DOI: 10.1126/science.1217069. Quantum Algorithms for Quantum Field Theories

Quantum Algorithms for Quantum Field Theories

10.1126/science.1217069

Crossref journal-article

American Association for the Advancement of Science (AAAS)

Science (221)

Abstract

Quantum Leap? Quantum computers are expected to be able to solve some of the most difficult problems in mathematics and physics. It is not known, however, whether quantum field theories (QFTs) can be simulated efficiently with a quantum computer. QFTs are used in particle and condensed matter physics and have an infinite number of degrees of freedom; discretization is necessary to simulate them digitally. Jordan et al. (p. 1130 ; see the Perspective by Hauke et al. ) present an algorithm for the efficient simulation of a particular kind of QFT (with quartic interactions) and estimate the error caused by discretization. Even for the most difficult case of strong interactions, the run time of the algorithm was polynomial (rather than exponential) in parameters such as the number of particles, their energy, and the prescribed precision, making it much more efficient than the best classical algorithms.

Bibliography

Jordan, S. P., Lee, K. S. M., & Preskill, J. (2012). Quantum Algorithms for Quantum Field Theories. Science, 336(6085), 1130â1133.

Authors 3

Stephen P. Jordan (first)
Keith S. M. Lee (additional)
John Preskill (additional)

References 45 Referenced 374

10.1007/BF02650179
10.1126/science.273.5278.1073
10.1103/PhysRevLett.79.2586
10.1098/rspa.1998.0162
10.1126/science.1208001
10.1088/1367-2630/13/8/085007
10.1038/nature09801
10.1103/PhysRevD.10.536
10.1007/BF01608544
10.1007/BF01609341
Osterwalder K., Sénéor R., The scattering matrix is nontrivial for weakly coupled P(ϕ)2 models. Helv. Phys. Acta 49, 525 (1976). / Helv. Phys. Acta / The scattering matrix is nontrivial for weakly coupled P(ϕ)2 models by Osterwalder K. (1976)
J.-P. Eckmann H. Epstein J. Fröhlich Asymptotic perturbation expansion for the S-matrix and the definition of time ordered functions in relativistic quantum field models. Ann. Inst. Henri Poincaré A 25 1 (1976).
10.1016/0003-4916(77)90349-9
10.1103/PhysRevA.73.022328
10.1103/PhysRevLett.95.040402
10.1103/PhysRevLett.107.275301
G. Szirmai E. Szirmai A. Zamora M. Lewenstein Gauge fields emerging from time reversal symmetry breaking for spin-5/2 fermions in a honeycomb lattice. Phys. Rev. A 84 011611(R) (2011). (10.1103/PhysRevA.84.011611)
10.1103/PhysRevLett.105.190403
10.1088/1367-2630/14/1/015007
10.1103/PhysRevA.83.033625
10.1103/PhysRevLett.105.190404
10.1016/j.physleta.2009.05.029
10.1209/0295-5075/92/50003
10.1103/PhysRevLett.103.085301
10.1103/PhysRevLett.98.160405
10.1038/nphys1614
10.1103/PhysRevLett.107.260501
Casanova J. Mezzacapo A. Lamata L. Solano E. http://arxiv.org/abs/1110.3730 (2011).
10.1103/PhysRevB.69.214501
10.1080/00018730701223200
10.1088/0953-4075/42/15/154009
10.1016/0375-9601(90)90962-N
10.1007/s00220-006-0150-x
Kitaev A. Webb W. A. http://arxiv.org/abs/0801.0342 (2008).
10.1090/S0025-5718-1974-0331751-8
10.1016/S0747-7171(08)80013-2
M. E. Peskin D. V. Schroeder An Introduction to Quantum Field Theory (Westview Boulder CO 1995).
Kitaev A. Y. http://arxiv.org/abs/quant-ph/9511026 (1995).
10.1016/0370-2693(94)01419-D
10.1016/0550-3213(91)90244-R
10.1103/PhysRevLett.39.95
10.1016/0550-3213(87)90177-5
A. Messiah Quantum Mechanics (Dover 1999). (Reprint of the two-volume edition published by Wiley 1961–1962.)
10.1063/1.2798382
10.1090/psapm/068/2762145

Dates

Type	When
Created	13 years, 3 months ago (May 31, 2012, 2:20 p.m.)
Deposited	1 year, 7 months ago (Jan. 10, 2024, 8:49 a.m.)
Indexed	1 week ago (Aug. 26, 2025, 2:52 a.m.)
Issued	13 years, 3 months ago (June 1, 2012)
Published	13 years, 3 months ago (June 1, 2012)
Published Print	13 years, 3 months ago (June 1, 2012)

Funders 0

None

BibTeX

@article{Jordan_2012, title={Quantum Algorithms for Quantum Field Theories}, volume={336}, ISSN={1095-9203}, url={http://dx.doi.org/10.1126/science.1217069}, DOI={10.1126/science.1217069}, number={6085}, journal={Science}, publisher={American Association for the Advancement of Science (AAAS)}, author={Jordan, Stephen P. and Lee, Keith S. M. and Preskill, John}, year={2012}, month=jun, pages={1130–1133} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        26
      ]
    ],
    "date-time": "2025-08-26T06:52:01Z",
    "timestamp": 1756191121899
  },
  "reference-count": 45,
  "publisher": "American Association for the Advancement of Science (AAAS)",
  "issue": "6085",
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        2012,
        6
      ]
    ]
  },
  "abstract": "<jats:title>Quantum Leap?</jats:title>\n          <jats:p>\n            Quantum computers are expected to be able to solve some of the most difficult problems in mathematics and physics. It is not known, however, whether quantum field theories (QFTs) can be simulated efficiently with a quantum computer. QFTs are used in particle and condensed matter physics and have an infinite number of degrees of freedom; discretization is necessary to simulate them digitally.\n            <jats:bold>\n              Jordan\n              <jats:italic>et al.</jats:italic>\n            </jats:bold>\n            (p.\n            <jats:related-article xmlns:xlink=\"http://www.w3.org/1999/xlink\" ext-link-type=\"doi\" page=\"1130\" related-article-type=\"in-this-issue\" vol=\"336\" xlink:href=\"10.1126/science.1217069\">1130</jats:related-article>\n            ; see the Perspective by\n            <jats:related-article xmlns:xlink=\"http://www.w3.org/1999/xlink\" ext-link-type=\"doi\" issue=\"6085\" page=\"1122\" related-article-type=\"in-this-issue\" vol=\"336\" xlink:href=\"10.1126/science.1223010\">\n              <jats:bold>\n                Hauke\n                <jats:italic>et al.</jats:italic>\n              </jats:bold>\n            </jats:related-article>\n            ) present an algorithm for the efficient simulation of a particular kind of QFT (with quartic interactions) and estimate the error caused by discretization. Even for the most difficult case of strong interactions, the run time of the algorithm was polynomial (rather than exponential) in parameters such as the number of particles, their energy, and the prescribed precision, making it much more efficient than the best classical algorithms.\n          </jats:p>",
  "DOI": "10.1126/science.1217069",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2012,
        5,
        31
      ]
    ],
    "date-time": "2012-05-31T18:20:39Z",
    "timestamp": 1338488439000
  },
  "page": "1130-1133",
  "source": "Crossref",
  "is-referenced-by-count": 374,
  "title": "Quantum Algorithms for Quantum Field Theories",
  "prefix": "10.1126",
  "volume": "336",
  "author": [
    {
      "given": "Stephen P.",
      "family": "Jordan",
      "sequence": "first",
      "affiliation": []
    },
    {
      "given": "Keith S. M.",
      "family": "Lee",
      "sequence": "additional",
      "affiliation": []
    },
    {
      "given": "John",
      "family": "Preskill",
      "sequence": "additional",
      "affiliation": []
    }
  ],
  "member": "221",
  "reference": [
    {
      "key": "e_1_3_2_2_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1007/BF02650179"
    },
    {
      "key": "e_1_3_2_3_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1126/science.273.5278.1073"
    },
    {
      "key": "e_1_3_2_4_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.79.2586"
    },
    {
      "key": "e_1_3_2_5_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1098/rspa.1998.0162"
    },
    {
      "key": "e_1_3_2_6_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1126/science.1208001"
    },
    {
      "key": "e_1_3_2_7_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1088/1367-2630/13/8/085007"
    },
    {
      "key": "e_1_3_2_8_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1038/nature09801"
    },
    {
      "key": "e_1_3_2_9_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevD.10.536"
    },
    {
      "key": "e_1_3_2_10_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1007/BF01608544"
    },
    {
      "key": "e_1_3_2_11_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1007/BF01609341"
    },
    {
      "key": "e_1_3_2_12_2",
      "first-page": "525",
      "article-title": "The scattering matrix is nontrivial for weakly coupled P(\u03d5)2 models",
      "volume": "49",
      "author": "Osterwalder K.",
      "year": "1976",
      "unstructured": "Osterwalder K., S\u00e9n\u00e9or R., The scattering matrix is nontrivial for weakly coupled P(\u03d5)2 models. Helv. Phys. Acta 49, 525 (1976).",
      "journal-title": "Helv. Phys. Acta"
    },
    {
      "key": "e_1_3_2_13_2",
      "unstructured": "J.-P. Eckmann H. Epstein J. Fr\u00f6hlich Asymptotic perturbation expansion for the S-matrix and the definition of time ordered functions in relativistic quantum field models. Ann. Inst. Henri Poincar\u00e9 A 25 1 (1976)."
    },
    {
      "key": "e_1_3_2_14_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0003-4916(77)90349-9"
    },
    {
      "key": "e_1_3_2_15_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevA.73.022328"
    },
    {
      "key": "e_1_3_2_16_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.95.040402"
    },
    {
      "key": "e_1_3_2_17_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.107.275301"
    },
    {
      "key": "e_1_3_2_18_2",
      "doi-asserted-by": "crossref",
      "unstructured": "G. Szirmai E. Szirmai A. Zamora M. Lewenstein Gauge fields emerging from time reversal symmetry breaking for spin-5/2 fermions in a honeycomb lattice. Phys. Rev. A 84 011611(R) (2011).",
      "DOI": "10.1103/PhysRevA.84.011611"
    },
    {
      "key": "e_1_3_2_19_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.105.190403"
    },
    {
      "key": "e_1_3_2_20_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1088/1367-2630/14/1/015007"
    },
    {
      "key": "e_1_3_2_21_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevA.83.033625"
    },
    {
      "key": "e_1_3_2_22_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.105.190404"
    },
    {
      "key": "e_1_3_2_23_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/j.physleta.2009.05.029"
    },
    {
      "key": "e_1_3_2_24_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1209/0295-5075/92/50003"
    },
    {
      "key": "e_1_3_2_25_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.103.085301"
    },
    {
      "key": "e_1_3_2_26_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.98.160405"
    },
    {
      "key": "e_1_3_2_27_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1038/nphys1614"
    },
    {
      "key": "e_1_3_2_28_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.107.260501"
    },
    {
      "key": "e_1_3_2_29_2",
      "unstructured": "Casanova J. Mezzacapo A. Lamata L. Solano E. http://arxiv.org/abs/1110.3730 (2011)."
    },
    {
      "key": "e_1_3_2_30_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevB.69.214501"
    },
    {
      "key": "e_1_3_2_31_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1080/00018730701223200"
    },
    {
      "key": "e_1_3_2_32_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1088/0953-4075/42/15/154009"
    },
    {
      "key": "e_1_3_2_35_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0375-9601(90)90962-N"
    },
    {
      "key": "e_1_3_2_36_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1007/s00220-006-0150-x"
    },
    {
      "key": "e_1_3_2_37_2",
      "unstructured": "Kitaev A. Webb W. A. http://arxiv.org/abs/0801.0342 (2008)."
    },
    {
      "key": "e_1_3_2_38_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1090/S0025-5718-1974-0331751-8"
    },
    {
      "key": "e_1_3_2_39_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/S0747-7171(08)80013-2"
    },
    {
      "key": "e_1_3_2_40_2",
      "unstructured": "M. E. Peskin D. V. Schroeder An Introduction to Quantum Field Theory (Westview Boulder CO 1995)."
    },
    {
      "key": "e_1_3_2_41_2",
      "unstructured": "Kitaev A. Y. http://arxiv.org/abs/quant-ph/9511026 (1995)."
    },
    {
      "key": "e_1_3_2_42_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0370-2693(94)01419-D"
    },
    {
      "key": "e_1_3_2_43_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0550-3213(91)90244-R"
    },
    {
      "key": "e_1_3_2_44_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.39.95"
    },
    {
      "key": "e_1_3_2_45_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0550-3213(87)90177-5"
    },
    {
      "key": "e_1_3_2_46_2",
      "unstructured": "A. Messiah Quantum Mechanics (Dover 1999). (Reprint of the two-volume edition published by Wiley 1961\u20131962.)"
    },
    {
      "key": "e_1_3_2_47_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1063/1.2798382"
    },
    {
      "key": "e_1_3_2_48_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1090/psapm/068/2762145"
    }
  ],
  "container-title": "Science",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://www.science.org/doi/pdf/10.1126/science.1217069",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        1,
        10
      ]
    ],
    "date-time": "2024-01-10T13:49:46Z",
    "timestamp": 1704894586000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://www.science.org/doi/10.1126/science.1217069"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2012,
        6
      ]
    ]
  },
  "references-count": 45,
  "journal-issue": {
    "issue": "6085",
    "published-print": {
      "date-parts": [
        [
          2012,
          6
        ]
      ]
    }
  },
  "alternative-id": [
    "10.1126/science.1217069"
  ],
  "URL": "http://dx.doi.org/10.1126/science.1217069",
  "relation": {},
  "ISSN": [
    "0036-8075",
    "1095-9203"
  ],
  "subject": [],
  "container-title-short": "Science",
  "published": {
    "date-parts": [
      [
        2012,
        6
      ]
    ]
  }
}