632-2153/ad2aef · Cited by 226
“They also operate in an exponentially larger search space, which has the potential to enhance their performance [19–21].”
BackgroundStrategies for solving the Fermi-Hubbard model on near-term quantum computers
Cade, C., Mineh, L., Montanaro, A., & Stanisic, S. (2020) · Physical Review B · doi:10.1103/physrevb.102.235122 · Cited by 178
“in time polynomial in the system size [4]; by contrast, even to write down a classical description of the quantum system would take exponential time.”
BackgroundClassical boson sampling algorithms with superior performance to near-term experiments
Neville, A., Sparrow, C., Clifford, R., Johnston, E., Birchall, P. M., Montanaro, A., & Laing, A. (2017) · Nature Physics · doi:10.1038/nphys4270 · Cited by 180
QASMBench: A Low-Level Quantum Benchmark Suite for NISQ Evaluation and Simulation
Li, A., Stein, S., Krishnamoorthy, S., & Ang, J. (2023) · ACM Transactions on Quantum Computing · doi:10.1145/3550488 · Cited by 183
“It is designed to implement the Trotter [12, 77] steps for an actual molecule LiH at equilibrium geometry, so as to simulate basis molecular Hamiltonians taking the following form The circuit uses 4 qubits but is quite deep, challenging the T1 and T2 decay of a NISQ device.”
MethodJones, J. A. (2001) · Progress in Nuclear Magnetic Resonance Spectroscopy · doi:10.1016/s0079-6565(00)00033-9 · Cited by 177
Quantum simulation of the Hubbard model with ultracold fermions in optical lattices
Tarruell, L., & Sanchez-Palencia, L. (2018) · Comptes Rendus Physique · doi:10.1016/j.crhy.2018.10.013 · Cited by 194
Forbes, A., & Nape, I. (2019) · AVS Quantum Science · doi:10.1116/1.5112027 · Cited by 170
Hardware-efficient variational quantum algorithms for time evolution
Benedetti, M., Fiorentini, M., & Lubasch, M. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.033083 · Cited by 189
“Although significant progress has been made based on the original quantum algorithm for simulating time evolution [2], this algorithm faces obstacles on current quantum hardware which lacks quantum error correction [10–12].”
BackgroundNISQ computing: where are we and where do we go?
Lau, J. W. Z., Lim, K. H., Shrotriya, H., & Kwek, L. C. (2022) · AAPPS bulletin · doi:10.1007/s43673-022-00058-z · Cited by 199
“Due to its simplicity, there has been much theoretical analysis and experimental work on applying Trotterization on quantum computers [14, 130–135].”
MethodExperimental Quantum Computing to Solve Systems of Linear Equations
Cai, X.-D., Weedbrook, C., Su, Z.-E., Chen, M.-C., Gu, M., Zhu, M.-J., Li, L., Liu, N.-L., Lu, C.-Y., & Pan, J.-W. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.230501 · Cited by 173
Emerging quantum computing algorithms for quantum chemistry
Motta, M., & Rice, J. E. (2021) · Wiley Interdisciplinary Reviews Computational Molecular Science · doi:10.1002/wcms.1580 · Cited by 201
“We will focus on Hamiltonian dynamics, in particular, since at the current state of knowledge, it can be simulated with lower scaling on a digital quantum computer than on a conventional computer.(5,6) The idea of a quantum simulator is conceptually interesting and appealing, and the manufacturing, control, and operat…”
BackgroundU(1) Wilson lattice gauge theories in digital quantum simulators
Muschik, C. A., Heyl, M., Martinez, E. A., Monz, T., Schindler, P., Vogell, B., Dalmonte, M., Hauke, P., Blatt, R., & Zoller, P. (2017) · New Journal of Physics · doi:10.1088/1367-2630/aa89ab · Cited by 164
Analog quantum simulation of the Rabi model in the ultra-strong coupling regime
Braumüller, J., Marthaler, M., Schneider, A., Stehli, A., Rotzinger, H., Weides, M. P., & Ustinov, A. V. (2017) · Nature Communications · doi:10.1038/s41467-017-00894-w · Cited by 170
“∆ is valid for the transmon qubit since hopping between wells of the Josephson potential is suppressed in the spirit of a WKB approximation [2].”
Kivlichan, I. D., Gidney, C., Berry, D. W., Wiebe, N., McClean, J., Sun, W., Jiang, Z., Rubin, N., Fowler, A., Aspuru-Guzik, A., et al. (2020) · Quantum · doi:10.22331/q-2020-07-16-296 · Cited by 173
“While the dynamics of many such systems appear intractable for classical computers, quantum computers were originally introduced as universal simulators capable of efficient quantum dynamical simulation [1, 2].”
BackgroundDigitization of scalar fields for quantum computing
Klco, N., & A, M. J. S. (2019) · Physical Review A · doi:10.1103/physreva.99.052335 · Cited by 204
Analog Quantum Error Correction
Lloyd, S., & Slotine, J.-J. E. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.4088 · Cited by 176
Self-citationVariational quantum eigensolver with fewer qubits
Liu, J.-G., Zhang, Y.-H., Wan, Y., & Wang, L. (2019) · Physical Review Research · doi:10.1103/physrevresearch.1.023025 · Cited by 166
Standard model physics and the digital quantum revolution: thoughts about the interface
Klco, N., Roggero, A., & A, M. J. S. (2022) · Reports on Progress in Physics · doi:10.1088/1361-6633/ac58a4 · Cited by 209
Towards Quantum Simulation with Circular Rydberg Atoms
Nguyen, T. L., Raimond, J. M., Sayrin, C., Cortiñas, R. G., Cantat-Moltrecht, T., Assémat, F., Dotsenko, I., Gleyzes, S., Haroche, S., Roux, G., et al. (2018) · Physical Review X · doi:10.1103/physrevx.8.011032 · Cited by 187
“In principle, a general purpose quantum computer could be turned into a ‘digital’ quantum simulator at the expense of an embarrassingly high amount of resources [15, 17].”
BackgroundCooling in strongly correlated optical lattices: prospects and challenges
McKay, D. C., & DeMarco, B. (2011) · Reports on Progress in Physics · doi:10.1088/0034-4885/74/5/054401 · Cited by 172
“simulate models of many-particle quantum systems that are beyond the reach of any classical computer, a conjecture that was later proven by Seth Lloyd in 1996 [3].”
BackgroundA quantum algorithm for evolving open quantum dynamics on quantum computing devices
Hu, Z., Xia, R., & Kais, S. (2020) · Scientific Reports · doi:10.1038/s41598-020-60321-x · Cited by 172
Sawaya, N. P. D., Menke, T., Kyaw, T. H., Johri, S., Aspuru-Guzik, A., & Guerreschi, G. G. (2020) · npj Quantum Information · doi:10.1038/s41534-020-0278-0 · Cited by 163
Efficient representation of quantum many-body states with deep neural networks
Gao, X., & Duan, L.-M. (2017) · RePEc: Research Papers in Economics · Cited by 202
Quantum simulation of generic many-body open system dynamics using classical noise
Chenu, A., Beau, M., Cao, J., & del Campo, A. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.140403 · Cited by 160
Quantum Algorithms for Simulating the Lattice Schwinger Model
Shaw, A. F., Lougovski, P., Stryker, J. R., & Wiebe, N. (2020) · Quantum · doi:10.22331/q-2020-08-10-306 · Cited by 179
“For many locally-interacting quantum systems, the simulation gate count is polynomial in the number of qubits [25, 28], but for field theories, even research into the scaling of these costs is still in its infancy.”
BackgroundMethodQuantum Simulation of a System with Competing Two- and Three-Body Interactions
Peng, X., Zhang, J., Du, J., & Suter, D. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.140501 · Cited by 157
Is the Trotterized UCCSD Ansatz Chemically Well-Defined?
Grimsley, H. R., Claudino, D., Economou, S. E., Barnes, E., & Mayhall, N. J. (2019) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.9b01083 · Cited by 168
Observation of a Dissipation-Induced Classical to Quantum Transition
Raftery, J. J., Sadri, D. J., Schmidt, S., Türeci, H. E., & Houck, A. (2014) · Physical Review X · doi:10.1103/physrevx.4.031043 · Cited by 167
“classes of quantum simulations [24,25] of important but difficult to study problems [26–31].”
BackgroundQuantum Computers as Universal Quantum Simulators: State‐of‐the‐Art and Perspectives
Tacchino, F., Chiesa, A., Carretta, S., & Gerace, D. (2019) · Advanced Quantum Technologies · doi:10.1002/qute.201900052 · Cited by 172
Dissipative Quantum Church-Turing Theorem
Kliesch, M., Barthel, T., Gogolin, C., Kastoryano, M., & Eisert, J. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.120501 · Cited by 154
Faster ground state preparation and high-precision ground energy estimation with fewer qubits
Ge, Y., Tura, J., & Cirac, J. I. (2019) · Journal of Mathematical Physics · doi:10.1063/1.5027484 · Cited by 185
Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges
Fauseweh, B. (2024) · Nature Communications · doi:10.1038/s41467-024-46402-9 · Cited by 152
“In its original formulation it involves discretizing the time evolution of the system and breaking it up into a series of small time steps, which can be implemented using quantum gates 20 .”
Digital Quantum Simulation of Minimal AdS/CFT
García-Álvarez, L., Egusquiza, I. L., Lamata, L., del Campo, A., Sonner, J., & Solano, E. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.040501 · Cited by 154
Machine learning method for state preparation and gate synthesis on photonic quantum computers
Arrazola, J. M., Bromley, T. R., Izaac, J., Myers, C. R., Brádler, K., & Killoran, N. (2018) · Quantum Science and Technology · doi:10.1088/2058-9565/aaf59e · Cited by 153
Application of fermionic marginal constraints to hybrid quantum algorithms
Rubin, N. C., Babbush, R., & McClean, J. (2018) · New Journal of Physics · doi:10.1088/1367-2630/aab919 · Cited by 152
Quantum Simulation of Helium Hydride Cation in a Solid-State Spin Register
Wang, Y., Dolde, F., Biamonte, J., Babbush, R., Bergholm, V., Yang, S., Jakobi, I., Neumann, P., Aspuru‐Guzik, A., Whitfield, J. D., et al. (2015) · ACS Nano · doi:10.1021/acsnano.5b01651 · Cited by 155
Quantum spin dynamics with pairwise-tunable, long-range interactions
Hung, C.-L., González-Tudela, A., Cirac, J. I., & Kimble, H. J. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1603777113 · Cited by 155
“It can be shown [51] that higher order error terms give smaller error bounds.”
BackgroundA quantum–quantum Metropolis algorithm
Yung, M., & Aspuru‐Guzik, A. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1111758109 · Cited by 168
Quantum Algorithm for Simulating Real Time Evolution of Lattice Hamiltonians
Haah, J., Hastings, M. B., Kothari, R., & Low, G. H. (2021) · SIAM Journal on Computing · doi:10.1137/18m1231511 · Cited by 205
“On the other hand, from the early days of quantum computing [1], [3] it was known that quantum computers can solve this problem in polynomial time.”
BackgroundMethodA quantum machine learning algorithm based on generative models
Gao, X.-S., Zhang, Z., & Duan, L. (2018) · Science Advances · doi:10.1126/sciadv.aat9004 · Cited by 177
Focus beyond Quadratic Speedups for Error-Corrected Quantum Advantage
Babbush, R., McClean, J. R., Newman, M., Gidney, C., Boixo, S., & Neven, H. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.010103 · Cited by 148
“But what valuable and classically challenging problems could we actually solve on such a device? Among the most compelling applications are quantum simulation [1,2] and prime factoring [3].”
BackgroundDissipative quantum error correction and application to quantum sensing with trapped ions
Reiter, F., Sørensen, A. S., Zoller, P., & Muschik, C. A. (2017) · Nature Communications · doi:10.1038/s41467-017-01895-5 · Cited by 155
“Errors and correction ( 000 + 111 ) / √2 ( 000 + e 111 ) / √2 x (1) x (2) x (3)”
BackgroundA non-orthogonal variational quantum eigensolver
Huggins, W. J., Lee, J., Baek, U., O’Gorman, B., & Whaley, K. B. (2020) · New Journal of Physics · doi:10.1088/1367-2630/ab867b · Cited by 148
“For example, such devices will be able to efficiently simulate long-time dynamics [1], and through phase estimation, measure the energy of a trial wavefunction while projecting it into the eigen-basis of the Hamiltonian [2].”
BackgroundFidelity Decay as an Efficient Indicator of Quantum Chaos
Emerson, J., Weinstein, Y. S., Lloyd, S., & Cory, D. G. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.284102 · Cited by 147
Self-citationExperimental perfect state transfer of an entangled photonic qubit
Chapman, R. J., Santandrea, M., Huang, Z., Corrielli, G., Crespi, A., Yung, M. H., Osellame, R., & Peruzzo, A. (2016) · Nature Communications · doi:10.1038/ncomms11339 · Cited by 148
Faster quantum chemistry simulation on fault-tolerant quantum computers
Cody Jones, N., Whitfield, J. D., McMahon, P. L., Yung, M.-H., Meter, R. V., Aspuru-Guzik, A., & Yamamoto, Y. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/11/115023 · Cited by 145
“Several possible simulators have been proposed and studied [12, 17–20], but we focus on fault-tolerant circuit-model quantum simulation in this investigation [2, 4, 7, 13,21–24].”
BackgroundMethodInfluentialComputational advantage of quantum random sampling
Hangleiter, D., & Eisert, J. (2023) · Reviews of Modern Physics · doi:10.1103/revmodphys.95.035001 · Cited by 145
Entanglement of spin waves among four quantum memories
Choi, K. S., Goban, A., Papp, S. B., van Enk, S. J., & Kimble, H. J. (2010) · Nature · doi:10.1038/nature09568 · Cited by 146
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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