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The Fröhlich Hamiltonian models the interaction of electrons with phonons.
“The Fr¨ ohlich Hamiltonian [26] models the interaction of electrons with phonons,”
From Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions (2012) · cites this paper as [26]
Problems in chemistry and molecular biology require mapping electron representation onto qubit structure, often using Jordan-Wigner or Bravyi-Kitaev transforms.
“Common to problems from both chemistry and molecular biology is the necessity of mapping the representation of electrons onto the qubit structure.This mapping is often done with the Jordan-Wigner [121] or the Bravyi-Kitaev transform, [122,123]”
From Quantum Computing for Molecular Biology** (2023) · cites this paper as [121]
In the Jordan-Wigner mapping, the number of gates needed to realize the basic creation and annihilation operators increases linearly with the number of electrons, whereas the Bravyi-Kitaev encoding leads to logarithmic scaling.
“In the case of the Jordan–Wigner mapping this means that the number of gates needed to realize the basic creation and annihilation operators increases linearly with the number of electrons in the system. Other encodings, such as the one devised by Bravyi–Kitaev [98], lead instead to a more convenient logarithmic scaling.”
From Quantum computing algorithms: getting closer to critical problems in computational biology (2022) · cites this paper as [97]
Cites
Born, M., Heisenberg, W. K., & Jordan, P. (1926) · The European Physical Journal A · doi:10.1007/bf01379806 · Cited by 1,017 · see citing works
Self-citationZum Mehrk�rperproblem der Quantentheorie
Jordan, P., & Klein, O. (1927) · The European Physical Journal A · doi:10.1007/bf01329553 · Cited by 187 · see citing works
Self-citationZur Quantenmechanik der Gasentartung
Jordan, P. (1927) · The European Physical Journal A · doi:10.1007/bf01397395 · Cited by 109 · see citing works
Self-citation�ber eine neue Begr�ndung der Quantenmechanik. II.
Jordan, P. (1927) · The European Physical Journal A · doi:10.1007/bf01391714 · Cited by 72 · see citing works
Self-citation�ber Wellen und Korpuskeln in der Quantenmechanik
Jordan, P. (1927) · The European Physical Journal A · doi:10.1007/bf01329554 · Cited by 46 · see citing works
Self-citationÜber die thermodynamische Gleichgewichts-konzentration der kosmischen Materie
Jordan, P. (1927) · Zeitschrift für Physik A Hadrons and Nuclei · doi:10.1007/bf01454791 · Cited by 11 · see citing works
Self-citationThermodynamische Gleichgewichte und Wechselwirkungen in der neuen Gastheorie
Bothe, W. (1928) · The European Physical Journal A · doi:10.1007/bf01390557 · Cited by 6 · see citing works
Flagged first, then by citations
Cited by
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A variational eigenvalue solver on a photonic quantum processor
Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.-H., Zhou, X.-Q., Love, P. J., Aspuru-Guzik, A., & O’Brien, J. L. (2014) · Nature Communications · doi:10.1038/ncomms5213 · Cited by 4,552 · see citing works
Two soluble models of an antiferromagnetic chain
Lieb, É. H., Schultz, T. D., & Mattis, D. C. (1961) · Annals of Physics · doi:10.1016/0003-4916(61)90115-4 · Cited by 4,292 · see citing works
Introduction to Quantum Field Theory
Milonni, P. W. (1994) · Elsevier eBooks · doi:10.1016/b978-0-08-057149-2.50014-x · Cited by 4,037 · see citing works
Die gegenw�rtige Situation in der Quantenmechanik
Schr�dinger, E. (1935) · Die Naturwissenschaften · doi:10.1007/bf01491891 · Cited by 3,392 · see citing works
New Approach to the Theory of Superexchange Interactions
Anderson, P. W. (1959) · Physical Review · doi:10.1103/physrev.115.2 · Cited by 2,637 · see citing works
From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics
D’Alessio, L., Kafri, Y., Polkovnikov, A., & Rigol, M. (2016) · Advances In Physics · doi:10.1080/00018732.2016.1198134 · Cited by 2,420 · see citing works
The theory of variational hybrid quantum-classical algorithms
McClean, J. R., Romero, J., Babbush, R., & Aspuru-Guzik, A. (2016) · New Journal of Physics · doi:10.1088/1367-2630/18/2/023023 · Cited by 2,227 · 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
An introduction to lattice gauge theory and spin systems
Kogut, J. B. (1979) · Reviews of Modern Physics · doi:10.1103/revmodphys.51.659 · Cited by 2,029 · see citing works
Colloquium : Many-body localization, thermalization, and entanglement
Abanin, D. A., Altman, E., Bloch, I., & Serbyn, M. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.021001 · Cited by 1,803 · see citing works
“(5), using a Jordan-Wigner transformation (Jordan and Wigner, 1928).”
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
Teoria simmetrica dell’elettrone e del positrone
Majorana, E. (1937) · Il Nuovo Cimento · doi:10.1007/bf02961314 · Cited by 1,729 · 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
Albash, T., & Lidar, D. A. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.015002 · Cited by 1,546 · see citing works
Entanglement in a simple quantum phase transition
Osborne, T. J., & Nielsen, M. A. (2002) · Physical Review A · doi:10.1103/physreva.66.032110 · Cited by 1,472 · see citing works
Effective Harmonic-Fluid Approach to Low-Energy Properties of One-Dimensional Quantum Fluids
Haldane, F. D. M. (1981) · Physical Review Letters · doi:10.1103/physrevlett.47.1840 · Cited by 1,214 · see citing works
The Physical Principles of the Quantum Theory
Compton, A. H., & Heisenberg, W. K. (1984) · Springer eBooks · doi:10.1007/978-3-642-61742-3_10 · Cited by 1,161 · see citing works
One dimensional bosons: From condensed matter systems to ultracold gases
Cazalilla, M. A., Citro, R., Giamarchi, T., Orignac, E., & Rigol, M. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.1405 · Cited by 1,099 · see citing works
“Following Jordan and Wigner (1928), we introduce the transformation by relating fermions to spins (Jordan and Wigner, 1928; Katsura, 1962; Lieb et al., 1961; Niemeijer, 1967): σ̂+j = ĉ † j e −iπ∑m<j ĉ † mĉm , σ̂−j = e iπ ∑ m<j ĉ † mĉm ĉj , σ̂zj = ĉ † j ĉj − 1/2, (21) where {ĉi, ĉ†j} = δij…”
The 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 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
“way to do this was invented a long time ago in the form of the Jordan-Wigner (JW) transformation [401].”
BackgroundTwo-Dimensional Ising Model as a Soluble Problem of Many Fermions
Schultz, T. D., Mattis, D. C., & Lieb, É. H. (1964) · Reviews of Modern Physics · doi:10.1103/revmodphys.36.856 · Cited by 936 · see citing works
Programmable 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
Quantum entanglement in condensed matter systems
Laflorencie, N. (2016) · Physics Reports · doi:10.1016/j.physrep.2016.06.008 · Cited by 790 · see citing works
Crystal Statistics. II. Partition Function Evaluated by Spinor Analysis
Kaufman, B. (1949) · Physical Review · doi:10.1103/physrev.76.1232 · Cited by 778 · see citing works
Haldane, F. D. M. (1980) · Physical Review Letters · doi:10.1103/physrevlett.45.1358 · Cited by 760 · see citing works
Generalized Gibbs ensemble in integrable lattice models
Vidmar, L., & Rigol, M. (2016) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2016/06/064007 · Cited by 739 · see citing works
“It can be straightforwardly solved using the Jordan-Wigner transformation [15, 77], which maps spin-1/2 operators (and therefore hard-core bosons) onto spinless fermions:”
MethodDynamics of a quantum phase transition and relaxation to a steady state
Dziarmaga, J. (2010) · Advances In Physics · doi:10.1080/00018732.2010.514702 · Cited by 712 · see citing works
Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz
Romero, J., Babbush, R., McClean, J. R., Hempel, C., Love, P. J., & Aspuru-Guzik, A. (2019) · Quantum Science and Technology · doi:10.1088/2058-9565/aad3e4 · Cited by 726 · see citing works
Dynamics of a Quantum Phase Transition: Exact Solution of the Quantum Ising Model
Dziarmaga, J. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.245701 · Cited by 673 · 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
“Among those, the JordanWigner mapping [79] is particularly intuitive: It is based on a one-to-one mapping of fermionic to qubit occupations, i.”
BackgroundMethodClassical and quantum mechanics of the damped harmonic oscillator
Dekker, H. (1981) · Physics Reports · doi:10.1016/0370-1573(81)90033-8 · Cited by 641 · see citing works
Duality in field theory and statistical systems
Savit, R. S. (1980) · Reviews of Modern Physics · doi:10.1103/revmodphys.52.453 · Cited by 619 · see citing works
Hilbert spaces of analytic functions and generalized coherent states
Arık, M., & Coon, D. D. (1976) · Journal of Mathematical Physics · doi:10.1063/1.522937 · Cited by 614 · 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
“The most common schemes for this transformation are the Jordan-Wigner transformation [73, 74] and the BravyiKitaev transformation [68, 74–79].”
MethodFIDELITY APPROACH TO QUANTUM PHASE TRANSITIONS
GU, S.-J. (2010) · International Journal of Modern Physics B · doi:10.1142/s0217979210056335 · Cited by 663 · see citing works
Entanglement in the quantum Heisenberg XY model
Wang, X. (2001) · Physical Review A · doi:10.1103/physreva.64.012313 · Cited by 576 · see citing works
The 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
“erest, like electronic systems. There indeed exist explicit mappings between spin models, that can be implemented natively with Pasqal devices, and electronic Hamiltonians, known as the Jordan-Wigner [61,62] and the Bravyi-Kitaev [63] transformations (see Box 4 for details about the Jordan-Wigner transform). Future in…”
BackgroundMethodOn Bound States and Scattering in Positron Theory
Furry, W. H. (1951) · Physical Review · doi:10.1103/physrev.81.115 · Cited by 549 · see citing works
Phase diagrams and correlation exponents for quantum spin chains of arbitrary spin quantum number
Schulz, H. J. (1986) · Physical review. B, Condensed matter · doi:10.1103/physrevb.34.6372 · Cited by 537 · see citing works
Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states
McClean, J. R., Kimchi-Schwartz, M. E., Carter, J., & de Jong, W. A. (2017) · Physical Review A · doi:10.1103/physreva.95.042308 · Cited by 516 · see citing works
Haldane, F. D. M. (1982) · Physical review. B, Condensed matter · doi:10.1103/physrevb.25.4925 · Cited by 523 · see citing works
The action option and a Feynman quantization of spinor fields in terms of ordinary c-numbers
Klauder, J. R. (1960) · Annals of Physics · doi:10.1016/0003-4916(60)90131-7 · Cited by 508 · see citing works
OpenFermion: the electronic structure package for quantum computers
McClean, J. R., Rubin, N. C., Sung, K. J., Kivlichan, I., Bonet-Monroig, X., Cao, Y., Dai, C., Fried, E., Gidney, C., Gimby, B., et al. (2020) · Quantum Science and Technology · doi:10.1088/2058-9565/ab8ebc · Cited by 525 · see citing works
Simulation of electronic structure Hamiltonians using quantum computers
Whitfield, J. D., Biamonte, J., & Aspuru-Guzik, A. (2011) · Molecular Physics · doi:10.1080/00268976.2011.552441 · Cited by 472 · see citing works
Exactly Solvable Models for Many-Body Systems Far from Equilibrium
Schutz, G. M. (2001) · Phase transitions and critical phenomena · doi:10.1016/s1062-7901(01)80015-x · Cited by 475 · see citing works
Nobel Lecture: Topological quantum matter
Haldane, F. D. M. (2017) · Reviews of Modern Physics · doi:10.1103/revmodphys.89.040502 · Cited by 439 · see citing works
Quantum-classical computation of Schwinger model dynamics using quantum computers
Klco, N., Dumitrescu, E., McCaskey, A., Morris, T., Pooser, R. C., Sanz, M., Solano, E., Lougovski, P., & A, M. J. S. (2018) · Physical Review A · doi:10.1103/physreva.98.032331 · Cited by 428 · see citing works
Die allgemeinen Prinzipien der Wellenmechanik
Pauli, W. E. F. (1933) · Springer eBooks · doi:10.1007/978-3-642-52619-0_2 · Cited by 438 · see citing works
Quantum chaos and thermalization in isolated systems of interacting particles
Borgonovi, F., Izrailev, F. M., Santos, L. F., & Zelevinsky, V. G. (2016) · Physics Reports · doi:10.1016/j.physrep.2016.02.005 · Cited by 429 · see citing works
“It is integrable and can be mapped onto a system of noninterac ting spinless fermions [44] or hardcore bosons [45].”
BackgroundEntropic uncertainty relations—a survey
Wehner, S., & Winter, A. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/2/025009 · Cited by 396 · see citing works
“This representation can be obtained via the famous Jordan-Wigner transformation (Jordan and Wigner, 1928): for j = 1 , . . . , n , where we use X , Y and Z to denote the Pauli matrices.”
MethodQuantum Theory of Angular Momentum
Mattis, D. C. (1981) · Springer series in solid-state sciences · doi:10.1007/978-3-642-83238-3_3 · Cited by 399 · see citing works
Bose-Einstein condensation in quantum magnets
Zapf, V. S., Jaime, M., & Batista, C. D. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.563 · Cited by 382 · see citing works
Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
Babbush, R., Gidney, C., Berry, D. W., Wiebe, N., McClean, J., Paler, A., Fowler, A., & Neven, H. (2018) · Physical Review X · doi:10.1103/physrevx.8.041015 · Cited by 383 · see citing works
“Mapping to qubits under the Jordan-Wigner transformation [61,76], Eq.”
MethodConnection between Spin, Statistics, and Kinks
Finkelstein, D., & Rubinstein, J. (1968) · Journal of Mathematical Physics · doi:10.1063/1.1664510 · Cited by 377 · see citing works
Spin- and density-resolved microscopy of antiferromagnetic correlations in Fermi-Hubbard chains
Boll, M., Hilker, T. A., Salomon, G., Omran, A., Nespolo, J., Pollet, L., Bloch, I., & Gross, C. (2016) · Science · doi:10.1126/science.aag1635 · Cited by 414 · see citing works
Garrahan, J. P., Jack, R. L., Lecomte, V., Pitard, E., van Duijvendijk, K., & van Wijland, F. (2009) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/42/7/075007 · Cited by 370 · see citing works
dos Santos, L. F., & Rigol, M. (2010) · Physical Review E · doi:10.1103/physreve.81.036206 · Cited by 361 · see citing works
Barkoutsos, P. K., Gonthier, J. F., Sokolov, I., Moll, N., Salis, G., Fuhrer, A., Ganzhorn, M., Egger, D. J., Troyer, M., Mezzacapo, A., et al. (2018) · Physical Review A · doi:10.1103/physreva.98.022322 · Cited by 363 · see citing works
The Uncertainty Principle Determines the Nonlocality of Quantum Mechanics
Oppenheim, J., & Wehner, S. (2010) · Science · doi:10.1126/science.1192065 · Cited by 360 · see citing works
“[19] P.”
MethodSimulating physical phenomena by quantum networks
Somma, R. D., Ortíz, G., Gubernatis, J. E., Knill, E. H., & Laflamme, R. (2002) · Physical Review A · doi:10.1103/physreva.65.042323 · Cited by 364 · see citing works
Polarization Propagator Calculations
Oddershede, J. (1978) · Advances in quantum chemistry · doi:10.1016/s0065-3276(08)60240-3 · Cited by 357 · see citing works
Introduction to the Unified Field Theory of Elementary Particles
Heisenberg, W. K. (1984) · Springer eBooks · doi:10.1007/978-3-642-61742-3_62 · Cited by 357 · see citing works
Graded Lie algebras in mathematics and physics (Bose-Fermi symmetry)
Corwin, L. J., Ne’eman, Y., & Sternberg, S. (1975) · Reviews of Modern Physics · doi:10.1103/revmodphys.47.573 · Cited by 357 · see citing works
Quantum algorithms for fermionic simulations
Ortiz, G., Gubernatis, J. E., Knill, E., & Laflamme, R. (2001) · Physical Review A · doi:10.1103/physreva.64.022319 · Cited by 347 · see citing works
Coupled ladders in a magnetic field
Giamarchi, T., & Tsvelik, A. M. (1999) · Physical review. B, Condensed matter · doi:10.1103/physrevb.59.11398 · Cited by 354 · see citing works
Generalized Thermalization in an Integrable Lattice System
Cassidy, A., Clark, C. W., & Rigol, M. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.140405 · Cited by 352 · see citing works
Ground-state energy estimation of the water molecule on a trapped-ion quantum computer
Nam, Y., Chen, J.-S., Pisenti, N. C., Wright, K., Delaney, C. P., Maslov, D., Brown, K. R., Allen, S., Amini, J., Apisdorf, J., et al. (2020) · npj Quantum Information · doi:10.1038/s41534-020-0259-3 · Cited by 346 · see citing works
“The c p and c y p operators can be represented as Pauli operators acting on individual qubits using the JW transformation 40 , and we use the UCC method to generate an ansatz state 41 – 43 with the fi rst-order Trotter formula and one Trotter step.”
MethodDigital quantum simulation of fermionic models with a superconducting circuit
Barends, R., Lamata, L., Kelly, J., García-Álvarez, L., Fowler, A. G., Megrant, A., Jeffrey, E. R., White, T., Sank, D., Mutus, J., et al. (2015) · Nature Communications · doi:10.1038/ncomms8654 · Cited by 329 · see citing works
Quantum Theory of Dispersion (Continued). Parts VI and VII
BREIT, G. A. (1933) · Reviews of Modern Physics · doi:10.1103/revmodphys.5.91 · Cited by 336 · see citing works
Quantum Simulation for High-Energy Physics
Bauer, C., Davoudi, Z., Balantekin, A. B., Tanmoy Bhattacharya, A., Carena, M. S., de Jong, W. A., Draper, P., El-Khadra, A. X., Gemelke, N., Hanada, M., et al. (2023) · PRX Quantum · doi:10.1103/prxquantum.4.027001 · Cited by 356 · see citing works
Classical simulation of noninteracting-fermion quantum circuits
Terhal, B. M., & DiVincenzo, D. P. (2002) · Physical Review A · doi:10.1103/physreva.65.032325 · Cited by 329 · see citing works
PERFECT, EFFICIENT, STATE TRANSFER AND ITS APPLICATION AS A CONSTRUCTIVE TOOL
Kay, A. (2010) · International Journal of Quantum Information · doi:10.1142/s0219749910006514 · Cited by 318 · see citing works
The ergodic side of the many‐body localization transition
Luitz, D. J., & Lev, Y. B. (2017) · Annalen der Physik · doi:10.1002/andp.201600350 · Cited by 315 · see citing works
Hase, M., Terasaki, I., Sasago, Y., Uchinokura, K., & Obara, H. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.4059 · Cited by 314 · see citing works
Temme, K., Osborne, T. J., Vollbrecht, K. G., Poulin, D., & Verstraete, F. (2011) · Nature · doi:10.1038/nature09770 · Cited by 305 · see citing works
Gate-count estimates for performing quantum chemistry on small quantum computers
Wecker, D., Bauer, B., Clark, B. K., Hastings, M. B., & Troyer, M. (2014) · Physical Review A · doi:10.1103/physreva.90.022305 · Cited by 296 · see citing works
On the History of Unified Field Theories
Goenner, H. (2004) · Living Reviews in Relativity · doi:10.12942/lrr-2004-2 · Cited by 299 · see citing works
“In spite of this, the construction of quantum field theory had begun already around 1927 [52, 173, 177, 174, 178].”
BackgroundQulacs: a fast and versatile quantum circuit simulator for research purpose
Suzuki, Y., Kawase, Y., Masumura, Y., Hiraga, Y., Nakadai, M., Chen, J., Nakanishi, K. M., Mitarai, K., Imai, R., Tamiya, S., et al. (2021) · Quantum · doi:10.22331/q-2021-10-06-559 · Cited by 303 · see citing works
Strong-coupling calculations of lattice gauge theories: (1 + 1)-dimensional exercises
Banks, T., Susskind, L., & Kogut, J. B. (1976) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.13.1043 · Cited by 296 · see citing works
Jordan-Wigner transformation for quantum-spin systems in two dimensions and fractional statistics
Fradkin, E. (1989) · Physical Review Letters · doi:10.1103/physrevlett.63.322 · Cited by 294 · see citing works
Qubit Coupled Cluster Method: A Systematic Approach to Quantum Chemistry on a Quantum Computer
Ryabinkin, I. G., Yen, T.-C., Genin, S. N., & Izmaylov, A. F. (2018) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.8b00932 · Cited by 287 · see citing works
The density matrix renormalization group for ab initio quantum chemistry
Wouters, S., & Neck, D. V. (2014) · The European Physical Journal D · doi:10.1140/epjd/e2014-50500-1 · Cited by 281 · see citing works
“For an odd number, there should be an additional phase (−1)n(i−1)↑+n(i−1)↓ at the right-hand side (RHS) due to the Jordan-Wigner transformation [138].”
MethodQuantum Computation of Electronic Transitions Using a Variational Quantum Eigensolver
Parrish, R. M., Hohenstein, E. G., McMahon, P. L., & Martínez, T. J. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.230401 · Cited by 282 · see citing works
Atomtronics: Ultracold-atom analogs of electronic devices
Seaman, B. T., Krämer, M., Anderson, D. Z., & Holland, M. (2007) · Physical Review A · doi:10.1103/physreva.75.023615 · Cited by 273 · see citing works
Exploring Localization in Nuclear Spin Chains
Wei, K. X., Ramanathan, C., & Cappellaro, P. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.070501 · Cited by 271 · see citing works
Spin transport in a tunable Heisenberg model realized with ultracold atoms
Jepsen, N., Amato-Grill, J., Dimitrova, I., Ho, W. W., Demler, E., & Ketterle, W. (2020) · Nature · doi:10.1038/s41586-020-3033-y · Cited by 266 · see citing works
Gard, B. T., Zhu, L., Barron, G. S., Mayhall, N. J., Economou, S. E., & Barnes, E. (2020) · npj Quantum Information · doi:10.1038/s41534-019-0240-1 · Cited by 266 · see citing works
“In this work, we focus on mapping chemistry problems onto quantum processors using the Jordan-Wigner mapping, 3,29 in which each qubit in the quantum processor corresponds to a particular spin-orbital, and the qubit states 0 j i and 1 j i encode the occupation of that spin-orbital.”
MethodMeasurement optimization in the variational quantum eigensolver using a minimum clique cover
Verteletskyi, V., Yen, T.-C., & Izmaylov, A. F. (2020) · The Journal of Chemical Physics · doi:10.1063/1.5141458 · Cited by 269 · see citing works
Low-Depth Quantum Simulation of Materials
Babbush, R., Wiebe, N., McClean, J., McClain, J., Neven, H., & Chan, G. K.-L. (2018) · Physical Review X · doi:10.1103/physrevx.8.011044 · Cited by 335 · see citing works
“The oldest (and simplest) mapping to qubit operators which reproduces these commutation relations is the JordanWigner transformation [45].”
BackgroundMethodProbing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasiperiodic Systems
Bordia, P., Lüschen, H. P., Scherg, S., Gopalakrishnan, S., Knap, M., Schneider, U., & Bloch, I. (2017) · Max Planck Digital Library · doi:10.17863/cam.27153 · Cited by 254 · see citing works
Scalable architecture for a room temperature solid-state quantum information processor
Yao, N. Y., Jiang, L., Gorshkov, A. V., Maurer, P. C., Giedke, G., Cirac, J. I., & Lukin, M. D. (2012) · Nature Communications · doi:10.1038/ncomms1788 · Cited by 242 · see citing works
Fermionic neural-network states for ab-initio electronic structure
Choo, K., Mezzacapo, A., & Carleo, G. (2020) · Nature Communications · doi:10.1038/s41467-020-15724-9 · Cited by 252 · see citing works
Rigol, M., Muramatsu, A., & Olshanii, M. (2006) · Physical Review A · doi:10.1103/physreva.74.053616 · Cited by 247 · see citing works
Quantum quenches and thermalization in one-dimensional fermionic systems
Rigol, M. (2009) · Physical Review A · doi:10.1103/physreva.80.053607 · Cited by 245 · see citing works
Conceptual Developments of 20th Century Field Theories
Cao, T. Y. (1997) · Cambridge University Press eBooks · doi:10.1017/cbo9780511563997 · Cited by 245 · see citing works
Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasiperiodic Systems
Bordia, P., Lüschen, H., Scherg, S., Gopalakrishnan, S., Knap, M., Schneider, U., & Bloch, I. (2017) · Physical Review X · doi:10.1103/physrevx.7.041047 · Cited by 243 · see citing works
“In one dimension, the hard core limit of infinitely strong interactions in the absence of doublons can be mapped back onto a non-interacting model [10, 40].”
BackgroundEntropic uncertainty relations – A surveyPreprint
Wehner, S., & Winter, A. (2009) · Cited by 239 · see citing works
- Authors
- Jordan, P., & Wigner, E.
- Affiliations
- University of Göttingen (DE)
- ORCID
- Jordan, P.
- Venue
- Zeitschrift f�r Physik
- Published
- 1928-09
- Volume
- 47
- Issue
- 9-10
- Pages
- 631-651
- ISSN
- 1434-6001 (ISSN-L)
- 1434-601X
- OpenAlex
- W1663839511
- Cited by
- 2,597
- References
- 7
- Citations by year
- 2026: 148 · 2025: 267 · 2024: 206 · 2023: 158 · 2022: 156 · 2021: 172 · 2020: 132 · 2019: 111 · 2018: 81 · 2017: 86 · 2016: 63 · 2015: 63 · 2014: 58 · 2013: 45 · 2012: 42
- FWCI
- 2.67
- Type
- journal article
- Language
- de
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- The European Physical Journal A (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Keywords
- Pauli exclusion principle, noncommutative multiplication, wave amplitude, ideal gas, non-ideal gas
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