Built on

P. Hauke, H. G. Katzgraber, W. Lechner, H. Nishimori, and W. D. Oliver, Perspectives of quantum annealing: methods and implementations, Reports on Progress in Physics 83
Original
1903
Earlier work this paper cites.
I. Ozfidan, C. Deng, et al. , Demonstration of a Nonstoquastic Hamiltonian in Coupled Superconducting Flux Qubits, Phys. Rev. Applied 13
Original
1903
Earlier work this paper cites.
E. Zohar and J. I. Cirac, Removing Staggered Fermionic Matter in U ⁡ ( N ) U(N) and S U ( N ) SU(N) Lattice Gauge Theories, Phys. Rev. D 99
Original
1905
Earlier work this paper cites.
A. Pearson, M. A., I. Hen, and D. A. Lidar, Analog errors in quantum annealing: doom and hope, npj Quantum Information 5
Original
1907
Earlier work this paper cites.
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. Mil, T. V. Zache, A. Hegde, A. Xia, R. P. Bhatt, M. K. Oberthaler, P. Hauke, J. Berges, and F. Jendrzejewski, A scalable realization of local U(1) gauge invariance in cold atomic mixtures, Science 367
Original
1909
Earlier work this paper cites.
K. Jałowiecki, A. Wieckowski, P. Gawron, and B. Gardas, Parallel in time dynamics with quantum annealers, Scientific Reports 10
Original
1909
Earlier work this paper cites.
M. Bañuls et al. , Simulating Lattice Gauge Theories within Quantum Technologies, Eur. Phys. J. D 74
Original
1911
Earlier work this paper cites.
N. T. Nguyen, G. T. Kenyon, and B. Yoon, A regression algorithm for accelerated lattice QCD that exploits sparse inference on the D-Wave quantum annealer, Sci. Rep. 10
Original
1911
Earlier work this paper cites.
A. King, J, Raymond, T. Lanting et al., Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets, Nature Commun. 12
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.
H. F. Trotter, On the Product of Semi-Groups of Operators, Proceedings of the American Mathematical Society 10
1959
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.
R. P. Feynman, Quantum Mechanical Computers, Optics News 11
1985
Earlier work this paper cites.
D. Varshalovich, A. Moskalev, and V. Khersonsky, Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3nj Symbols, World Scientific, Singapore (1988)
1988
Earlier work this paper cites.
M. Suzuki, General Decomposition Theory of Ordered Exponentials, Proceedings of the Japan Academy, Series B 69
1993
Earlier work this paper cites.
W. J. Thompson, Angular Momentum, John Wiley & Sons Inc., New Jersey (1994)
1994
Earlier work this paper cites.
S. Chandrasekharan and U. Wiese, Quantum link models: A Discrete approach to gauge theories, Nucl. Phys. B 492
1997
Earlier work this paper cites.
T. Kadowaki and H. Nishimori, Quantum annealing in the transverse Ising model, Phys. Rev. E 58
1998
Earlier work this paper cites.
E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, Quantum Computation by Adiabatic Evolution, arXiv:quant-ph/0001106 (2000)
2000
Earlier work this paper cites.
E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda, A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem, Science 292
2001
Earlier work this paper cites.
B. Chakraborty, M. Honda, T. Izubuchi, Y. Kikuchi, and A. Tomiya, Digital Quantum Simulation of the Schwinger Model with Topological Term via Adiabatic State Preparation, (2020), arXiv:2001.00485 [hep-lat]
Original
2001
Earlier work this paper cites.
J. Roland and N. J. Cerf, Quantum search by local adiabatic evolution, Phys. Rev. A 65
2002
Earlier work this paper cites.

Similar

A. Kitaev, A. Shen, and M. Vyalyi, Classical and Quantum Computation, American Mathematical Society, Providence, RI (2002)
2002
Cited alongside, same era.
B. Yang, H. Sun, R. Ott, H.-Y. Wang, T. V. Zache, J. C. Halimeh, Z.-S. Yuan, P. Hauke, and J.-W. Pan, Observation of gauge invariance in a 71-site Bose–Hubbard quantum simulator, Nature 587
Original
2003
Cited alongside, same era.
D. Aharonov, W. van Dam, J. Kempe, Z. Landau, S. Lloyd, and O. Regev, Adiabatic quantum computation is equivalent to standard quantum computation, in 45th Annual IEEE Symposium on Foundations of Computer Science (2004) pp. 42–51
2004
Cited alongside, same era.
M. Mathur, Harmonic oscillator prepotentials in SU(2) lattice gauge theory, J. Phys. A 38
2005
Cited alongside, same era.
Y. Ji, H. Lamm, and S. Zhu (NuQS), Gluon Field Digitization via Group Space Decimation for Quantum Computers, Phys. Rev. D 102

Then

E. Martinez, C. Muschik, et al. , Real-time dynamics of lattice gauge theories with a few-qubit quantum computer, Nature 534
Original
2016
Later among the works it cites.
C. Gattringer and K. Langfeld, Approaches to the sign problem in lattice field theory, Int. J. Mod. Phys. A 31
Original
2016
Later among the works it cites.
G. D. Kribs and E. T. Neil, Review of strongly-coupled composite dark matter models and lattice simulations, Int. J. Mod. Phys. A 31
Original
2016
Later among the works it cites.
P. Silvi, E. Rico, M. Dalmonte, F. Tschirsich, and S. Montangero, Finite-density phase diagram of a (1+1)-d non-abelian lattice gauge theory with tensor networks, Quantum 1
Original
2017
Later among the works it cites.
M. C. Bañuls, K. Cichy, J. I. Cirac, K. Jansen, and S. Kühn, Efficient basis formulation for 1+1 dimensional SU(2) lattice gauge theory: Spectral calculations with matrix product states, Phys. Rev. X 7

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2021

SU(2) lattice gauge theory on a quantum annealer

Rahman, Sarmed A, Lewis, Randy, Mendicelli, Emanuele et al.

Understand

Lattice gauge theory is an essential tool for strongly interacting non-Abelian fields, such as those in quantum chromodynamics where lattice results have been of central importance for several decades.

Recent studies suggest that quantum computers could extend the reach of lattice gauge theory in dramatic ways, but the usefulness of quantum annealing hardware for lattice gauge theory has not yet been explored.
In this work, we implement SU(2) pure gauge theory on a quantum annealer for lattices comprising a few plaquettes in a row with a periodic boundary condition.
These plaquettes are in two spatial dimensions and calculations use the Hamiltonian formulation where time is not discretized.

Built on

P. Hauke, H. G. Katzgraber, W. Lechner, H. Nishimori, and W. D. Oliver, Perspectives of quantum annealing: methods and implementations, Reports on Progress in Physics 83
Original
1903
Earlier work this paper cites.
I. Ozfidan, C. Deng, et al. , Demonstration of a Nonstoquastic Hamiltonian in Coupled Superconducting Flux Qubits, Phys. Rev. Applied 13
Original
1903
Earlier work this paper cites.
E. Zohar and J. I. Cirac, Removing Staggered Fermionic Matter in U ⁡ ( N ) U(N) and S U ( N ) SU(N) Lattice Gauge Theories, Phys. Rev. D 99
Original
1905
Earlier work this paper cites.
A. Pearson, M. A., I. Hen, and D. A. Lidar, Analog errors in quantum annealing: doom and hope, npj Quantum Information 5
Original
1907
Earlier work this paper cites.
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. Mil, T. V. Zache, A. Hegde, A. Xia, R. P. Bhatt, M. K. Oberthaler, P. Hauke, J. Berges, and F. Jendrzejewski, A scalable realization of local U(1) gauge invariance in cold atomic mixtures, Science 367
Original
1909
Earlier work this paper cites.
K. Jałowiecki, A. Wieckowski, P. Gawron, and B. Gardas, Parallel in time dynamics with quantum annealers, Scientific Reports 10
Original
1909
Earlier work this paper cites.
M. Bañuls et al. , Simulating Lattice Gauge Theories within Quantum Technologies, Eur. Phys. J. D 74
Original
1911
Earlier work this paper cites.
N. T. Nguyen, G. T. Kenyon, and B. Yoon, A regression algorithm for accelerated lattice QCD that exploits sparse inference on the D-Wave quantum annealer, Sci. Rep. 10
Original
1911
Earlier work this paper cites.
A. King, J, Raymond, T. Lanting et al., Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets, Nature Commun. 12
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.
H. F. Trotter, On the Product of Semi-Groups of Operators, Proceedings of the American Mathematical Society 10
1959
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.
R. P. Feynman, Quantum Mechanical Computers, Optics News 11
1985
Earlier work this paper cites.
D. Varshalovich, A. Moskalev, and V. Khersonsky, Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3nj Symbols, World Scientific, Singapore (1988)
1988
Earlier work this paper cites.
M. Suzuki, General Decomposition Theory of Ordered Exponentials, Proceedings of the Japan Academy, Series B 69
1993
Earlier work this paper cites.
W. J. Thompson, Angular Momentum, John Wiley & Sons Inc., New Jersey (1994)
1994
Earlier work this paper cites.
S. Chandrasekharan and U. Wiese, Quantum link models: A Discrete approach to gauge theories, Nucl. Phys. B 492
1997
Earlier work this paper cites.
T. Kadowaki and H. Nishimori, Quantum annealing in the transverse Ising model, Phys. Rev. E 58
1998
Earlier work this paper cites.
E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, Quantum Computation by Adiabatic Evolution, arXiv:quant-ph/0001106 (2000)
2000
Earlier work this paper cites.
E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda, A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem, Science 292
2001
Earlier work this paper cites.
B. Chakraborty, M. Honda, T. Izubuchi, Y. Kikuchi, and A. Tomiya, Digital Quantum Simulation of the Schwinger Model with Topological Term via Adiabatic State Preparation, (2020), arXiv:2001.00485 [hep-lat]
Original
2001
Earlier work this paper cites.
J. Roland and N. J. Cerf, Quantum search by local adiabatic evolution, Phys. Rev. A 65
2002
Earlier work this paper cites.

Similar

A. Kitaev, A. Shen, and M. Vyalyi, Classical and Quantum Computation, American Mathematical Society, Providence, RI (2002)
2002
Cited alongside, same era.
B. Yang, H. Sun, R. Ott, H.-Y. Wang, T. V. Zache, J. C. Halimeh, Z.-S. Yuan, P. Hauke, and J.-W. Pan, Observation of gauge invariance in a 71-site Bose–Hubbard quantum simulator, Nature 587
Original
2003
Cited alongside, same era.
D. Aharonov, W. van Dam, J. Kempe, Z. Landau, S. Lloyd, and O. Regev, Adiabatic quantum computation is equivalent to standard quantum computation, in 45th Annual IEEE Symposium on Foundations of Computer Science (2004) pp. 42–51
2004
Cited alongside, same era.
M. Mathur, Harmonic oscillator prepotentials in SU(2) lattice gauge theory, J. Phys. A 38
2005
Cited alongside, same era.
Y. Ji, H. Lamm, and S. Zhu (NuQS), Gluon Field Digitization via Group Space Decimation for Quantum Computers, Phys. Rev. D 102

Then

E. Martinez, C. Muschik, et al. , Real-time dynamics of lattice gauge theories with a few-qubit quantum computer, Nature 534
Original
2016
Later among the works it cites.
C. Gattringer and K. Langfeld, Approaches to the sign problem in lattice field theory, Int. J. Mod. Phys. A 31
Original
2016
Later among the works it cites.
G. D. Kribs and E. T. Neil, Review of strongly-coupled composite dark matter models and lattice simulations, Int. J. Mod. Phys. A 31
Original
2016
Later among the works it cites.
P. Silvi, E. Rico, M. Dalmonte, F. Tschirsich, and S. Montangero, Finite-density phase diagram of a (1+1)-d non-abelian lattice gauge theory with tensor networks, Quantum 1
Original
2017
Later among the works it cites.
M. C. Bañuls, K. Cichy, J. I. Cirac, K. Jansen, and S. Kühn, Efficient basis formulation for 1+1 dimensional SU(2) lattice gauge theory: Spectral calculations with matrix product states, Phys. Rev. X 7

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

Original

2005

Cited alongside, same era.

T. Byrnes and Y. Yamamoto, Simulating lattice gauge theories on a quantum computer, Phys. Rev. A 73

2006

Cited alongside, same era.

V. Kasper, G. Juzeliunas, M. Lewenstein, F. Jendrzejewski, and E. Zohar, From the Jaynes–Cummings model to non-abelian gauge theories: a guided tour for the quantum engineer, New J. Phys. 22

Original

2006

Cited alongside, same era.

A. Das and B. K. Chakrabarti, Colloquium: Quantum annealing and analog quantum computation, Reviews of Modern Physics 80

Original

2008

Cited alongside, same era.

J. D. Biamonte and P. J. Love, Realizable Hamiltonians for universal adiabatic quantum computers, Phys. Rev. A 78

Original

2008

Cited alongside, same era.

D. Aharonov, W. van Dam, J. Kempe, Z. Landau, S. Lloyd, and O. Regev, Adiabatic quantum computation is equivalent to standard quantum computation, SIAM Rev. 50(4)

2008

Cited alongside, same era.

A. Teplukhin, B. K. Kendrick, S. Tretiak, and P. A. Dub, Electronic structure with direct diagonalization on a D-wave quantum annealer, Scientific Reports 10

Original

2009

Cited alongside, same era.

A. Teplukhin, B. K. Kendrick, and D. Babikov, Solving complex eigenvalue problems on a quantum annealer with applications to quantum scattering resonances, Phys. Chem. Chem. Phys. 22

Original

2009

Cited alongside, same era.

Original

2017