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“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]
In the citing paper
“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 citing paper
“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]
Citations
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Self-citationZur Quantenmechanik der Gasentartung
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Self-citation�ber eine neue Begr�ndung der Quantenmechanik. II.
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Self-citation�ber Wellen und Korpuskeln in der Quantenmechanik
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Self-citationÜber die thermodynamische Gleichgewichts-konzentration der kosmischen Materie
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Self-citationThermodynamische Gleichgewichte und Wechselwirkungen in der neuen Gastheorie
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Two soluble models of an antiferromagnetic chain
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Die gegenw�rtige Situation in der Quantenmechanik
Schr�dinger, E. (1935) · Die Naturwissenschaften · doi:10.1007/bf01491891 · Cited by 3,392
New Approach to the Theory of Superexchange Interactions
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“(5), using a Jordan-Wigner transformation (Jordan and Wigner, 1928).”
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One dimensional bosons: From condensed matter systems to ultracold gases
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“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
Quantum information processing with superconducting circuits: a review
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“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
Programmable quantum simulations of spin systems with trapped ions
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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
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Quantum entanglement in condensed matter systems
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Crystal Statistics. II. Partition Function Evaluated by Spinor Analysis
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Quantum optimization using variational algorithms on near-term quantum devices
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“Among those, the JordanWigner mapping [79] is particularly intuitive: It is based on a one-to-one mapping of fermionic to qubit occupations, i.”
BackgroundMethodGeneralized 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 758
“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
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Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz
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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
Classical and quantum mechanics of the damped harmonic oscillator
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Duality in field theory and statistical systems
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Hilbert spaces of analytic functions and generalized coherent states
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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 629
“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
Entanglement in the quantum Heisenberg XY model
Wang, X. (2001) · Physical Review A · doi:10.1103/physreva.64.012313 · Cited by 572
The Bravyi-Kitaev transformation for quantum computation of electronic structure
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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
“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
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Phase diagrams and correlation exponents for quantum spin chains of arbitrary spin quantum number
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Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states
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The action option and a Feynman quantization of spinor fields in terms of ordinary c-numbers
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OpenFermion: the electronic structure package for quantum computers
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Simulation of electronic structure Hamiltonians using quantum computers
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Exactly Solvable Models for Many-Body Systems Far from Equilibrium
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Nobel Lecture: Topological quantum matter
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Quantum chaos and thermalization in isolated systems of interacting particles
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BackgroundEntropic uncertainty relations—a survey
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“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
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Bose-Einstein condensation in quantum magnets
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Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
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“Mapping to qubits under the Jordan-Wigner transformation [61,76], Eq.”
MethodConnection between Spin, Statistics, and Kinks
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Spin- and density-resolved microscopy of antiferromagnetic correlations in Fermi-Hubbard chains
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The Uncertainty Principle Determines the Nonlocality of Quantum Mechanics
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MethodSimulating physical phenomena by quantum networks
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Polarization Propagator Calculations
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Introduction to the Unified Field Theory of Elementary Particles
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Graded Lie algebras in mathematics and physics (Bose-Fermi symmetry)
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Quantum algorithms for fermionic simulations
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Coupled ladders in a magnetic field
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Generalized Thermalization in an Integrable Lattice System
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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 381
“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 347
Quantum Theory of Dispersion (Continued). Parts VI and VII
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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
“The oldest (and simplest) mapping to qubit operators which reproduces these commutation relations is the JordanWigner transformation [45].”
BackgroundMethodQuantum 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 503
Classical simulation of noninteracting-fermion quantum circuits
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PERFECT, EFFICIENT, STATE TRANSFER AND ITS APPLICATION AS A CONSTRUCTIVE TOOL
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The ergodic side of the many‐body localization transition
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Gate-count estimates for performing quantum chemistry on small quantum computers
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On the History of Unified Field Theories
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“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 357
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
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
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
The density matrix renormalization group for ab initio quantum chemistry
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“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
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 265
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 281
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 278
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
“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
Probing 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
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 245
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 280
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“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].”
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Metadata
- 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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