Mô phỏng lượng tử lý thuyết gauge qua mạng orbifold

Alexander J. Buser1, Hrant Gharibyan1, Masanori Hanada2, Masazumi Honda3, Junyu Liu1
1Walter Burke Institute for Theoretical Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, 91125, USA
2Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH, U.K.
3Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto, 606-8502, Japan

Tóm tắt

Tóm tắt

Chúng tôi đề xuất một khung mới để mô phỏng lý thuyết U(k) Yang-Mills trên một máy tính lượng tử phổ quát. Cấu trúc này sử dụng công thức mạng orbifold được đề xuất bởi Kaplan, Katz và Unsal, những người ban đầu đã áp dụng nó cho các lý thuyết gauge siêu đối xứng. Phương pháp mà chúng tôi đề xuất mang lại một góc nhìn mới về mô phỏng lượng tử các lý thuyết trường lượng tử, mang lại một số lợi ích so với công thức Kogut-Susskind thông thường. Chúng tôi thảo luận về việc ứng dụng các cấu trúc của chúng tôi vào việc tính toán các tính chất tĩnh và động lực học theo thời gian thực của các lý thuyết Yang-Mills, từ các phép đo glueball cho đến AdS/CFT, sử dụng nhiều kỹ thuật thông tin lượng tử khác nhau bao gồm qubit hóa, xử lý tín hiệu lượng tử, giới hạn Jordan-Lee-Preskill và hình ảnh bóng. Việc tổng quát cho một số lý thuyết Yang-Mills siêu đối xứng dường như là dễ dàng, cung cấp một lộ trình cho mô phỏng lượng tử của trọng lực lượng tử thông qua tính đối ngẫu holographic.

Từ khóa


Tài liệu tham khảo

J. Preskill, Quantum computing in the nisq era and beyond, Quantum 2 (2018) 79.

J. Preskill, Simulating quantum field theory with a quantum computer, PoS LATTICE2018 (2018) 024 [arXiv:1811.10085] [INSPIRE].

J. Liu, Does Richard Feynman Dream of Electric Sheep? Topics on Quantum Field Theory, Quantum Computing, and Computer Science, Ph.D. Thesis, Caltech (2021) [DOI] [INSPIRE].

S.P. Jordan, K.S.M. Lee and J. Preskill, Quantum Algorithms for Quantum Field Theories, Science 336 (2012) 1130 [arXiv:1111.3633] [INSPIRE].

S.P. Jordan, K.S.M. Lee and J. Preskill, Quantum Computation of Scattering in Scalar Quantum Field Theories, Quant. Inf. Comput. 14 (2014) 1014 [arXiv:1112.4833] [INSPIRE].

N. Klco and M.J. Savage, Digitization of scalar fields for quantum computing, Phys. Rev. A 99 (2019) 052335 [arXiv:1808.10378] [INSPIRE].

H. Singh and S. Chandrasekharan, Qubit regularization of the O(3) sigma model, Phys. Rev. D 100 (2019) 054505 [arXiv:1905.13204] [INSPIRE].

A.J. Buser, T. Bhattacharya, L. Cincio and R. Gupta, State preparation and measurement in a quantum simulation of the O(3) sigma model, Phys. Rev. D 102 (2020) 114514 [arXiv:2006.15746] [INSPIRE].

R. Brower, S. Chandrasekharan and U.J. Wiese, QCD as a quantum link model, Phys. Rev. D 60 (1999) 094502 [hep-th/9704106] [INSPIRE].

S. Chandrasekharan and U.J. Wiese, Quantum link models: A Discrete approach to gauge theories, Nucl. Phys. B 492 (1997) 455 [hep-lat/9609042] [INSPIRE].

J.B. Kogut and L. Susskind, Hamiltonian Formulation of Wilson’s Lattice Gauge Theories, Phys. Rev. D 11 (1975) 395 [INSPIRE].

D.B. Kaplan, E. Katz and M. Ünsal, Supersymmetry on a spatial lattice, JHEP 05 (2003) 037 [hep-lat/0206019] [INSPIRE].

A.G. Cohen, D.B. Kaplan, E. Katz and M. Ünsal, Supersymmetry on a Euclidean space-time lattice. 1. A Target theory with four supercharges, JHEP 08 (2003) 024 [hep-lat/0302017] [INSPIRE].

A.G. Cohen, D.B. Kaplan, E. Katz and M. Ünsal, Supersymmetry on a Euclidean space-time lattice. 2. Target theories with eight supercharges, JHEP 12 (2003) 031 [hep-lat/0307012] [INSPIRE].

D.B. Kaplan and M. Ünsal, A Euclidean lattice construction of supersymmetric Yang-Mills theories with sixteen supercharges, JHEP 09 (2005) 042 [hep-lat/0503039] [INSPIRE].

F. Sugino, A Lattice formulation of superYang-Mills theories with exact supersymmetry, JHEP 01 (2004) 015 [hep-lat/0311021] [INSPIRE].

F. Sugino, SuperYang-Mills theories on the two-dimensional lattice with exact supersymmetry, JHEP 03 (2004) 067 [hep-lat/0401017] [INSPIRE].

F. Sugino, Various super Yang-Mills theories with exact supersymmetry on the lattice, JHEP 01 (2005) 016 [hep-lat/0410035] [INSPIRE].

S. Catterall, Lattice supersymmetry and topological field theory, JHEP 05 (2003) 038 [hep-lat/0301028] [INSPIRE].

S. Catterall, A Geometrical approach to N = 2 super Yang-Mills theory on the two dimensional lattice, JHEP 11 (2004) 006 [hep-lat/0410052] [INSPIRE].

M. Hanada and I. Kanamori, Lattice study of two-dimensional N = (2, 2) super Yang-Mills at large-N, Phys. Rev. D 80 (2009) 065014 [arXiv:0907.4966] [INSPIRE].

M. Hanada and I. Kanamori, Absence of sign problem in two-dimensional N = (2, 2) super Yang-Mills on lattice, JHEP 01 (2011) 058 [arXiv:1010.2948] [INSPIRE].

S. Catterall, R. Galvez, A. Joseph and D. Mehta, On the sign problem in 2D lattice super Yang-Mills, JHEP 01 (2012) 108 [arXiv:1112.3588] [INSPIRE].

E. Giguère and D. Kadoh, Restoration of supersymmetry in two-dimensional SYM with sixteen supercharges on the lattice, JHEP 05 (2015) 082 [arXiv:1503.04416] [INSPIRE].

K.G. Wilson, Confinement of Quarks, Phys. Rev. D 10 (1974) 2445 [INSPIRE].

D.B. Kaplan, A Method for simulating chiral fermions on the lattice, Phys. Lett. B 288 (1992) 342 [hep-lat/9206013] [INSPIRE].

H. Neuberger, Exactly massless quarks on the lattice, Phys. Lett. B 417 (1998) 141 [hep-lat/9707022] [INSPIRE].

H. Gharibyan, M. Hanada, M. Honda and J. Liu, Toward simulating Superstring/M-theory on a quantum computer, JHEP 07 (2021) 140 [arXiv:2011.06573] [INSPIRE].

N. Arkani-Hamed, A.G. Cohen and H. Georgi, (De)constructing dimensions, Phys. Rev. Lett. 86 (2001) 4757 [hep-th/0104005] [INSPIRE].

M. Ünsal, Compact gauge fields for supersymmetric lattices, JHEP 11 (2005) 013 [hep-lat/0504016] [INSPIRE].

M. Hanada, S. Matsuura and F. Sugino, Two-dimensional lattice for four-dimensional N = 4 supersymmetric Yang-Mills, Prog. Theor. Phys. 126 (2011) 597 [arXiv:1004.5513] [INSPIRE].

M. Hanada, A proposal of a fine tuning free formulation of 4d N = 4 super Yang-Mills, JHEP 11 (2010) 112 [arXiv:1009.0901] [INSPIRE].

M. Hanada, S. Matsuura and F. Sugino, Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges, Nucl. Phys. B 857 (2012) 335 [arXiv:1109.6807] [INSPIRE].

I. Kanamori, Lattice formulation of two-dimensional N = (2, 2) super Yang-Mills with SU(N) gauge group, JHEP 07 (2012) 021 [arXiv:1202.2101] [INSPIRE].

M. Hanada, H. Shimada and N. Wintergerst, Color confinement and Bose-Einstein condensation, JHEP 08 (2021) 039 [arXiv:2001.10459] [INSPIRE].

E. Rinaldi et al., Matrix Model simulations using Quantum Computing, Deep Learning, and Lattice Monte Carlo, arXiv:2108.02942 [INSPIRE].

K. Wan and I. Kim, Fast digital methods for adiabatic state preparation, arXiv:2004.04164.

E. Berkowitz, M. Hanada, E. Rinaldi and P. Vranas, Gauged And Ungauged: A Nonperturbative Test, JHEP 06 (2018) 124 [arXiv:1802.02985] [INSPIRE].

J. Maldacena and A. Milekhin, To gauge or not to gauge?, JHEP 04 (2018) 084 [arXiv:1802.00428] [INSPIRE].

G.H. Low and I.L. Chuang, Hamiltonian simulation by qubitization, arXiv:1610.06546.

G.H. Low and I.L. Chuang, Optimal hamiltonian simulation by quantum signal processing, Phys. Rev. Lett. 118 (2017) 010501.

R. Babbush, D.W. Berry and H. Neven, Quantum Simulation of the Sachdev-Ye-Kitaev Model by Asymmetric Qubitization, Phys. Rev. A 99 (2019) 040301 [arXiv:1806.02793] [INSPIRE].

C.J. Morningstar and M.J. Peardon, The Glueball spectrum from an anisotropic lattice study, Phys. Rev. D 60 (1999) 034509 [hep-lat/9901004] [INSPIRE].

M.L.L. da Silva, D. Hadjimichef and C.A.Z. Vasconcellos, Glueball-glueball scattering in a constituent gluon model, AIP Conf. Proc. 739 (2004) 690 [hep-ph/0407114] [INSPIRE].

N. Yamanaka, H. Iida, A. Nakamura and M. Wakayama, Glueball scattering cross section in lattice SU(2) Yang-Mills theory, Phys. Rev. D 102 (2020) 054507 [arXiv:1910.07756] [INSPIRE].

J.M. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].

A. Kitaev, Quantum measurements and the Abelian stabilizer problem, quant-ph/9511026.

D.S. Abrams and S. Lloyd, A Quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors, Phys. Rev. Lett. 83 (1999) 5162 [quant-ph/9807070] [INSPIRE].

H.-Y. Huang, R. Kueng and J. Preskill, Predicting many properties of a quantum system from very few measurements, Nature Phys. 16 (2020) 1050.

S.L. Braunstein and P. van Loock, Quantum information with continuous variables, Rev. Mod. Phys. 77 (2005) 513 [quant-ph/0410100] [INSPIRE].

T. Byrnes and Y. Yamamoto, Simulating lattice gauge theories on a quantum computer, Phys. Rev. A 73 (2006) 022328 [quant-ph/0510027] [INSPIRE].

A. Alex, M. Kalus, A. Huckleberry and J. von Delft, A Numerical algorithm for the explicit calculation of SU(N) and SL(N, ℂ) Clebsch-Gordan coefficients, J. Math. Phys. 52 (2011) 023507 [arXiv:1009.0437] [INSPIRE].

D. Rowe and J. Repka, An algebraic algorithm for calculating Clebsch-Gordan coefficients; application to SU(2) and SU(3), J. Math. Phys. 38 (1997) 4363.

L.C. Biedenharn and J.D. Louck, A pattern calculus for tensor operators in the unitary groups, Commun. Math. Phys. 8 (1968) 89.

D. Bacon, I.L. Chuang and A.W. Harrow, Efficient quantum circuits for schur and clebsch-gordan transforms, Phys. Rev. Lett. 97 (2006) 170502.

S.P. Jordan, Fast quantum algorithms for approximating some irreducible representations of groups, arXiv:0811.0562.

NuQS collaboration, General Methods for Digital Quantum Simulation of Gauge Theories, Phys. Rev. D 100 (2019) 034518 [arXiv:1903.08807] [INSPIRE].

L. García-Álvarez, I.L. Egusquiza, L. Lamata, A. del Campo, J. Sonner and E. Solano, Digital Quantum Simulation of Minimal AdS/CFT, Phys. Rev. Lett. 119 (2017) 040501 [arXiv:1607.08560] [INSPIRE].

S. McArdle, S. Endo, A. Aspuru-Guzik, S.C. Benjamin and X. Yuan, Quantum computational chemistry, Rev. Mod. Phys. 92 (2020) 015003.

J. Liu and Y. Xin, Quantum simulation of quantum field theories as quantum chemistry, JHEP 12 (2020) 011 [arXiv:2004.13234] [INSPIRE].

A.R. Brown et al., Quantum Gravity in the Lab: Teleportation by Size and Traversable Wormholes, arXiv:1911.06314 [INSPIRE].

I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from Conformal Field Theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].

S. El-Showk and K. Papadodimas, Emergent Spacetime and Holographic CFTs, JHEP 10 (2012) 106 [arXiv:1101.4163] [INSPIRE].

J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].

E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].

B. Sundborg, The Hagedorn transition, deconfinement and N = 4 SYM theory, Nucl. Phys. B 573 (2000) 349 [hep-th/9908001] [INSPIRE].

O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The Hagedorn-deconfinement phase transition in weakly coupled large N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].

M. Hanada and J. Maltz, A proposal of the gauge theory description of the small Schwarzschild black hole in AdS5 × S5, JHEP 02 (2017) 012 [arXiv:1608.03276] [INSPIRE].

M. Hanada, G. Ishiki and H. Watanabe, Partial Deconfinement, JHEP 03 (2019) 145 [Erratum ibid. 10 (2019) 029] [arXiv:1812.05494] [INSPIRE].

M. Hanada, A. Jevicki, C. Peng and N. Wintergerst, Anatomy of Deconfinement, JHEP 12 (2019) 167 [arXiv:1909.09118] [INSPIRE].

D. Berenstein, Submatrix deconfinement and small black holes in AdS, JHEP 09 (2018) 054 [arXiv:1806.05729] [INSPIRE].

R.D. Peccei and H.R. Quinn, CP Conservation in the Presence of Instantons, Phys. Rev. Lett. 38 (1977) 1440 [INSPIRE].

XENON collaboration, Excess electronic recoil events in XENON1T, Phys. Rev. D 102 (2020) 072004 [arXiv:2006.09721] [INSPIRE].

G. Ortiz, J.E. Gubernatis, E. Knill and R. Laflamme, Quantum algorithms for fermionic simulations, Phys. Rev. A 64 (2001) 022319 [Erratum ibid. 65 (2002) 029902] [cond-mat/0012334] [INSPIRE].

C. Alexandrou et al., Comparison of topological charge definitions in Lattice QCD, Eur. Phys. J. C 80 (2020) 424 [arXiv:1708.00696] [INSPIRE].

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, arXiv:2001.00485 [INSPIRE].

NuQS collaboration, Gluon Field Digitization for Quantum Computers, Phys. Rev. D 100 (2019) 114501 [arXiv:1906.11213] [INSPIRE].

E. Zohar and M. Burrello, Formulation of lattice gauge theories for quantum simulations, Phys. Rev. D 91 (2015) 054506 [arXiv:1409.3085] [INSPIRE].