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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The quantum simulation algorithm runs in time polynomial in the size of the system being simulated and the desired evolution time, giving an exponential speedup over the best general classical algorithms known.
“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]
A general-purpose quantum computer can efficiently simulate quantum mechanics for many physically realistic cases, such as systems with locality restrictions on their interactions.
“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]
We can program quantum computers to simulate localized quantum systems.
“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]
With a universal approach, a wide range of quantum problems can be simulated to the desired accuracy with a polynomial increase in quantum resources only.
“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
The quantum computational cost of quantum chemistry algorithms has continued to be reduced.
“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]
It was demonstrated that the Trotter errors depend on the maximum nuclear charge rather than the number of spin-orbitals.
“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]
The number of gates for the highly nonlocal coupling b†_1 b_10 + b†_10 b_1 can be as small as 10 per Trotter step with the proposed method, whereas in the general case it would require about 10^6 elementary gates.
“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]
The resulting dynamics are decomposed in efficient steps with Trotter methods, yielding an overall protocol that employs only polynomial resources.
“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]
For bounded Hamiltonians, the Trotter expansion associated with the exponential of the polynomial sum of efficiently implementable nonlocal terms is efficient, i.e., it only requires polynomial resources.
“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]
On a fault-tolerant computer, full-CI energy can be measured by preparing a wave function ansatz and applying Quantum Phase Estimation, which projects into an energy eigenstate.
“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]
A proposed solution is to use highly controlled laboratory quantum systems themselves to perform such simulations.
“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]
Simulating quantum mechanics using conventional computers rapidly becomes intractable as the physical systems to which it is applied grow larger.
“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]
According to the Lieb-Robinson theorem, after a sufficiently large time, states can become strongly entangled.
“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]
Quantum dynamics is in general computationally hard.
“or that the quantum dynamics is in general computationally hard [96, 97].”
From Can one trust quantum simulators? (2012) · cites this paper as [96]
Cites
Algorithms for quantum computation: discrete logarithms and factoring
Shor, P. W. (2002) · Proceedings 35th Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1994.365700 · Cited by 8,713 · see citing works
Simulating physics with computers
Feynman, R. P. (1982) · International Journal of Theoretical Physics · doi:10.1007/bf02650179 · Cited by 7,691 · see citing works
Metropolis, N., & Ulam, S. (1949) · Journal of the American Statistical Association · doi:10.1080/01621459.1949.10483310 · Cited by 6,474 · see citing works
Quantum theory, the Church–Turing principle and the universal quantum computer
Deutsch, D. (1985) · Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences · doi:10.1098/rspa.1985.0070 · Cited by 4,597 · see citing works
Scheme for reducing decoherence in quantum computer memory
Shor, P. W. (1995) · Physical Review A · doi:10.1103/physreva.52.r2493 · Cited by 4,479 · see citing works
Hammersley, J. M., & Handscomb, D. C. (1964) · Springer eBooks · doi:10.1007/978-94-009-5819-7 · Cited by 4,085 · see citing works
Quantum Computations with Cold Trapped Ions
Cirac, J. I., & Zoller, P. (1995) · Physical Review Letters · doi:10.1103/physrevlett.74.4091 · Cited by 3,733 · see citing works
Rapid solution of problems by quantum computation
Deutsch, D., & Jozsa, R. (1992) · Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences · doi:10.1098/rspa.1992.0167 · Cited by 2,700 · see citing works
Self-Organization of CdSe Nanocrystallites into Three-Dimensional Quantum Dot Superlattices
Murray, C. B., Kagan, C. R., & Bawendi, M. G. (1995) · Science · doi:10.1126/science.270.5240.1335 · Cited by 2,225 · see citing works
Feynman, R. P. (1986) · Foundations of Physics · doi:10.1007/bf01886518 · Cited by 1,770 · see citing works
DiVincenzo, D. P. (1995) · Science · doi:10.1126/science.270.5234.255 · Cited by 1,651 · see citing works
Demonstration of a Fundamental Quantum Logic Gate
Monroe, C., Meekhof, D. M., King, B. E., Itano, W. M., & Wineland, D. J. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.4714 · Cited by 1,586 · see citing works
Measurement of Conditional Phase Shifts for Quantum Logic
Turchette, Q. A., Hood, C. J., Lange, W., Mabuchi, H., & Kimble, H. J. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.4710 · Cited by 1,409 · see citing works
Quantum computational networks
Deutsch, D. E. (1989) · Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences · doi:10.1098/rspa.1989.0099 · Cited by 1,270 · see citing works
Benioff, P. (1980) · Journal of Statistical Physics · doi:10.1007/bf01011339 · Cited by 1,244 · see citing works
Two-bit gates are universal for quantum computation
DiVincenzo, D. P. (1995) · Physical Review A · doi:10.1103/physreva.51.1015 · Cited by 1,069 · see citing works
Feynman, R. P. (1985) · Optics News · doi:10.1364/on.11.2.000011 · Cited by 1,023 · see citing works
Conditional Quantum Dynamics and Logic Gates
Barenco, A., Deutsch, D., EKERT, A. K., & Jozsa, R. (1995) · Physical Review Letters · doi:10.1103/physrevlett.74.4083 · Cited by 966 · see citing works
Quantum computers and dissipation
(1996) · Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rspa.1996.0029 · Cited by 899 · see citing works
Reversible logic and quantum computers
Peres, A. (1985) · Physical Review A · doi:10.1103/physreva.32.3266 · Cited by 897 · see citing works
Landauer, R. W. (1991) · Physics Today · doi:10.1063/1.881299 · Cited by 804 · see citing works
Almost Any Quantum Logic Gate is Universal
Lloyd, S. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.346 · Cited by 690 · see citing works
Self-citationA Potentially Realizable Quantum Computer
Lloyd, S. (1993) · Science · doi:10.1126/science.261.5128.1569 · Cited by 649 · see citing works
Self-citationMaintaining coherence in quantum computers
Unruh, W. G. (1995) · Physical Review A · doi:10.1103/physreva.51.992 · Cited by 594 · see citing works
Realizable Universal Quantum Logic Gates
Sleator, T., & Weinfurter, H. (1995) · Physical Review Letters · doi:10.1103/physrevlett.74.4087 · Cited by 515 · see citing works
Milburn, G. J. (1989) · Physical Review Letters · doi:10.1103/physrevlett.62.2124 · Cited by 440 · see citing works
Quantum mechanical Hamiltonian models of Turing machines
Benioff, P. (1982) · Journal of Statistical Physics · doi:10.1007/bf01342185 · Cited by 402 · see citing works
Synthesis of arbitrary quantum states via adiabatic transfer of Zeeman coherence
Parkins, A. S., Marte, P., Zoller, P., & Kimble, H. J. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.3095 · Cited by 396 · see citing works
Controllability of molecular systems
Ramakrishna, V., Salapaka, M. V., Dahleh, M., RABITZ, H. A., & Peirce, A. P. (1995) · Physical Review A · doi:10.1103/physreva.51.960 · Cited by 368 · see citing works
Universality in quantum computation
Deutsch, D. E., Barenco, A., & Ekert, A. (1995) · Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences · doi:10.1098/rspa.1995.0065 · Cited by 346 · see citing works
A Crosslinked Cofactor in Lysyl Oxidase: Redox Function for Amino Acid Side Chains
Wang, S. X., Mure, M., Medzihradszky, K. F., Burlingame, A. L., Brown, D. E., Dooley, D. M., Smith, A. J., Kagan, H. M., & Klinman, J. P. (1996) · Science · doi:10.1126/science.273.5278.1078 · Cited by 338 · see citing works
Universality in Quantum ComputationPreprint
Deutsch, D., Barenco, A., & Ekert, A. (1995) · Cited by 322 · see citing works
Quantum Mechanical Models of Turing Machines That Dissipate No Energy
Benioff, P. A. (1982) · Physical Review Letters · doi:10.1103/physrevlett.48.1581 · Cited by 295 · see citing works
Quantum Computers, Factoring, and Decoherence
Chuang, I. L., Laflamme, R., Shor, P. W., & Zurek, W. H. (1995) · Science · doi:10.1126/science.270.5242.1633 · Cited by 289 · see citing works
(1993) · Springer eBooks · doi:10.1007/978-1-4615-3176-0 · Cited by 269 · see citing works
Brune, M., Nussenzveig, P., Schmidt‐Kaler, F., Bernardot, F., Maali, A., Raimond, J. M., & Haroche, S. (1994) · Physical Review Letters · doi:10.1103/physrevlett.72.3339 · Cited by 251 · see citing works
Dissipation and noise immunity in computation and communication
Landauer, R. (1988) · Nature · doi:10.1038/335779a0 · Cited by 208 · see citing works
Theory of selective excitation of multiple-quantum transitions
Warren, W. S., Weitekamp, D. P., & Pines, A. (1980) · The Journal of Chemical Physics · doi:10.1063/1.440403 · Cited by 193 · see citing works
Simple cavity-QED two-bit universal quantum logic gate: The principle and expected performances
Domokos, P., Raimond, J. M., Brune, M., & Haroche, S. (1995) · Physical Review A · doi:10.1103/physreva.52.3554 · Cited by 174 · see citing works
Atom galleries for whispering atoms: binding atoms in stable orbits around an optical resonator
Mabuchi, H., & Kimble, H. J. (1994) · Optics Letters · doi:10.1364/ol.19.000749 · Cited by 127 · see citing works
Landauer, R. (1995) · Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences · doi:10.1098/rsta.1995.0106 · Cited by 124 · see citing works
Reversibility and Stability of Information Processing Systems
Zurek, W. H. (1984) · Physical Review Letters · doi:10.1103/physrevlett.53.391 · Cited by 111 · see citing works
Uncertainty principle and minimal energy dissipation in the computer
Landauer, R. W. (1982) · International Journal of Theoretical Physics · doi:10.1007/bf01857731 · Cited by 88 · see citing works
Landauer, R. W. (1995) · Springer eBooks · doi:10.1007/978-94-011-0041-0_33 · Cited by 74 · see citing works
Structural basis of multistationary quantum systems. II. Effective few-particle dynamics
Teich, W. G., Obermayer, K., & Mahler, G. (1988) · Physical Review B · doi:10.1103/physrevb.37.8111 · Cited by 64 · see citing works
Envisioning a Quantum Supercomputer
Lloyd, S. (1994) · Science · doi:10.1126/science.263.5147.695 · Cited by 60 · see citing works
Self-citationStochastic dynamics of individual quantum systems: Stationary rate equations
Teich, W. G., & Mahler, G. (1992) · Physical Review A · doi:10.1103/physreva.45.3300 · Cited by 55 · see citing works
Structural basis of multistationary quantum systems. I. Effective single-particle dynamics
Obermayer, K., Teich, W. G., & Mahler, G. (1988) · Physical Review B · doi:10.1103/physrevb.37.8096 · Cited by 48 · see citing works
Computation and physics: Wheeler's meaning circuit?
Landauer, R. W. (1986) · Foundations of Physics · doi:10.1007/bf01886520 · Cited by 45 · see citing works
Advanced technology and truth in advertising
Landauer, R. W. (1990) · Physica A Statistical Mechanics and its Applications · doi:10.1016/0378-4371(90)90359-z · Cited by 44 · see citing works
Can We Switch by Control of Quantum Mechanical Transmission?
Landauer, R. W. (1989) · Physics Today · doi:10.1063/1.2811186 · Cited by 40 · see citing works
Quantum Mechanical Hamiltonian Models of Computersa
Benioff, P. A. (1986) · Annals of the New York Academy of Sciences · doi:10.1111/j.1749-6632.1986.tb12450.x · Cited by 39 · see citing works
Quantum Computation <sup>a</sup>
MARGOLUS, N. (1986) · Annals of the New York Academy of Sciences · doi:10.1111/j.1749-6632.1986.tb12451.x · Cited by 38 · see citing works
Quantum nondemolition detection of single photons in an open resonator by atomic beam deflection
Matsko, A. B., Vyatchanin, S. P., Mabuchi, H., & Kimble, H. J. (1994) · Physics Letters A · doi:10.1016/0375-9601(94)90240-2 · Cited by 20 · see citing works
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Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., & Lloyd, S. (2017) · Nature · doi:10.1038/nature23474 · Cited by 4,779 · see citing works
“see that the density matrix for the quantum version of the data is the covariance matrix, up to an overall factor. Repeatedly sampling the data, and using a trick called density matrix exponentiation [42] combined with the quantum phase estimation algorithm [39], which nds eigenvectors and eigenvalues of matrices, all…”
Self-citationPolynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Shor, P. W. (1999) · SIAM Review · doi:10.1137/s0036144598347011 · Cited by 3,904 · see citing works
Quantum information with continuous variables
Braunstein, S. L., & van Loock, P. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.513 · Cited by 3,858 · see citing works
Quantum Algorithm for Linear Systems of Equations
Harrow, A. W., Hassidim, A., & Lloyd, S. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.150502 · Cited by 3,325 · see citing works
“[2] S.”
BackgroundSelf-citationVariational quantum algorithms
Cerezo, M., Arrasmith, A., Babbush, R., Benjamin, S. C., Endo, S., Fujii, K., McClean, J. R., Mitarai, K., Yuan, X., Cincio, L., et al. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00348-9 · Cited by 3,385 · see citing works
“Shor’s quantum algorithm was proposed to factor numbers with exponential speedup over classical methods [2], dynamical quantum simulation algorithms were developed [3], and quantum algorithms for solving linear systems of equations were identified [4].”
MethodGeorgescu, I. M., Ashhab, S., & Nori, F. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.153 · Cited by 2,932 · see citing works
“First, one could exploit the natural decoherence of the simulator, as first suggested in (Lloyd, 1996) and investigated experimentally in (Tseng et al., 2000) (see also the discussion in Section V.”
BackgroundMethodInfluentialManipulating quantum entanglement with atoms and photons in a cavity
Raimond, J. M., Brune, M., & Haroche, S. (2001) · Reviews of Modern Physics · doi:10.1103/revmodphys.73.565 · Cited by 2,669 · see citing works
Superconducting Circuits for Quantum Information: An Outlook
Devoret, M., & Schoelkopf, R. J. (2013) · Science · doi:10.1126/science.1231930 · Cited by 2,122 · see citing works
A quantum engineer's guide to superconducting qubits
Krantz, P., Kjærgaard, M., Yan, F., Orlando, T. P., Gustavsson, S., & Oliver, W. D. (2019) · Applied Physics Reviews · doi:10.1063/1.5089550 · Cited by 2,056 · see citing works
Noisy intermediate-scale quantum algorithms
Bharti, K., Cervera-Lierta, A., Kyaw, T. H., Haug, T., Alperin-Lea, S., Anand, A., Degroote, M., Heimonen, H., Kottmann, J. S., Menke, T., et al. (2022) · Reviews of Modern Physics · doi:10.1103/revmodphys.94.015004 · Cited by 1,726 · see citing works
Measurement-based quantum computation on cluster states
Raussendorf, R., Browne, D. E., & Briegel, H. J. (2003) · Physical Review A · doi:10.1103/physreva.68.022312 · Cited by 1,655 · see citing works
“Among the further applications of a quantum computer which have so far been envisioned are a data base with faster access to unsorted data [2], and a universal simulator of quantum systems [3, 4].”
BackgroundQuantum simulations with trapped ions
Blatt, R., & Roos, C. F. (2012) · Nature Physics · doi:10.1038/nphys2252 · Cited by 1,629 · see citing works
Quantum computational chemistry
McArdle, S., Endo, S., Aspuru-Guzik, A., Benjamin, S. C., & Yuan, X. (2020) · Reviews of Modern Physics · doi:10.1103/revmodphys.92.015003 · Cited by 1,621 · see citing works
Dicke quantum phase transition with a superfluid gas in an optical cavity
Baumann, K., Guerlin, C., Brennecke, F., & Esslinger, T. (2010) · Nature · doi:10.1038/nature09009 · Cited by 1,530 · see citing works
Quantum Chemistry in the Age of Quantum Computing
Cao, Y., Romero, J., Olson, J. P., Degroote, M., Johnson, P. D., Kieferová, M., Kivlichan, I. D., Menke, T., Peropadre, B., Sawaya, N. P. D., et al. (2019) · Chemical Reviews · doi:10.1021/acs.chemrev.8b00803 · Cited by 1,560 · see citing works
“itrary subsets, H = P jHj. The criteria for grouping can dier depending on the target Hamiltonian as shown below. The variational ansatz is dened as j#TAB#()i= YS b=1 UH j (b j):::UH 1( b 1) ! j 0i; (37) where j 0ican be chosen to match the desired symmetry properties of the target ground 84 state, UH k (b k) = exp b…”
BackgroundSuperconducting Qubits: Current State of Play
Kjaergaard, M., Schwartz, M. E., Braumüller, J., Krantz, P., Wang, J. I.-J., Gustavsson, S., & Oliver, W. D. (2020) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-031119-050605 · Cited by 1,544 · see citing works
Lvovsky, A. I., Sanders, B. C., & Tittel, W. (2009) · Nature Photonics · doi:10.1038/nphoton.2009.231 · Cited by 1,489 · see citing works
“Furthermore quantum dynamics becomes efficiently simulatable on a quantum computer [3].”
BackgroundSimulated Quantum Computation of Molecular Energies
Aspuru-Guzik, A., Dutoi, A. D., Love, P. J., & Head-Gordon, M. (2005) · Science · doi:10.1126/science.1113479 · Cited by 1,418 · see citing works
Quantum principal component analysis
Lloyd, S., Mohseni, M., & Rebentrost, P. (2014) · Nature Physics · doi:10.1038/nphys3029 · Cited by 1,385 · see citing works
Self-citationTrapped-ion quantum computing: Progress and challenges
Bruzewicz, C. D., Chiaverini, J., McConnell, R., & Sage, J. M. (2019) · Applied Physics Reviews · doi:10.1063/1.5088164 · Cited by 1,483 · see citing works
High-performance semiconductor quantum-dot single-photon sources
Senellart, P., Solomon, G. S., & White, A. G. (2017) · Nature Nanotechnology · doi:10.1038/nnano.2017.218 · Cited by 1,275 · see citing works
Many-body physics with individually controlled Rydberg atoms
Browaeys, A., & Lahaye, T. (2020) · Nature Physics · doi:10.1038/s41567-019-0733-z · Cited by 1,248 · see citing works
Quantum computation and decision trees
Farhi, E., & Gutmann, S. (1998) · Physical Review A · doi:10.1103/physreva.58.915 · Cited by 1,215 · see citing works
Chemical Diversity in the Sialic Acids and Related α-Keto Acids: An Evolutionary Perspective
Angata, T., & Varki, A. P. (2002) · Chemical Reviews · doi:10.1021/cr000407m · Cited by 1,232 · see citing works
Steane, A. (1998) · Reports on Progress in Physics · doi:10.1088/0034-4885/61/2/002 · Cited by 1,391 · see citing works
“Some work has been done on simulating Hamiltonians on quantum computers [1, 24, 33], but I do not believe this question has been completely addressed yet.”
Quantum computing with trapped ions
HAFFNER, H., ROOS, C., & BLATT, R. (2008) · Physics Reports · doi:10.1016/j.physrep.2008.09.003 · Cited by 1,154 · see citing works
“In particular, the study of quantum mechanical many body systems would benefit considerably from such a device (Feynman, 1982; Lloyd, 1996).”
BackgroundQuantum Chemistry in the Age of Quantum Computing
Cao, Y., Romero, J., Olson, J., Degroote, M., Johnson, P., Kieferová, M., Kivlichan, I., Menke, T., Peropadre, B., Sawaya, N., et al. (n.d.) · OPUS - Open Publications of UTS Scholars (University of Technology Sydney) · Cited by 1,265 · see citing works
Ultimate physical limits to computation
Lloyd, S. (2000) · Nature · doi:10.1038/35023282 · Cited by 1,120 · see citing works
Self-citation14-Qubit Entanglement: Creation and Coherence
Monz, T., Schindler, P., Barreiro, J. T., Chwalla, M., Nigg, D., Coish, W. A., Harlander, M., Hänsel, W., Hennrich, M., & Blatt, R. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.130506 · Cited by 1,110 · see citing works
An open-system quantum simulator with trapped ions
Barreiro, J. T., Müller, M., Schindler, P., Nigg, D., Monz, T., Chwalla, M., Hennrich, M., Roos, C. F., Zoller, P., & Blatt, R. (2011) · Nature · doi:10.1038/nature09801 · Cited by 1,100 · see citing works
Superconducting Qubits: Current State of PlayPreprint
Kjærgaard, M., Schwartz, M. E., Braumüller, J., Krantz, P., Wang, J. I.-J., Gustavsson, S., & Oliver, W. D. (2020) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 1,182 · see citing works
Ultrastrong coupling regimes of light-matter interaction
Forn-Díaz, P., Lamata, L., Rico, E., Kono, J., & Solano, E. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.025005 · Cited by 1,087 · see citing works
“(38)] is simulated by a digital expansion (Lloyd, 1996) by interleaving the different interactions.”
BackgroundSuppressing quantum errors by scaling a surface code logical qubit
Google Quantum, A. I., Acharya, R., Aleiner, I., Allen, R., Andersen, T. I., Ansmann, M., Arute, F., Arya, K., Asfaw, A., Atalaya, J., et al. (2023) · Nature · doi:10.1038/s41586-022-05434-1 · Cited by 1,103 · see citing works
“Since Feynman’s proposal to compute using quantum mechanics [3], many potential applications have emerged, including factoring [4], optimization [5], machine learning [6], quantum simulation [7], and quantum chemistry [8].”
Quantum algorithms: an overview
Montanaro, A. (2016) · npj Quantum Information · doi:10.1038/npjqi.2015.23 · Cited by 1,071 · see citing works
“A general-purpose quantum computer can indeed e(cid:14)ciently simulate quantum mechanics in this sense for many physically realistic cases, such as systems with locality restrictions on their interactions [64].”
An adaptive variational algorithm for exact molecular simulations on a quantum computer
Grimsley, H. R., Economou, S. E., Barnes, E., & Mayhall, N. J. (2019) · Nature Communications · doi:10.1038/s41467-019-10988-2 · Cited by 1,033 · see citing works
“[5] Lloyd, S.”
MethodThe Variational Quantum Eigensolver: A review of methods and best practices
Tilly, J., Chen, H., Cao, S., Picozzi, D., Setia, K., Li, Y., Grant, E., Wossnig, L., Rungger, I., Booth, G. H., et al. (2022) · Physics Reports · doi:10.1016/j.physrep.2022.08.003 · Cited by 1,031 · see citing works
Quantum Computation Over Continuous Variables
Lloyd, S., & Braunstein, S. L. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.1784 · Cited by 1,145 · see citing works
Self-citationPreskill, J. (1998) · Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rspa.1998.0167 · Cited by 994 · see citing works
“First of all, quantum computers can do other things besides factoring, and some of these other tasks (in particular quantum simulation — Lloyd 1996) might be accomplished with a less reliable or smaller device. Furthermore, our estimate of the accuracy threshold might be too conservative for a number of reasons. For e…”
Quantum information processing with superconducting circuits: a review
Wendin, G. P. (2017) · Reports on Progress in Physics · doi:10.1088/1361-6633/aa7e1a · Cited by 970 · see citing works
Jaksch, D., & Zoller, P. (2005) · Annals of Physics · doi:10.1016/j.aop.2004.09.010 · Cited by 976 · see citing works
Ensemble quantum computing by NMR spectroscopy
Cory, D. G., Fahmy, A. F., & Havel, T. F. (1997) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.94.5.1634 · Cited by 964 · see citing works
Goals and opportunities in quantum simulation
Cirac, J. I., & Zoller, P. (2012) · Nature Physics · doi:10.1038/nphys2275 · Cited by 891 · see citing works
Power of One Bit of Quantum Information
Knill, E. H., & Laflamme, R. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.5672 · Cited by 880 · see citing works
Effective Quantum Spin Systems with Trapped Ions
Porras, D., & Cirac, J. I. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.207901 · Cited by 872 · see citing works
Buluta, I., & Nori, F. (2009) · Science · doi:10.1126/science.1177838 · Cited by 876 · see citing works
Atom-chip-based generation of entanglement for quantum metrology
Riedel, M. F., Böhi, P., Li, Y., Hänsch, T. W., Sinatra, A., & Treutlein, P. (2010) · Nature · doi:10.1038/nature08988 · Cited by 865 · see citing works
“With the experimental method presented here but with a more sophisticated analysis [9], the density matrix of arbitrary spin states that spread over the whole Bloch sphere can be reconstructed.”
MethodWeimer, H., Müller, M., Lesanovsky, I., Zoller, P., & Büchler, H. P. (2010) · Nature Physics · doi:10.1038/nphys1614 · Cited by 867 · see citing works
“For purely coherent dynamics governed by the Hamiltonian, this is the familiar‘digital quantum simulato”
MethodHamiltonian Simulation by Qubitization
Low, G. H., & Chuang, I. L. (2019) · Quantum · doi:10.22331/q-2019-07-12-163 · Cited by 854 · see citing works
“The first explicit quantum algorithms were discovered by Lloyd [31] for local interactions, and then generalized by Aharonov and Ta-Shma [3] to sparse Hamiltonians.”
MethodQuantum Algorithm Providing Exponential Speed Increase for Finding Eigenvalues and Eigenvectors
Abrams, D. S., & Lloyd, S. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.5162 · Cited by 817 · see citing works
Self-citationExponential algorithmic speedup by a quantum walk
Childs, A. M., Cleve, R., Deotto, E., Farhi, E., Gutmann, S., & Spielman, D. A. (2003) · Proceedings of the thirty-fifth annual ACM symposium on Theory of computing · doi:10.1145/780542.780552 · Cited by 825 · see citing works
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
Martinez, E. A., Muschik, C. A., Schindler, P., Nigg, D., Erhard, A., Heyl, M., Hauke, P., Dalmonte, M., Monz, T., Zoller, P., et al. (2016) · Nature · doi:10.1038/nature18318 · Cited by 789 · see citing works
“This provides the tools for universal digital quantum simulation [16], where the time evolution of a quantum system is approximated as a stroboscopic sequence of quantum gates [17].”
MethodQuantum Algorithms for Quantum Chemistry and Quantum Materials Science
Bauer, B., Bravyi, S., Motta, M., & Chan, G. K.-L. (2020) · Chemical Reviews · doi:10.1021/acs.chemrev.9b00829 · Cited by 848 · see citing works
Scalable Quantum Simulation of Molecular Energies
O’Malley, P. J. J., Babbush, R., Kivlichan, I. D., Romero, J., McClean, J. R., Barends, R., Kelly, J., Roushan, P., Tranter, A., Ding, N., et al. (2016) · Physical Review X · doi:10.1103/physrevx.6.031007 · Cited by 1,059 · see citing works
“Universal and efficient simulation of physical systems [1] is among the most compelling applications of quantum”
BackgroundProgrammable quantum simulations of spin systems with trapped ions
Monroe, C. R., Campbell, W. C., Duan, L.-M., Gong, Z., Gorshkov, A. V., Hess, P., Islam, R., Kim, K., Linke, N. M., Pagano, G., et al. (2021) · Reviews of Modern Physics · doi:10.1103/revmodphys.93.025001 · Cited by 807 · see citing works
Programmable Quantum Simulations of Spin Systems with Trapped Ions
Monroe, C., Campbell, W. C., Duan, L. M., Gong, Z. X., Gorshkov, A. V., Hess, P., Islam, R., Kim, K., Linke, N., Pagano, G., et al. (2019) · arXiv · doi:10.48550/arxiv.1912.07845 · Cited by 806
Towards quantum chemistry on a quantum computer
Lanyon, B. P., Whitfield, J. D., Gillett, G. G., Goggin, M. E., Almeida, M. P., Kassal, I., Biamonte, J. D., Mohseni, M., Powell, B. J., Barbieri, M., et al. (2010) · Nature Chemistry · doi:10.1038/nchem.483 · Cited by 796 · see citing works
“The challenge of first-principles calculations arises because the computational resources required to obtain exact (that is, full configuration interaction) solutions of the Schrodinger equation on a conventional computer generally increase exponentially with the number of atoms involve”
BackgroundChen, X., Gu, Z.-C., & Wen, X.-G. (2010) · Physical Review B · doi:10.1103/physrevb.82.155138 · Cited by 891 · see citing works
Entanglement and quantum computation with ions in thermal motion
Sørensen, A. S., & Mølmer, K. (2000) · Physical Review A · doi:10.1103/physreva.62.022311 · Cited by 770 · see citing works
Optimal Hamiltonian Simulation by Quantum Signal Processing
Low, G. H., & Chuang, I. L. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.010501 · Cited by 770 · see citing works
“[11] S. Lloyd, Science 273, 1073 (1996).”
BackgroundSimulation of Many-Body Fermi Systems on a Universal Quantum Computer
Abrams, D. S., & Lloyd, S. (1997) · Physical Review Letters · doi:10.1103/physrevlett.79.2586 · Cited by 745 · see citing works
Self-citationElucidating reaction mechanisms on quantum computers
Reiher, M., Wiebe, N., Svore, K. M., Wecker, D., & Troyer, M. (2017) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1619152114 · Cited by 745 · see citing works
“[5] Seth Lloyd, “Universal quantum simulators,” Science 273, 1073 (1996).”
MethodQuantum error correction below the surface code threshold
Collaborators, G. Q. A. A., Acharya, R., Abanin, D. A., Aghababaie-Beni, L., Aleiner, I., Andersen, T. I., Ansmann, M., Arute, F., Arya, K., Asfaw, A., et al. (2025) · Nature · doi:10.1038/s41586-024-08449-y · Cited by 778 · see citing works
“Quantum computing promises computational speedups in quantum chemistry [5], quantum simulation [6], cryptography [7], and optimization [8].”
Simulating Hamiltonian Dynamics with a Truncated Taylor Series
Berry, D. W., Childs, A. M., Cleve, R., Kothari, R., & Somma, R. D. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.090502 · Cited by 742 · see citing works
Photonic quantum information processing: a review
Flamini, F., Spagnolo, N., & Sciarrino, F. (2018) · Reports on Progress in Physics · doi:10.1088/1361-6633/aad5b2 · Cited by 724 · see citing works
Matrix product states represent ground states faithfully
Verstraete, F., & Cirac, J. I. (2006) · Physical Review B · doi:10.1103/physrevb.73.094423 · Cited by 730 · see citing works
Motta, M., Sun, C., Tan, A. T. K., O’Rourke, M. J., Ye, E., Minnich, A. J., Brandão, F. G. S. L., & Chan, G. K.-L. (2020) · Nature Physics · doi:10.1038/s41567-019-0704-4 · Cited by 709 · see citing works
Efficient Quantum Algorithms for Simulating Sparse Hamiltonians
Berry, D. W., Ahokas, G., Cleve, R., & Sanders, B. C. (2007) · Communications in Mathematical Physics · doi:10.1007/s00220-006-0150-x · Cited by 692 · see citing works
“Here we apply the higher-order integrators of Suzuki [12, 13] to reduce the temporal scaling from t 3 / 2 [5] or t 2 [4] to the slightly superlinear scaling t 1+1 / 2 k , where k is the order of the integrator and may be an arbitrarily large integer.”
BackgroundMethodInfluentialEfficient Variational Quantum Simulator Incorporating Active Error Minimization
Li, Y., & Benjamin, S. C. (2017) · Physical Review X · doi:10.1103/physrevx.7.021050 · Cited by 686 · see citing works
“However, there are still many problems that cannot be solved using these powerful classical methods, so it is hoped that quantum computers can extend their reach [18,19,32].”
BackgroundPractical quantum advantage in quantum simulation
Daley, A. J., Bloch, I., Kokail, C., Flannigan, S., Pearson, N., Troyer, M., & Zoller, P. (2022) · Nature · doi:10.1038/s41586-022-04940-6 · Cited by 690 · see citing works
“Many of the algorithms used on a classical computer can be modified for use on a fault-tolerant digital quantum computer, and vice versa 16 .”
BackgroundMethodTopological quantum computation
Freedman, M. H., Kitaev, A., Larsen, M., & Wang, Z. (2002) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-02-00964-3 · Cited by 686 · see citing works
“In this context, there are three areas where remarkable algorithms have been found: searching a data base [15], abelian groups (factoring and discrete logarithm) [19], [27], and simulating physical systems [5], [ 21 ].”
The quantum technologies roadmap: a European community view
Acín, A., Bloch, I., Buhrman, H., Calarco, T., Eichler, C., Eisert, J., Esteve, D., Gisin, N., Glaser, S. J., Jelezko, F., et al. (2018) · New Journal of Physics · doi:10.1088/1367-2630/aad1ea · Cited by 648 · see citing works
Quantum optimization using variational algorithms on near-term quantum devices
Moll, N., Barkoutsos, P., Bishop, L. S., Chow, J. M., Cross, A., Egger, D. J., Filipp, S., Fuhrer, A., Gambetta, J. M., Ganzhorn, M., et al. (2018) · Quantum Science and Technology · doi:10.1088/2058-9565/aab822 · Cited by 744 · see citing works
Hamiltonian Simulation by Qubitization
Low, G. H., & Chuang, I. L. (2019) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 714 · see citing works
Contextuality supplies the ‘magic’ for quantum computation
Howard, M., Wallman, J. J., Veitch, V., & Emerson, J. (2014) · Nature · doi:10.1038/nature13460 · Cited by 606 · see citing works
“Quantum information enables dramatic new advantages for computation, such as Shor’s factoring algorithm [1] and quantum simulation algorithms [2].”
Universal Digital Quantum Simulation with Trapped Ions
Lanyon, B. P., Hempel, C., Nigg, D., Müller, M., Gerritsma, R., Zähringer, F., Schindler, P., Barreiro, J. T., Rambach, M., Kirchmair, G., et al. (2011) · Science · doi:10.1126/science.1208001 · Cited by 613 · see citing works
Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator
Hempel, C., Maier, C., Romero, J., McClean, J., Monz, T., Shen, H., Jurcevic, P., Lanyon, B. P., Love, P., Babbush, R., et al. (2018) · Physical Review X · doi:10.1103/physrevx.8.031022 · Cited by 597 · see citing works
“This can be done in a freely programmable way [7] that is amenable to quantum error correction [22, 23].”
BackgroundInfluentialDefining and detecting quantum speedup
Rønnow, T. F., Wang, Z., Job, J., Boixo, S., Isakov, S. V., Wecker, D., Martinis, J. M., Lidar, D. A., & Troyer, M. (2014) · Science · doi:10.1126/science.1252319 · Cited by 601 · see citing works
Simulating a quantum magnet with trapped ions
Friedenauer, A., Schmitz, H., Glueckert, J. T., Porras, D., & Schaetz, T. (2008) · Nature Physics · doi:10.1038/nphys1032 · Cited by 602 · see citing works
“Decoherence in the simulator might even mimic the influence of the natural environmen”
BackgroundSelf-verifying variational quantum simulation of lattice models
Kokail, C., Maier, C., van Bijnen, R., Brydges, T., Joshi, M. K., Jurcevic, P., Muschik, C. A., Silvi, P., Blatt, R., Roos, C. F., et al. (2019) · Nature · doi:10.1038/s41586-019-1177-4 · Cited by 594 · see citing works
A Modular Functor Which is Universal¶for Quantum Computation
Freedman, M. H., Larsen, M., & Wang, Z. (2002) · Communications in Mathematical Physics · doi:10.1007/s002200200645 · Cited by 573 · see citing works
Experimental Quantum Error Correction
Cory, D. G., Price, M. D., Maas, W., Knill, E., Laflamme, R., Zurek, W. H., Havel, T. F., & Somaroo, S. S. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.2152 · Cited by 581 · see citing works
Topological Quantum Computation
Wang, Z. (2010) · Regional conference series in mathematics · doi:10.1090/cbms/112 · Cited by 595 · see citing works
Computational Capacity of the Universe
Lloyd, S. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.237901 · Cited by 571 · see citing works
Self-citationThe cold atom Hubbard toolboxPreprint
Jaksch, D., & Zoller, P. (2004) · Cited by 568 · see citing works
Hybrid Quantum-Classical Algorithms and Quantum Error Mitigation
Endo, S., Cai, Z., Benjamin, S. C., & Yuan, X. (2021) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.90.032001 · Cited by 566 · see citing works
Toward the first quantum simulation with quantum speedup
Childs, A. M., Maslov, D., Nam, Y., Ross, N. J., & Su, Y. (2018) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1801723115 · Cited by 551 · see citing works
“Efficient quantum algorithms for simulating quantum dynamics have been known for over two decades (12).”
BackgroundThe Bravyi-Kitaev transformation for quantum computation of electronic structure
Seeley, J. T., Richard, M. J., & Love, P. J. (2012) · The Journal of Chemical Physics · doi:10.1063/1.4768229 · Cited by 585 · see citing works
Quantum computing with neutral atoms
Henriet, L., Beguin, L., Signoles, A., Lahaye, T., Browaeys, A., Reymond, G.-O., & Jurczak, C. (2020) · Quantum · doi:10.22331/q-2020-09-21-327 · Cited by 550 · see citing works
“For those models, the solution consists in using quantum circuits made of gates [53].”
MethodExperimental Ten-Photon Entanglement
Wang, X., Chen, L.-K., Li, W.-Y., Huang, H.-L., Liu, C., Chen, C., Luo, Y.-H., Su, Z.-E., Wu, D., Li, Z.-D., et al. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.210502 · Cited by 548 · see citing works
“[6] Type-II PPKTP, 20mm Pulsed, 160fs 521: 775+1590 ~ 334 ~44% (775 nm) ~7% (1590 nm) 91%”
Ising machines as hardware solvers of combinatorial optimization problems
Mohseni, N., McMahon, P. L., & Byrnes, T. (2022) · Nature Reviews Physics · doi:10.1038/s42254-022-00440-8 · Cited by 558 · see citing works
“Quantum simulation was in fact one of the early motivations for realizing a quantum computer, based on Feynman’s conjecture that a quantum computer should be able to simulate quantum systems more efficiently than classical computers 14 — proven true later by Lloyd 17 .”
BackgroundTheory of Trotter Error with Commutator Scaling
Childs, A. M., Su, Y., Tran, M. C., Wiebe, N., & Zhu, S. (2021) · Physical Review X · doi:10.1103/physrevx.11.011020 · Cited by 545 · see citing works
Quantum Computation by Adiabatic Evolution
Farhi, E., Goldstone, J., Gutmann, S., & Sipser, M. (2000) · arXiv · doi:10.48550/arxiv.quant-ph/0001106 · Cited by 536 · see citing works
“In any case, our algorithm can be recast within the conventional quantum computing paradigm using the technique introduced by Lloyd [5].”
MethodHigh-fidelity readout and control of a nuclear spin qubit in silicon
Pla, J. J., Tan, K. Y., Dehollain, J. P., Lim, W. H., Morton, J. J. L., Zwanenburg, F. A., Jamieson, D. N., Dzurak, A. S., & Morello, A. (2013) · Nature · doi:10.1038/nature12011 · Cited by 527 · see citing works
“30(1) MHz is close to, but not identical with, the bulk value of 117.”
Background(2016) · doi:10.1103/physrevlett.117.060505 · Cited by 540 · see citing works
Quantum Algorithms for Quantum Field Theories
Jordan, S. P., Lee, K. S. M., & Preskill, J. P. (2012) · Science · doi:10.1126/science.1217069 · Cited by 511 · see citing works
The physical nature of information
Landauer, R. W. (1996) · Physics Letters A · doi:10.1016/0375-9601(96)00453-7 · Cited by 514 · see citing works
A scalable quantum computer with ions in an array of microtraps
Cirac, J. I., & Zoller, P. (2000) · Nature · doi:10.1038/35007021 · Cited by 506 · see citing works
“Finally, we would like to stress that apart from using it for quantum computations, our scheme can emulate Ising (and similar) model”
MethodDeterministic Preparation of a Tunable Few-Fermion System
Serwane, F., Zürn, G., Lompe, T., Ottenstein, T. B., Wenz, A. N., & Jochim, S. (2011) · Science · doi:10.1126/science.1201351 · Cited by 509 · see citing works
Noise tailoring for scalable quantum computation via randomized compiling
Wallman, J. J., & Emerson, J. (2016) · Physical Review A · doi:10.1103/physreva.94.052325 · Cited by 535 · see citing works
“The rich complexity of quantum states and processes enables powerful new protocols for processing and communicating quantum information, as illustrated by Shor’s factoring algorithm [1] and quantum simulation algorithms [2].”
Nobel Lecture: Superposition, entanglement, and raising Schrödinger’s cat
Wineland, D. J. (2013) · Reviews of Modern Physics · doi:10.1103/revmodphys.85.1103 · Cited by 493 · see citing works
- 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 › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- quantum simulation, quantum computing hardware, quantum computing
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