Built on

N. Klco, J.R. Stryker and M.J. Savage, SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers , Phys. Rev. D 101
Original
1908
Earlier work this paper cites.
A. Schotte, J. Carrasco, B. Vanhecke, J. Haegeman, L. Vanderstraeten, F. Verstraete et al., Tensor-network approach to phase transitions in string-net models , Phys. Rev. B 100
Original
1909
Earlier work this paper cites.
M.C. Bañuls and K. Cichy, Review on Novel Methods for Lattice Gauge Theories , Rept. Prog. Phys. 83
Original
1910
Earlier work this paper cites.
M.C. Bañuls et al., Simulating Lattice Gauge Theories within Quantum Technologies , Eur. Phys. J. D 74
Original
1911
Earlier work this paper cites.
I. Raychowdhury and J.R. Stryker, Loop, string, and hadron dynamics in SU(2) Hamiltonian lattice gauge theories , Phys. Rev. D 101
Original
1912
Earlier work this paper cites.
R. Penrose, Angular momentum: an approach to combinatorial space-time , Quantum theory and beyond 151
1971
Earlier work this paper cites.
J.B. Kogut and L. Susskind, Hamiltonian Formulation of Wilson’s Lattice Gauge Theories , Phys. Rev. D 11
1975
Earlier work this paper cites.
J. Ambjorn, P. Olesen and C. Peterson, Stochastic Confinement and Dimensional Reduction. 1. Four-Dimensional SU(2) Lattice Gauge Theory , Nucl. Phys. B 240
1984
Earlier work this paper cites.
J. Ambjorn, P. Olesen and C. Peterson, Stochastic Confinement and Dimensional Reduction. 2. Three-dimensional SU(2) Lattice Gauge Theory , Nucl. Phys. B 240
1984
Earlier work this paper cites.
L. Begin, P. Mathieu and M.A. Walton, SU(3)-k fusion coefficients , Mod. Phys. Lett. A 7
1992
Earlier work this paper cites.
C. Rovelli and L. Smolin, Spin networks and quantum gravity , Phys. Rev. D 52
1995
Earlier work this paper cites.
J.C. Baez, Spin network states in gauge theory , Adv. Math. 117
1996
Earlier work this paper cites.
D. Bonatsos and C. Daskaloyannis, Quantum groups and their applications in nuclear physics , Prog. Part. Nucl. Phys. 43
1999
Earlier work this paper cites.
G. Burgio, R. De Pietri, H.A. Morales-Tecotl, L.F. Urrutia and J.D. Vergara, The Basis of the physical Hilbert space of lattice gauge theories , Nucl. Phys. B 566
2000
Earlier work this paper cites.
S. Deldar, Static SU(3) potentials for sources in various representations , Phys. Rev. D 62
2000
Earlier work this paper cites.
G.S. Bali, Casimir scaling of SU(3) static potentials , Phys. Rev. D 62
2000
Earlier work this paper cites.
W.J. Cunningham, B. Dittrich and S. Steinhaus, Tensor Network Renormalization with Fusion Charges—Applications to 3D Lattice Gauge Theory , Universe 6
Original
2002
Earlier work this paper cites.
M.A. Levin and X.-G. Wen, String net condensation: A Physical mechanism for topological phases , Phys. Rev. B 71
2005
Earlier work this paper cites.

Similar

T. Byrnes and Y. Yamamoto, Simulating lattice gauge theories on a quantum computer , Phys. Rev. A 73
2006
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A. Kitaev, Anyons in an exactly solved model and beyond , Annals Phys. 321
2006
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R. Coquereaux, D. Hammaoui, G. Schieber and E.H. Tahri, Comments about quantum symmetries of SU(3) graphs , J. Geom. Phys. 57
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A. Alexandru, G. Basar, P.F. Bedaque and N.C. Warrington, Complex paths around the sign problem , Rev. Mod. Phys. 94
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Then

S. Dusuel and J. Vidal, Mean-field ansatz for topological phases with string tension , Phys. Rev. B 92
Original
2015
Later among the works it cites.
G. Aarts, Introductory lectures on lattice QCD at nonzero baryon number , J. Phys. Conf. Ser. 706
Original
2016
Later among the works it cites.
M. Dalmonte and S. Montangero, Lattice gauge theory simulations in the quantum information era , Contemp. Phys. 57
Original
2016
Later among the works it cites.
L. Vanderstraeten, M. Mariën, J. Haegeman, N. Schuch, J. Vidal and F. Verstraete, Bridging perturbative expansions with tensor networks , Phys. Rev. Lett. 119
2017
Later among the works it cites.
J. Preskill, Simulating quantum field theory with a quantum computer , PoS LATTICE2018

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alphaXiv searches the wider corpus for related work and actual follow-ups.

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2023

$q$ deformed formulation of Hamiltonian SU(3) Yang-Mills theory

Hayata, Tomoya, Hidaka, Yoshimasa

Understand

We study $\mathrm{SU}(3)$ Yang-Mills theory in $(2+1)$ dimensions based on networks of Wilson lines.

With the help of the $q$ deformation, networks respect the (discretized) $\mathrm{SU}(3)$ gauge symmetry as a quantum group, i.e., $\mathrm{SU}(3)_k$, and may enable implementations of $\mathrm{SU}(3)$ Yang-Mills theory in quantum and classical algorithms by referring to those of the stringnet model.
As a demonstration, we perform a mean-field computation of the groundstate of $\mathrm{SU}(3)_k$ Yang-Mills theory, which is in good agreement with the conventional Monte Carlo simulation by taking sufficiently large $k$.
The variational ansatz of the mean-field computation can be represented by the tensor networks called infinite projected entangled pair states.

Built on

N. Klco, J.R. Stryker and M.J. Savage, SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers , Phys. Rev. D 101
Original
1908
Earlier work this paper cites.
A. Schotte, J. Carrasco, B. Vanhecke, J. Haegeman, L. Vanderstraeten, F. Verstraete et al., Tensor-network approach to phase transitions in string-net models , Phys. Rev. B 100
Original
1909
Earlier work this paper cites.
M.C. Bañuls and K. Cichy, Review on Novel Methods for Lattice Gauge Theories , Rept. Prog. Phys. 83
Original
1910
Earlier work this paper cites.
M.C. Bañuls et al., Simulating Lattice Gauge Theories within Quantum Technologies , Eur. Phys. J. D 74
Original
1911
Earlier work this paper cites.
I. Raychowdhury and J.R. Stryker, Loop, string, and hadron dynamics in SU(2) Hamiltonian lattice gauge theories , Phys. Rev. D 101
Original
1912
Earlier work this paper cites.
R. Penrose, Angular momentum: an approach to combinatorial space-time , Quantum theory and beyond 151
1971
Earlier work this paper cites.
J.B. Kogut and L. Susskind, Hamiltonian Formulation of Wilson’s Lattice Gauge Theories , Phys. Rev. D 11
1975
Earlier work this paper cites.
J. Ambjorn, P. Olesen and C. Peterson, Stochastic Confinement and Dimensional Reduction. 1. Four-Dimensional SU(2) Lattice Gauge Theory , Nucl. Phys. B 240
1984
Earlier work this paper cites.
J. Ambjorn, P. Olesen and C. Peterson, Stochastic Confinement and Dimensional Reduction. 2. Three-dimensional SU(2) Lattice Gauge Theory , Nucl. Phys. B 240
1984
Earlier work this paper cites.
L. Begin, P. Mathieu and M.A. Walton, SU(3)-k fusion coefficients , Mod. Phys. Lett. A 7
1992
Earlier work this paper cites.
C. Rovelli and L. Smolin, Spin networks and quantum gravity , Phys. Rev. D 52
1995
Earlier work this paper cites.
J.C. Baez, Spin network states in gauge theory , Adv. Math. 117
1996
Earlier work this paper cites.
D. Bonatsos and C. Daskaloyannis, Quantum groups and their applications in nuclear physics , Prog. Part. Nucl. Phys. 43
1999
Earlier work this paper cites.
G. Burgio, R. De Pietri, H.A. Morales-Tecotl, L.F. Urrutia and J.D. Vergara, The Basis of the physical Hilbert space of lattice gauge theories , Nucl. Phys. B 566
2000
Earlier work this paper cites.
S. Deldar, Static SU(3) potentials for sources in various representations , Phys. Rev. D 62
2000
Earlier work this paper cites.
G.S. Bali, Casimir scaling of SU(3) static potentials , Phys. Rev. D 62
2000
Earlier work this paper cites.
W.J. Cunningham, B. Dittrich and S. Steinhaus, Tensor Network Renormalization with Fusion Charges—Applications to 3D Lattice Gauge Theory , Universe 6
Original
2002
Earlier work this paper cites.
M.A. Levin and X.-G. Wen, String net condensation: A Physical mechanism for topological phases , Phys. Rev. B 71
2005
Earlier work this paper cites.

Similar

T. Byrnes and Y. Yamamoto, Simulating lattice gauge theories on a quantum computer , Phys. Rev. A 73
2006
Cited alongside, same era.
A. Kitaev, Anyons in an exactly solved model and beyond , Annals Phys. 321
2006
Cited alongside, same era.
R. Coquereaux, D. Hammaoui, G. Schieber and E.H. Tahri, Comments about quantum symmetries of SU(3) graphs , J. Geom. Phys. 57
2006
Cited alongside, same era.
A. Alexandru, G. Basar, P.F. Bedaque and N.C. Warrington, Complex paths around the sign problem , Rev. Mod. Phys. 94
Original
2007
Cited alongside, same era.
P. Bonderson, K. Shtengel and J.K. Slingerland, Interferometry of non-Abelian Anyons , Annals Phys. 323
Original
2008
Cited alongside, same era.

Then

S. Dusuel and J. Vidal, Mean-field ansatz for topological phases with string tension , Phys. Rev. B 92
Original
2015
Later among the works it cites.
G. Aarts, Introductory lectures on lattice QCD at nonzero baryon number , J. Phys. Conf. Ser. 706
Original
2016
Later among the works it cites.
M. Dalmonte and S. Montangero, Lattice gauge theory simulations in the quantum information era , Contemp. Phys. 57
Original
2016
Later among the works it cites.
L. Vanderstraeten, M. Mariën, J. Haegeman, N. Schuch, J. Vidal and F. Verstraete, Bridging perturbative expansions with tensor networks , Phys. Rev. Lett. 119
2017
Later among the works it cites.
J. Preskill, Simulating quantum field theory with a quantum computer , PoS LATTICE2018

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

P. de Forcrand, Simulating QCD at finite density , PoS LAT2009

Original

2009

Cited alongside, same era.

P. Bialas, L. Daniel, A. Morel and B. Petersson, Thermodynamics of SU(3) Gauge Theory in 2 + 1 Dimensions , Nucl. Phys. B 807

Original

2009

Cited alongside, same era.

Z.-C. Gu, M. Levin, B. Swingle and X.-G. Wen, Tensor-product representations for string-net condensed states , Phys. Rev. B 79

2009

Cited alongside, same era.

O. Buerschaper, M. Aguado and G. Vidal, Explicit tensor network representation for the ground states of string-net models , Phys. Rev. B 79

2009

Cited alongside, same era.

E. Ardonne and J. Slingerland, Clebsch–gordan and 6j-coefficients for rank 2 quantum groups , Journal of Physics A: Mathematical and Theoretical 43

Original

2010

Cited alongside, same era.

R. Koenig, G. Kuperberg and B.W. Reichardt, Quantum computation with Turaev–Viro codes , Annals Phys. 325

Original

2010

Cited alongside, same era.

J.I. Cirac, D. Perez-Garcia, N. Schuch and F. Verstraete, Matrix product states and projected entangled pair states: Concepts, symmetries, theorems , Rev. Mod. Phys. 93

Original

2011

Cited alongside, same era.

Original

2018