搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

光源相位噪声对高斯玻色采样的影响

覃俭

引用本文:
Citation:

光源相位噪声对高斯玻色采样的影响

覃俭

Investigation of Gaussian boson sampling under phase noise of the light source

Qin Jian
PDF
HTML
导出引用
  • 高斯玻色采样是实现量子计算优势的主要途径之一, 同时也有望应用于加速稠密子图、量子化学等问题. 然而, 实验中必不可少的噪声却可能阻碍高斯玻色采样的量子优势. 此前的研究主要关注于光子损失和光子非全同噪声. 本文通过数值模拟研究了另一种噪声—光源相位噪声对高斯玻色采样的影响. 采用蒙特卡罗方法近似计算相位噪声下高斯玻色采样的输出概率分布, 发现随着探测光子数的增加, 相位噪声带来的误差逐渐加大. 同时, 相位噪声会导致采样出大概率样本的能力, 即HOG (heavy output generation)值显著降低. 最后发现, 在输入平均光子数相同时, 有光子损失的高斯玻色采样相比无损失情形对于相位噪声有更大的容忍性. 本文的研究有助于大规模高斯玻色采样中更好地抑制相位噪声.
    Gaussian boson sampling is one of the main promising approaches to realizing the quantum computational advantage, which also offers potential applications such as in dense subgraphs problem and quantum chemistry. However, the inevitable noise in experiment may weaken the quantum advantage of Gaussian boson sampling. Photon loss and photon partial indistinguishability are two major sources of noise. Their influence on the complexity of Gaussian boson sampling has been extensively studied in previous work. However, the phase noise of the input light source, a noise which is suitable for tailored for Gaussian boson sampling, has not been studied so far. Here, we investigate the phase noise of the input light source in Gaussian boson sampling through numerical simulation. We use the Monte Carlo method to calculate the output probability distribution under phase noise approximately. It is found that the phase noise of the light source can cause the input state to change from a Gaussian state into a non-Gaussian mixed state. For a given phase noise level, the fidelity of the non-Gaussian mixed state and the noise-free ideal state decreases monotonically as the mean photon number of input increases. Meanwhile, owing to the phase noise the deviation of the output probability distribution gradually increases with the number of detected photons increasing. Furthermore, the phase noise results in the capability of heavy sample generation (HOG), significantly decreasing. Finally, it is found that Gaussian boson sampling with photon loss is more tolerant to phase noise than the lossless case given that the mean photon number of input is the same. Our study is helpful in suppressing the phase noise in large-scale Gaussian boson sampling experiments.
      通信作者: 覃俭, qj1993@mail.ustc.edu.cn
    • 基金项目: 国家重点研发计划(批准号: 2019YFA0308700)和上海市市级科技重大专项(批准号: 2019SHZDZX01)资助的课题
      Corresponding author: Qin Jian, qj1993@mail.ustc.edu.cn
    • Funds: Project supported by the National Key R&D Program of China (Grant No. 2019YFA0308700) and the Shanghai Municipal Science and Technology Major Project, China (Grant No. 2019SHZDZX01)
    [1]

    Harrow A W, Montanaro A 2017 Nature 549 203Google Scholar

    [2]

    Aaronson S, Arkhipov A 2011 Proceedings of the Forty-third Annual ACM Symposium on Theory of Computing New York, USA, June 6, 2011 p333

    [3]

    Broome M A, Fedrizzi A, Rahimi-Keshari S, Dove J, Aaronson S, Ralph T C, White A G 2013 Science 339 794Google Scholar

    [4]

    Spring J B, Metcalf B J, Humphreys P C, Kolthammer W S, Jin X M, Barbieri M, Datta A, Thomas-Peter N, Langford N K, Kundys D, Gates J C, Smith B J, Smith P G R, Walmsley I A 2013 Science 339 798Google Scholar

    [5]

    Crespi A, Osellame R, Ramponi R, Brod D J, Galvão E F, Spagnolo N, Vitelli C, Maiorino E, Mataloni P, Sciarrino F 2013 Nat. Photonics 7 545Google Scholar

    [6]

    Wang H, He Y, Li Y H, Su Z E, Li B, Huang H L, Ding X, Chen M C, Liu C, Qin J, Li J P, He Y M, Schneider C, Kamp M, Peng C Z, Höfling S, Lu C Y, Pan J W 2017 Nat. Photonics 11 361Google Scholar

    [7]

    He Y, Ding X, Su Z E, Huang H L, Qin J, Wang C, Unsleber S, Chen C, Wang H, He Y M, Wang X L, Zhang W J, Chen S J, Schneider C, Kamp M, You L X, Wang Z, Höfling S, Lu C Y, Pan J W 2017 Phys. Rev. Lett. 118 190501Google Scholar

    [8]

    Wang H, Li W, Jiang X, He Y M, Li Y H, Ding X, Chen M C, Qin J, Peng C Z, Schneider C, Kamp M, Zhang W J, Li H, You L X, Wang Z, Dowling J P, Höfling S, Lu C Y, Pan J W 2018 Phys. Rev. Lett. 120 230502Google Scholar

    [9]

    Zhong H S, Peng L C, Li Y, Hu Y, Li W, Qin J, Wu D, Zhang W, Li H, Zhang L, Wang Z, You L, Jiang X, Li L, Liu N L, Dowling J P, Lu C Y, Pan J W 2019 Sci. Bull. 64 511Google Scholar

    [10]

    Wang H, Qin J, Ding X, Chen M C, Chen S, You X, He Y M, Jiang X, You L, Wang Z, Schneider C, Renema J J, Höfling S, Lu C Y, Pan J W 2019 Phys. Rev. Lett. 123 250503Google Scholar

    [11]

    Walschaers M, Kuipers J, Urbina J D, Mayer K, Tichy M C, Richter K, Buchleitner A 2016 New J. Phys. 18 032001Google Scholar

    [12]

    Spagnolo N, Vitelli C, Bentivegna M, Brod D J, Crespi A, Flamini F, Giacomini S, Milani G, Ramponi R, Mataloni P, Osellame R, Galvão E F, Sciarrino F 2014 Nat. Photonics 8 615Google Scholar

    [13]

    Aaronson S, Brod D J 2016 Phys. Rev. A 93 012335Google Scholar

    [14]

    Renema J J, Menssen A, Clements W R, Triginer G, Kolthammer W S, Walmsley I A 2018 Phys. Rev. Lett. 120 220502Google Scholar

    [15]

    Shchesnovich V S 2019 Phys. Rev. A 100 012340Google Scholar

    [16]

    Qi H, Brod D J, Quesada N, García-Patrón R 2020 Phys. Rev. Lett. 124 100502Google Scholar

    [17]

    Lund A P, Laing A, Rahimi-Keshari S, Rudolph T, O’Brien J L, Ralph T C 2014 Phys. Rev. Lett. 113 100502Google Scholar

    [18]

    Hamilton C S, Kruse R, Sansoni L, Barkhofen S, Silberhorn C, Jex I 2017 Phys. Rev. Lett. 119 170501Google Scholar

    [19]

    Deshpande A, Mehta A, Vincent T, Quesada N, Hinsche M, Ioannou M, Madsen L, Lavoie J, Qi H, Eisert J, Hangleiter D, Fefferman B, Dhand I 2022 Sci. Adv. 8 eabi7894Google Scholar

    [20]

    Zhong H S, Wang H, Deng Y H, Chen M C, Peng L C, Luo Y H, Qin J, Wu D, Ding X, Hu Y, Hu P, Yang X Y, Zhang W J, Li H, Li Y, Jiang X, Gan L, Yang G, You L, Wang Z, Li L, Liu N L, Lu C Y, Pan J W 2020 Science 370 1460Google Scholar

    [21]

    Zhong H S, Deng Y H, Qin J, Wang H, Chen M C, Peng L C, Luo Y H, Wu D, Gong S Q, Su H, Hu Y, Hu P, Yang X Y, Zhang W J, Li H, Li Y, Jiang X, Gan L, Yang G, You L, Wang Z, Li L, Liu N L, Renema J J, Lu C Y, Pan J W 2021 Phys. Rev. Lett. 127 180502Google Scholar

    [22]

    Madsen L S, Laudenbach F, Askarani M Falamarzi, Rortais F, Vincent T, Bulmer J F F, Miatto F M, Neuhaus L, Helt L G, Collins M J, Lita A E, Gerrits T, Nam S W, Vaidya V D, Menotti M, Dhand I, Vernon Z, Quesada N, Lavoie J 2022 Nature 606 75Google Scholar

    [23]

    Bulmer J F F, Bell B A, Chadwick R S, Jones A E, Moise D, Rigazzi A, Thorbecke J, Haus U U, Van Vaerenbergh T, Patel R B, Walmsley I A, Laing A 2022 Sci. Adv. 8 eabl9236Google Scholar

    [24]

    Oh C, Lim Y, Fefferman B, Jiang L 2022 Phys. Rev. Lett. 128 190501Google Scholar

    [25]

    Mandel L 1986 Phys. Scr. 1986 34Google Scholar

    [26]

    Campos R A, Saleh B E, Teich M C 1989 Phys. Rev. A 40 1371Google Scholar

    [27]

    Arrazola J M, Bromley T R 2018 Phys. Rev. Lett. 121 030503Google Scholar

    [28]

    Banchi L, Fingerhuth M, Babej T, Ing C, Arrazola J M 2020 Sci. Adv. 6 eaax1950Google Scholar

  • 图 1  不同相位噪声下单模压缩真空态的Wigner函数

    Fig. 1.  Wigner function of single-mode squeezed vacuum state under different phase noise

    图 2  相位噪声压缩态和理想态的保真度 (a)不同单模平均光子数$ \bar{n} $下保真度随噪声大小σ的变化; (b)输入压缩态个数$ K = 100 $时, 总保真度随$ \bar{n} $σ的变化

    Fig. 2.  Fidelity between squeezed state under phase noise and the ideal state: (a) Fidelity as a function of phase noise level σ under different single-mode mean photon number $ \bar{n} $; (b) when the number of input squeezed states is $ K = 100 $, the total fidelity as a function of $ \bar{n} $ and σ.

    图 3  相位噪声对输出概率分布的影响 (a)不同相位噪声下, 噪声输出分布和理想分布的海林格距离随探测光子数的变化, 图中每个点代表10个随机干涉网络结果的均值; (b)光子数$ k = 8 $时, 典型的相位噪声下样本概率和理想样本概率(蓝色曲线)的相对误差的对数曲线(浅红色), 红色曲线为浅红色曲线的步长为15的移动平均值, 相位噪声$ \sigma = 0.8 $; (c) $ \Delta {\rm HOG} $随相位噪声大小的变化; 图(a)—(c)采用的参数为输入压缩态个数$ K = 5 $, 单模平均光子数$ \bar{n} = 1 $, 模式数$ m = 9 $

    Fig. 3.  Effect of phase noise on output probability distribution: (a) Hellinger distance of phase noisy distribution and ideal distribution as a function of total detected photon number k under different noise level, each point is the mean result of 10 random choosed interferometer; (b) logarithmic curve (light red) of relative error of noisy sample probability and ideal sample probability (blue curve), the red curve is the 15-point moving mean of light red curve, phase noise $ \sigma = 0.8 $; (c) $ \Delta {\rm HOG} $ as a function of phase noise. In panels (a)−(c), the number of input squeezed states is $ K = 5 $, the single-mode mean photon number is $ \bar{n} = 1 $, the mode number is $ m = 9 $

    图 4  光子损失的影响, 保持输入平均光子数$ \bar{n} = 1 $不变 (a)不同光子损耗η下保真度和相位噪声大小的关系; (b)在相位噪声$ \sigma = 0.8 $时, 比较有光子损失$ \eta = 0.7 $情形(蓝色点)和无光子损失(红色点)下噪声分布和理想分布的海林格距离, 可以看出有损耗时海林格距离显著降低了

    Fig. 4.  The effect of photon loss. Keeping the mean photon number $ \bar{n} = 1 $ unchanged: (a) Relationship between fidelity and phase noise under different photon losses; (b) for $ \sigma = 0.8 $, comparing the Hellinger distance of phase noisy distribution and the ideal distribution with photon loss $ \eta = 0.7 $ (blue point) and without photon loss (red point). The Hellinger distance is significantly lower with the photon loss case

  • [1]

    Harrow A W, Montanaro A 2017 Nature 549 203Google Scholar

    [2]

    Aaronson S, Arkhipov A 2011 Proceedings of the Forty-third Annual ACM Symposium on Theory of Computing New York, USA, June 6, 2011 p333

    [3]

    Broome M A, Fedrizzi A, Rahimi-Keshari S, Dove J, Aaronson S, Ralph T C, White A G 2013 Science 339 794Google Scholar

    [4]

    Spring J B, Metcalf B J, Humphreys P C, Kolthammer W S, Jin X M, Barbieri M, Datta A, Thomas-Peter N, Langford N K, Kundys D, Gates J C, Smith B J, Smith P G R, Walmsley I A 2013 Science 339 798Google Scholar

    [5]

    Crespi A, Osellame R, Ramponi R, Brod D J, Galvão E F, Spagnolo N, Vitelli C, Maiorino E, Mataloni P, Sciarrino F 2013 Nat. Photonics 7 545Google Scholar

    [6]

    Wang H, He Y, Li Y H, Su Z E, Li B, Huang H L, Ding X, Chen M C, Liu C, Qin J, Li J P, He Y M, Schneider C, Kamp M, Peng C Z, Höfling S, Lu C Y, Pan J W 2017 Nat. Photonics 11 361Google Scholar

    [7]

    He Y, Ding X, Su Z E, Huang H L, Qin J, Wang C, Unsleber S, Chen C, Wang H, He Y M, Wang X L, Zhang W J, Chen S J, Schneider C, Kamp M, You L X, Wang Z, Höfling S, Lu C Y, Pan J W 2017 Phys. Rev. Lett. 118 190501Google Scholar

    [8]

    Wang H, Li W, Jiang X, He Y M, Li Y H, Ding X, Chen M C, Qin J, Peng C Z, Schneider C, Kamp M, Zhang W J, Li H, You L X, Wang Z, Dowling J P, Höfling S, Lu C Y, Pan J W 2018 Phys. Rev. Lett. 120 230502Google Scholar

    [9]

    Zhong H S, Peng L C, Li Y, Hu Y, Li W, Qin J, Wu D, Zhang W, Li H, Zhang L, Wang Z, You L, Jiang X, Li L, Liu N L, Dowling J P, Lu C Y, Pan J W 2019 Sci. Bull. 64 511Google Scholar

    [10]

    Wang H, Qin J, Ding X, Chen M C, Chen S, You X, He Y M, Jiang X, You L, Wang Z, Schneider C, Renema J J, Höfling S, Lu C Y, Pan J W 2019 Phys. Rev. Lett. 123 250503Google Scholar

    [11]

    Walschaers M, Kuipers J, Urbina J D, Mayer K, Tichy M C, Richter K, Buchleitner A 2016 New J. Phys. 18 032001Google Scholar

    [12]

    Spagnolo N, Vitelli C, Bentivegna M, Brod D J, Crespi A, Flamini F, Giacomini S, Milani G, Ramponi R, Mataloni P, Osellame R, Galvão E F, Sciarrino F 2014 Nat. Photonics 8 615Google Scholar

    [13]

    Aaronson S, Brod D J 2016 Phys. Rev. A 93 012335Google Scholar

    [14]

    Renema J J, Menssen A, Clements W R, Triginer G, Kolthammer W S, Walmsley I A 2018 Phys. Rev. Lett. 120 220502Google Scholar

    [15]

    Shchesnovich V S 2019 Phys. Rev. A 100 012340Google Scholar

    [16]

    Qi H, Brod D J, Quesada N, García-Patrón R 2020 Phys. Rev. Lett. 124 100502Google Scholar

    [17]

    Lund A P, Laing A, Rahimi-Keshari S, Rudolph T, O’Brien J L, Ralph T C 2014 Phys. Rev. Lett. 113 100502Google Scholar

    [18]

    Hamilton C S, Kruse R, Sansoni L, Barkhofen S, Silberhorn C, Jex I 2017 Phys. Rev. Lett. 119 170501Google Scholar

    [19]

    Deshpande A, Mehta A, Vincent T, Quesada N, Hinsche M, Ioannou M, Madsen L, Lavoie J, Qi H, Eisert J, Hangleiter D, Fefferman B, Dhand I 2022 Sci. Adv. 8 eabi7894Google Scholar

    [20]

    Zhong H S, Wang H, Deng Y H, Chen M C, Peng L C, Luo Y H, Qin J, Wu D, Ding X, Hu Y, Hu P, Yang X Y, Zhang W J, Li H, Li Y, Jiang X, Gan L, Yang G, You L, Wang Z, Li L, Liu N L, Lu C Y, Pan J W 2020 Science 370 1460Google Scholar

    [21]

    Zhong H S, Deng Y H, Qin J, Wang H, Chen M C, Peng L C, Luo Y H, Wu D, Gong S Q, Su H, Hu Y, Hu P, Yang X Y, Zhang W J, Li H, Li Y, Jiang X, Gan L, Yang G, You L, Wang Z, Li L, Liu N L, Renema J J, Lu C Y, Pan J W 2021 Phys. Rev. Lett. 127 180502Google Scholar

    [22]

    Madsen L S, Laudenbach F, Askarani M Falamarzi, Rortais F, Vincent T, Bulmer J F F, Miatto F M, Neuhaus L, Helt L G, Collins M J, Lita A E, Gerrits T, Nam S W, Vaidya V D, Menotti M, Dhand I, Vernon Z, Quesada N, Lavoie J 2022 Nature 606 75Google Scholar

    [23]

    Bulmer J F F, Bell B A, Chadwick R S, Jones A E, Moise D, Rigazzi A, Thorbecke J, Haus U U, Van Vaerenbergh T, Patel R B, Walmsley I A, Laing A 2022 Sci. Adv. 8 eabl9236Google Scholar

    [24]

    Oh C, Lim Y, Fefferman B, Jiang L 2022 Phys. Rev. Lett. 128 190501Google Scholar

    [25]

    Mandel L 1986 Phys. Scr. 1986 34Google Scholar

    [26]

    Campos R A, Saleh B E, Teich M C 1989 Phys. Rev. A 40 1371Google Scholar

    [27]

    Arrazola J M, Bromley T R 2018 Phys. Rev. Lett. 121 030503Google Scholar

    [28]

    Banchi L, Fingerhuth M, Babej T, Ing C, Arrazola J M 2020 Sci. Adv. 6 eaax1950Google Scholar

  • [1] 邢雪燕, 李霞霞, 陈宇辉, 张向东. 基于光子晶体微腔的回波光量子存储. 物理学报, 2022, 71(11): 114201. doi: 10.7498/aps.71.20220083
    [2] 周湃, 李霞霞, 邢雪燕, 陈宇辉, 张向东. 基于掺铒晶体的光量子存储和调控. 物理学报, 2022, 71(6): 064203. doi: 10.7498/aps.71.20211803
    [3] 周文豪, 王耀, 翁文康, 金贤敏. 集成光量子计算的研究进展. 物理学报, 2022, 71(24): 240302. doi: 10.7498/aps.71.20221782
    [4] 范思晨, 杨帆, 阮军. 蓝宝石谐振体内的回音壁模电磁场分布. 物理学报, 2022, 71(23): 234101. doi: 10.7498/aps.71.20221156
    [5] 邢泽宇, 李志浩, 冯田峰, 周晓祺. 光量子芯片中级联移相器的快速标定方法. 物理学报, 2021, 70(18): 184207. doi: 10.7498/aps.70.20210401
    [6] 周湃, 李霞霞, 邢雪燕, 陈宇辉, 张向东. 基于掺铒晶体的光量子存储和调控. 物理学报, 2021, (): . doi: 10.7498/aps.70.20211803
    [7] 邵晓东, 韩海年, 魏志义. 基于光学频率梳的超低噪声微波频率产生. 物理学报, 2021, 70(13): 134204. doi: 10.7498/aps.70.20201925
    [8] 孙太平, 吴玉椿, 郭国平. 量子生成模型. 物理学报, 2021, 70(14): 140304. doi: 10.7498/aps.70.20210930
    [9] 张茜, 李萌, 龚旗煌, 李焱. 飞秒激光直写光量子逻辑门. 物理学报, 2019, 68(10): 104205. doi: 10.7498/aps.68.20190024
    [10] 姜海峰. 超稳光生微波源研究进展. 物理学报, 2018, 67(16): 160602. doi: 10.7498/aps.67.20180751
    [11] 项晓, 王少锋, 侯飞雁, 权润爱, 翟艺伟, 王盟盟, 周聪华, 许冠军, 董瑞芳, 刘涛, 张首刚. 利用共振无源腔分析和抑制飞秒脉冲激光噪声的理论和实验研究. 物理学报, 2016, 65(13): 134203. doi: 10.7498/aps.65.134203
    [12] 王亚东, 甘雪涛, 俱沛, 庞燕, 袁林光, 赵建林. 利用非传统螺旋相位调控高阶涡旋光束的拓扑结构. 物理学报, 2015, 64(3): 034204. doi: 10.7498/aps.64.034204
    [13] 刘志民, 赵谡玲, 徐征, 高松, 杨一帆. 红光量子点掺杂PVK体系的发光特性研究. 物理学报, 2014, 63(9): 097302. doi: 10.7498/aps.63.097302
    [14] 丁学利, 李玉叶. 相位噪声诱发神经放电的单次或两次相干共振. 物理学报, 2014, 63(24): 248701. doi: 10.7498/aps.63.248701
    [15] 刘丽想, 董丽娟, 刘艳红, 杨成全, 石云龙. 含特异材料的光量子阱频率特性研究. 物理学报, 2012, 61(13): 134210. doi: 10.7498/aps.61.134210
    [16] 陈伟, 孟洲, 周会娟, 罗洪. 远程干涉型光纤传感系统的非线性相位噪声分析. 物理学报, 2012, 61(18): 184210. doi: 10.7498/aps.61.184210
    [17] 冯明明, 秦小林, 周春源, 熊 利, 丁良恩. 偏振光量子随机源. 物理学报, 2003, 52(1): 72-76. doi: 10.7498/aps.52.72
    [18] 廖静, 梁创, 魏亚军, 吴令安, 潘少华, 姚德成. 基于光量子的真随机源. 物理学报, 2001, 50(3): 467-472. doi: 10.7498/aps.50.467
    [19] 刘文森, 马桂荣, 张九安, 梁九卿. 量子玻色流体中的压缩玻色子对数态. 物理学报, 1997, 46(9): 1699-1709. doi: 10.7498/aps.46.1699
    [20] 王之江. 红宝石光量子放大器. 物理学报, 1964, 20(1): 63-71. doi: 10.7498/aps.20.63
计量
  • 文章访问数:  2485
  • PDF下载量:  84
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-09-09
  • 修回日期:  2022-11-21
  • 上网日期:  2023-01-05
  • 刊出日期:  2023-03-05

/

返回文章
返回