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High-energy nuclear physics aims to explore and understand the physics of matter composed of quarks and gluons. However, it is intrinsically difficult to simulate high-energy nuclear physics from the first principle based quantum chromodynamics by using classical computers. In recent years, quantum computing has received intensive attention because it is expected to provide an ultimate solution for simulating high-energy nuclear physics. In this paper, we firstly review recent advances in quantum simulation of high-energy nuclear physics. Then we introduce some standard quantum algorithms, such as state preparation and measurements of light-cone correlation function. Finally, we demonstrate the advantage of quantum computing for solving the real-time evolution and the sign problems by studying hadronic scattering amplitude and phase structure of finite-temperature and finite-density matter, respectively.
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Keywords:
- high-energy nuclear physics /
- quantum algorithm /
- scattering amplitude /
- phase structure of nuclear matter
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图 1 变分法制备强子态的量子线路图. 其中量子计算机通过拟设U(θ)来生成试探波函数以及测量试探波函数下
$ E_l(\theta) $ 的值. 经典计算机负责更新和优化参数θFig. 1. Variational quantum algorithm for preparation of the hadronic state. The generation of trial state and the measurement of
$ E_l(\theta) $ are performed on a quantum computer, while the optimization of parameters θ is done with classical computing.图 2 可同时制备吉布斯态和计算自由能的变分算法量子线路图. 在量子计算机中执行的是初始混态的制备和参数化幺正演化
$ U(\phi) $ , 而参数$ (\theta, \phi) $ 的优化通过经典计算机来执行Fig. 2. A pictorial representation of the variational quantum algorithm, which can prepare thermal states and compute the corresponding free energy. The preparation of initial mixed state and the evolution
$ U(\phi) $ are done on a quantum computer, while the optimization of$ (\theta, \phi) $ should be done with a classical computer.图 3 计算动力学两点关联函数量子线路. 在辅助比特上测量
$ \sigma^1 $ 和$ \sigma^2 $ 即可得到关联函数的实部和虚部Fig. 3. Quantum circuit for calculation of the two point correlation function. The real and imaginary part of the correlation function can be obtained by performing measurements of
$ \sigma^1 $ and$ \sigma^2 $ on the auxiliary qubit, respectively.图 11 1+1维单味道NJL模型四点函数
$ G^{\alpha\beta\alpha\beta}_\Psi(p_1, $ $ k_1, k_2) $ 的实部. 其中外腿动量选定为$ k_1=(k_1^0, 0), \, k_2=(0, $ $ \pi/a), \, p_1=(0, 0) $ Fig. 11. Real part of
$ G^{\alpha\beta\alpha\beta}_\Psi(p_1, k_1, k_2) $ in the 1+1-dimensional 1-flavor NJL model as a function of$ k_1^0 a $ , with$ k_1=(k_1^0, 0), \, k_2=(0, \pi/a), \, p_1=(0, 0) $ .图 12 不同背景电场
$ \varepsilon $ 下的弦张力. 其中给定$ m=1, \;g=1,\; \varpi=1 $ ,$ N $ = 6 (a) 弦张力对$ \beta $ 的依赖; (b) 弦张力的对数对温度$ T $ 的依赖Fig. 12. String tensions under different
$ \varepsilon $ in the case$ m=1,\; g=1, \;\varpi=1 $ ,$ N $ = 6: (a) The string tension as a function of the inverse temperature$ \beta $ ; (b) logarithm of the string tension as a function of the temperature$ T $ .图 13 在给定参数
$ \varepsilon=0.5,\; m=1, \;g=1, \;\varpi=1,\; N=6 $ 下的弦张力 (a) 不同化学势 μ下弦张力对温度$ T $ 的依赖; (b) 弦张力对温度$ T $ 和化学势μ的依赖Fig. 13. The string tension in the case
$ \varepsilon=0.5,\; m=1,\; g=1,\; \varpi=1\;, N=6 $ : (a) At different μ, the string tension as a function of the temperature$ T $ ; (b) the string tension as a function of the temperature$ T $ and the chemical potential μ. -
[1] Alexandru A, Basar G, Bedaque P F, Vartak S, Warrington N C 2016 Phys. Rev. Lett. 117 081602
Google Scholar
[2] Troyer M, Wiese U J 2005 Phys. Rev. Lett. 94 170201
Google Scholar
[3] Feynman R P 1982 Int. J. Theor. Phys. 21 467
Google Scholar
[4] Jordan S P, Lee K S M, Preskill J 2012 Science 336 1130
Google Scholar
[5] Lamm H, Lawrence S, Yamauchi Y 2020 Phys. Rev. Res. 2 013272
Google Scholar
[6] Mueller N, Tarasov A, Venugopalan R 2020 Phys. Rev. D 102 016007
Google Scholar
[7] Echevarria M G, Egusquiza I L, Rico E, Schnell G 2021 Phys. Rev. D 104 014512
[8] Qian W, Basili R, Pal S, Luecke G, Vary J P 2022 Phys. Rev. Res. 4 043193
Google Scholar
[9] Li T, Guo X, Lai W K, Liu X, Wang E, Xing H, Zhang D B, Zhu S L 2022 Phys. Rev. D 10 5
[10] Li T, Guo X, Lai W K, Liu X, Wang E, Xing H, Zhang D B, Zhu S L 2023 Science China Physics, Mechanics & Astronomy 66 281011
[11] Bauer C W, de Jong W A, Nachman B, Provasoli D 2021 Phys. Rev. Lett. 126 062001
Google Scholar
[12] Bepari K, Malik S, Spannowsky M, Williams S 2022 Phys. Rev. D 106 056002
Google Scholar
[13] Hu Z, Xia R, Kais S 2020 Sci. Rep. 10 3301
Google Scholar
[14] De Jong W A, Metcalf M, Mulligan J, Płoskoń M, Ringer F, Yao X 2021 Phys. Rev. D 104 051501
[15] Yao X 2022 arXiv: 2205.07902 [High Energy Physics-Phenomenology
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[17] de Jong W A, Lee K, Mulligan J, Płoskoń M, Ringer F, Yao X 2022 Phys. Rev. D 106 054508
[18] Briceño R A, Guerrero J V, Hansen M T, Sturzu A M 2021 Phys. Rev. D 103 014506
[19] Li T, Lai W K, Wang E, Xing H 2023 arXiv: 2301.04179 [High Energy Physics - Phenomenology
[20] Martinez E A, Muschik C A, Schindler M, et al. 2016 Nature 534 516
Google Scholar
[21] Atas Y Y, Haase J F, Zhang J, Wei V, Pfaendler S M L, Lewis R, Muschik C A 2022 arXiv: 2207.03473 [Quantum Physics
[22] Czajka A M, Kang Z B, Ma H, Zhao F 2022 JHEP 08 209
[23] Davoudi Z, Mueller N, Powers C 2022 arXiv: 2208.13112 [High Energy Physics - Lattice
[24] Tomiya A 2023 PoS LATTICE2022 039
[25] Czajka A M, Kang Z B, Tee Y, Zhao F 2022 arXiv: 2210.03062 [High Energy Physics - Phenomenology
[26] Xie X D, Guo X, Xing H, Xue Z Y, Zhang D B, Zhu S L 2022 Phys. Rev. D 106 054509
[27] McClean J R, Kimchi-Schwartz M E, Carter J, de Jong W A 2017 Phys. Rev. A 95 042308
Google Scholar
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Google Scholar
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Google Scholar
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[32] Farhi E, Goldstone J, Gutmann S 2014 arXiv: 1411.4028 [Quantum Physics
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Google Scholar
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Google Scholar
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Google Scholar
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[37] Wu J, Hsieh T H 2019 Phys. Rev. Lett 123 220502
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[42] Nielsen M A, Chuang I L 2010 Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge: Cambridge University Press) pp206–208
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[48] Ji X 2014 Sci. China Phys. Mech. Astron. 57 1407
Google Scholar
[49] Ma Y Q, Qiu J W 2018 Phys. Rev. D 98 074021
Google Scholar
[50] Ma Y Q, Qiu J W 2018 Phys. Rev. Lett. 120 022003
Google Scholar
[51] Radyushkin A V 2017 Phys. Rev. D 96 034025
Google Scholar
[52] Orginos K, Radyushkin A, Karpie J, Zafeiropoulos S 2017 Phys. Rev. D 96 094503
[53] Liang J, Draper T, Liu K F, Rothkopf A, Yang Y B 2020 Phys. Rev. D 101 114503
Google Scholar
[54] Chambers A J, Horsley R, Nakamura Y, Perlt H, Rakow P E L, Schierholz G, Schiller A, Somfleth K, Young R D, Zanotti J M 2017 Phys. Rev. Lett. 118 242001
Google Scholar
[55] Sufian R S, Karpie J, Egerer C, Orginos K, Qiu J W, Richards D G 2019 Phys. Rev. D 99 074507
Google Scholar
[56] Izubuchi T, Jin L, Kallidonis C, Karthik N, Mukherjee S, Petreczky P, Shugert C, Syritsyn S 2019 Phys. Rev. D 100 034516
Google Scholar
[57] Lin H W, Chen J W, Fan Z, Zhang J H, Zhang R 2021 Phys. Rev. D 103 014516
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[70] Davoudi Z 2018 PoS LATTICE 2018 014
[71] Hansen M T, Sharpe S R 2019 Ann. Rev. Nucl. Part. Sci. 69 65
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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