基于辅助单比特测量的量子态读取算法

丁晨; 李坦; 张硕; 郭楚; 黄合良; 鲍皖苏

doi:10.7498/aps.70.20211066

摘要

在量子计算过程中, 需要通过量子测量读取计算结果. 然而, 受限于物理实现, 对量子态的测量往往存在较大误差, 直接影响量子计算结果的正确提取, 以及限制量子计算的大规模扩展. 本文针对一种特定形式的量子态, 提出基于辅助单比特测量的量子态间接读取算法, 避免多比特测量带来的大量测量误差. 理论和模拟结果表明, 当所读取的量子态比特数较大时, 该算法相比于直接读取具有更高的正确率, 可用于大规模量子纠错和量子态的高保真度读取.

关键词:

Abstract

Quantum state measurement is essential for reading-out a quantum computing outcome. Meanwhile, the readout results are always affected by the large noise of quantum measurements in physical implementation, which also hinders the large-scale expansion of quantum computing. In light of this, we present an indirect quantum state readout method based on a single ancilla qubit that can avoid the large noise of multiple-qubit measurements. The theoretical analysis and simulations indicate that our method is more robust against the measurement noise and promises to become a method of large-scale quantum error correction and high-fidelity quantum state readout.

Keywords:

作者及机构信息

河南省量子信息与量子密码重点实验室, 郑州　450004

通信作者: 黄合良, quanhhl@ustc.edu.cn ; 鲍皖苏, bws@qiclab.cn

基金项目: 青年人才托举工程 (批准号: 2020-JCJQ-QT-030)、国家自然科学基金(批准号: 11905294, 11805279)、国防科技大学高性能计算国家重点实验室开放课题(批准号: 201901-01)和中国博士后科学基金资助的课题

Authors and contacts

Henan Key Laboratory of Quantum Information and Cryptography, Zhengzhou 450004, China

Corresponding author: Huang He-Liang, quanhhl@ustc.edu.cn ; Bao Wan-Su, bws@qiclab.cn

Funds: Project supported by the Youth Talent Lifting Project, China (Grant No. 2020-JCJQ-QT-030), the National Natural Science Foundation of China (Grant Nos. 11905294, 11805279), the Open Research Fund from State Key Laboratory for High Performance Computing, National University of Defense Technology, China (Grant No. 201901-01), and the China Postdoctoral Science Foundation.

文章全文

参考文献

[1]	Shor P W 1994 Proceedings 35th Annual Symposium Foundations Computer Science Santa Fe, New Mexico, USA, November 20–22, 1994 pp124–134
[2]	Grover L K 1996 Proceedings 28th Annual ACM Symposium Theory Computing Philadelphia, Pennsylvania, USA, May 22–24, 1996 pp212–219
[3]	Harrow A W, Hassidim A, Lloyd S 2009 Phys. Rev. Lett. 103 150502 Google Scholar
[4]	Clarke J, Wilhelm F K 2008 Nature 453 1031 Google Scholar
[5]	Huang H L, Narożniak M, Liang F, Zhao Y, Castellano A D, Gong M, Wu Y, Wang S, Lin J, Xu Y, Deng H, Rong H, Dowling J P, Peng C Z, Byrnes T, Zhu X, Pan J W 2021 Phys. Rev. Lett. 126 090502 Google Scholar
[6]	Huang H L, Wu D, Fan D, Zhu X 2020 Sci. China Inf. Sci. 63 180501 Google Scholar
[7]	Kjaergaard M, Schwartz M E, Braumjller J, Krantz P, Wang J I J, Gustavsson S, Oliver W D 2020 Annu. Rev. Condens. Matter Phys. 11 369 Google Scholar
[8]	Krantz P, Kjaergaard M, Yan F, Orlando T P, Gustavsson S, Oliver W D 2019 Appl. Phys. Rev. 6 021318 Google Scholar
[9]	Gu X, Kockum A F, Miranowicz A, Liu Y X, Nori F 2017 Phys. Rep. 718–719 1 Google Scholar
[10]	Wendin G 2017 Rep. Prog. Phys. 80 106001 Google Scholar
[11]	You J Q, Nori F 2005 Phys. Today 58 42 Google Scholar
[12]	You J Q, Nori F 2011 Nature 474 589 Google Scholar
[13]	Nation P D, Johansson J R, Blencowe M P, Nori F 2012 Rev. Mod. Phys. 84 1 Google Scholar
[14]	O’Brien J L, Furusawa A, Vučković J 2009 Nat. Photonics 3 687 Google Scholar
[15]	Liu C, Huang H L, Chen C, Wang B Y, Wang X L, Yang T, Li L, Liu N L, Dowling J P, Byrnes T, Lu C Y, Pan J W 2019 Optica 6 264 Google Scholar
[16]	Huang H L, Luo Y H, Bai B, Deng Y H, Wang H, Zhao Q, Zhong H S, Nie Y Q, Jiang W H, Wang X L, Zhang J, Li L, Liu N L, Byrnes T, Dowling J P, Lu C Y, Pan J W 2019 Phys. Rev. A 100 012114 Google Scholar
[17]	Huang H L, Bao W S, Guo C 2019 Phys. Rev. A 100 032305 Google Scholar
[18]	Huang H L, Wang X L, Rohde P P, Luo Y H, Zhao Y W, Liu C, Li L, Liu N L, Lu C Y, Pan J W 2018 Optica 5 193 Google Scholar
[19]	Wang X L, Luo Y H, Huang H L, Chen M C, Su Z E, Liu C, Chen C, Li W, Fang Y Q, Jiang X, Zhang J, Li L, Liu N L, Lu C Y, Pan J W 2018 Phys. Rev. Lett. 120 260502 Google Scholar
[20]	Huang H L, Zhong H S, Li T, Li F G, Fu X Q, Zhang S, Wang X, Bao W S 2017 Sci. Rep. 7 15265 Google Scholar
[21]	Huang H L, Bao W S, Li T, Li F G, Fu X Q, Zhang S, Zhang H L, Wang X 2017 Phys. Lett. A 381 2673 Google Scholar
[22]	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 11 361 Google Scholar
[23]	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 190501 Google Scholar
[24]	Wang X L, Chen L K, Li W, Huang H L, Liu C, Chen C, Luo Y H, Su Z E, Wu D, Li Z D, Lu H, Hu Y, Jiang X, Peng C Z, Li L, Liu N L, Chen Y A, Lu C Y, Pan J W 2016 Phys. Rev. Lett. 117 210502 Google Scholar
[25]	Häffner H, Roos C F, Blatt R 2008 Phys. Rep. 469 155 Google Scholar
[26]	Kane B E 1998 Nature 393 133 Google Scholar
[27]	He Y, Gorman S K, Keith D, Kranz L, Keizer J G, Simmons M Y 2019 Nature 571 371 Google Scholar
[28]	Bloch I 2008 Nature 453 1016 Google Scholar
[29]	Arute F, Arya K, Babbush R, et al. 2019 Nature 574 505 Google Scholar
[30]	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 1460 Google Scholar
[31]	Guo C, Zhao Y, Huang H L 2021 Phys. Rev. Lett. 126 070502 Google Scholar
[32]	Guo C, Liu Y, Xiong M, Xue S, Fu X, Huang A, Qiang X, Xu P, Liu J, Zheng S, Huang H L, Deng M, Poletti D, Bao W S, Wu J 2019 Phys. Rev. Lett. 123 190501 Google Scholar
[33]	Wu Y, Bao W S, Cao S, Chen F, Chen M C, Chen X, Chung T H, Deng H, Du Y, Fan D, Gong M, Guo C, Guo C, Guo S, Han L, Hong L, Huang H L, Huo Y H, Li L, Li N, Li S, Li Y, Liang F, Lin C, Lin J, Qian H, Qiao D, Rong H, Su H, Sun L, Wang L, Wang S, Wu D, Xu Y, Yan K, Yang W, Yang Y, Ye Y, Yin J, Ying C, Yu J, Zha C, Zhang C, Zhang H, Zhang K, Zhang Y, Zhao H, Zhao Y, Zhou L, Zhu Q, Lu C Y, Peng C Z, Zhu X, Pan J W 2021 arXiv2106.14734[quant-ph]
[34]	Liu Y, Wang D, Xue S, Huang A, Fu X, Qiang X, Xu P, Huang H L, Deng M, Guo C, Yang X, Wu J 2020 Phys. Rev. A 101 052316 Google Scholar
[35]	Huang H L, Du Y, Gong M, Zhao Y, Wu Y, Wang C, Li S, Liang F, Lin J, Xu Y, Yang R, Liu T, Hsieh M H, Deng H, Rong H, Peng C Z, Lu C Y, Chen Y A, Tao D, Zhu X, Pan J W 2021 Phys. Rev. Appl. 16 024051
[36]	Liu J, Lim K H, Wood K L, Huang W, Guo C, Huang H L 2021 Sci. China-Phys. Mech. Astron. 64 290311 Google Scholar
[37]	Huang H L, Zhao Q, Ma X, Liu C, Su Z E, Wang X L, Li L, Liu N L, Sanders B C, Lu C Y, Pan J W 2017 Phys. Rev. Lett. 119 050503 Google Scholar
[38]	Huang H L, Bao W S, Li T, Li F G, Fu X Q, Zhang S, Zhang H L, Wang X 2017 Quantum Inf. Proc. 16 199 Google Scholar
[39]	Huang H L, nad Tan Li Y W Z, Li F G, Du Y T, Fu X Q, Zhang S, Wang X, Bao W S 2017 Front. Phys. 12 120305 Google Scholar
[40]	Abraham H, Akhalwaya I Y, Aleksandrowicz G, et al. 2019 Qiskit: An Open-source Framework for Quantum Computing

施引文献

图 1 两个算法随机读取多比特量子态的平均正确概率. 在左图中, 测量噪声$\eta$固定为0.05, 研究平均正确概率随测量噪声n的变化. 在右图中, 比特数n固定为3, 研究平均正确概率随测量噪声$\eta$的变化. 平均正确概率的计算方法为随机抽取1000个量子态计算对应的$P_1$和$P_2$, 并取平均

Fig. 1. Average probability of correctness of the two algorithms reading a n-qubit quantum state. In the left subgraph, the number of qubits is 3, and we investigate the dependence of average probability of correctness on the readout noise $\eta$. In the right subgraph, the readout noise $\eta=0.05$, and we investigate the dependence of average probability of correctness on the number of qubits. The values of average probability of correctness are calculated as the average of $P_1$ and $P_2$ on 1000 reading instances.

下载: 全尺寸图片幻灯片

图 2 两个算法在多种情况下的正确率比较. 其中实线是正确率, 色带是95%置信区间. 图例中, direct代表直接测量, our代表算法2

Fig. 2. Correctness rates of two algorithms under multiple circumstances. In the graph, the lines represent the correctness rates while the bands represent the 95% confidence intervals. In the legend, “direct” represents the direct method, “our” represents Alg. 2

下载: 全尺寸图片幻灯片

[1]	Shor P W 1994 Proceedings 35th Annual Symposium Foundations Computer Science Santa Fe, New Mexico, USA, November 20–22, 1994 pp124–134
[2]	Grover L K 1996 Proceedings 28th Annual ACM Symposium Theory Computing Philadelphia, Pennsylvania, USA, May 22–24, 1996 pp212–219
[3]	Harrow A W, Hassidim A, Lloyd S 2009 Phys. Rev. Lett. 103 150502 Google Scholar
[4]	Clarke J, Wilhelm F K 2008 Nature 453 1031 Google Scholar
[5]	Huang H L, Narożniak M, Liang F, Zhao Y, Castellano A D, Gong M, Wu Y, Wang S, Lin J, Xu Y, Deng H, Rong H, Dowling J P, Peng C Z, Byrnes T, Zhu X, Pan J W 2021 Phys. Rev. Lett. 126 090502 Google Scholar
[6]	Huang H L, Wu D, Fan D, Zhu X 2020 Sci. China Inf. Sci. 63 180501 Google Scholar
[7]	Kjaergaard M, Schwartz M E, Braumjller J, Krantz P, Wang J I J, Gustavsson S, Oliver W D 2020 Annu. Rev. Condens. Matter Phys. 11 369 Google Scholar
[8]	Krantz P, Kjaergaard M, Yan F, Orlando T P, Gustavsson S, Oliver W D 2019 Appl. Phys. Rev. 6 021318 Google Scholar
[9]	Gu X, Kockum A F, Miranowicz A, Liu Y X, Nori F 2017 Phys. Rep. 718–719 1 Google Scholar
[10]	Wendin G 2017 Rep. Prog. Phys. 80 106001 Google Scholar
[11]	You J Q, Nori F 2005 Phys. Today 58 42 Google Scholar
[12]	You J Q, Nori F 2011 Nature 474 589 Google Scholar
[13]	Nation P D, Johansson J R, Blencowe M P, Nori F 2012 Rev. Mod. Phys. 84 1 Google Scholar
[14]	O’Brien J L, Furusawa A, Vučković J 2009 Nat. Photonics 3 687 Google Scholar
[15]	Liu C, Huang H L, Chen C, Wang B Y, Wang X L, Yang T, Li L, Liu N L, Dowling J P, Byrnes T, Lu C Y, Pan J W 2019 Optica 6 264 Google Scholar
[16]	Huang H L, Luo Y H, Bai B, Deng Y H, Wang H, Zhao Q, Zhong H S, Nie Y Q, Jiang W H, Wang X L, Zhang J, Li L, Liu N L, Byrnes T, Dowling J P, Lu C Y, Pan J W 2019 Phys. Rev. A 100 012114 Google Scholar
[17]	Huang H L, Bao W S, Guo C 2019 Phys. Rev. A 100 032305 Google Scholar
[18]	Huang H L, Wang X L, Rohde P P, Luo Y H, Zhao Y W, Liu C, Li L, Liu N L, Lu C Y, Pan J W 2018 Optica 5 193 Google Scholar
[19]	Wang X L, Luo Y H, Huang H L, Chen M C, Su Z E, Liu C, Chen C, Li W, Fang Y Q, Jiang X, Zhang J, Li L, Liu N L, Lu C Y, Pan J W 2018 Phys. Rev. Lett. 120 260502 Google Scholar
[20]	Huang H L, Zhong H S, Li T, Li F G, Fu X Q, Zhang S, Wang X, Bao W S 2017 Sci. Rep. 7 15265 Google Scholar
[21]	Huang H L, Bao W S, Li T, Li F G, Fu X Q, Zhang S, Zhang H L, Wang X 2017 Phys. Lett. A 381 2673 Google Scholar
[22]	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 11 361 Google Scholar
[23]	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 190501 Google Scholar
[24]	Wang X L, Chen L K, Li W, Huang H L, Liu C, Chen C, Luo Y H, Su Z E, Wu D, Li Z D, Lu H, Hu Y, Jiang X, Peng C Z, Li L, Liu N L, Chen Y A, Lu C Y, Pan J W 2016 Phys. Rev. Lett. 117 210502 Google Scholar
[25]	Häffner H, Roos C F, Blatt R 2008 Phys. Rep. 469 155 Google Scholar
[26]	Kane B E 1998 Nature 393 133 Google Scholar
[27]	He Y, Gorman S K, Keith D, Kranz L, Keizer J G, Simmons M Y 2019 Nature 571 371 Google Scholar
[28]	Bloch I 2008 Nature 453 1016 Google Scholar
[29]	Arute F, Arya K, Babbush R, et al. 2019 Nature 574 505 Google Scholar
[30]	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 1460 Google Scholar
[31]	Guo C, Zhao Y, Huang H L 2021 Phys. Rev. Lett. 126 070502 Google Scholar
[32]	Guo C, Liu Y, Xiong M, Xue S, Fu X, Huang A, Qiang X, Xu P, Liu J, Zheng S, Huang H L, Deng M, Poletti D, Bao W S, Wu J 2019 Phys. Rev. Lett. 123 190501 Google Scholar
[33]	Wu Y, Bao W S, Cao S, Chen F, Chen M C, Chen X, Chung T H, Deng H, Du Y, Fan D, Gong M, Guo C, Guo C, Guo S, Han L, Hong L, Huang H L, Huo Y H, Li L, Li N, Li S, Li Y, Liang F, Lin C, Lin J, Qian H, Qiao D, Rong H, Su H, Sun L, Wang L, Wang S, Wu D, Xu Y, Yan K, Yang W, Yang Y, Ye Y, Yin J, Ying C, Yu J, Zha C, Zhang C, Zhang H, Zhang K, Zhang Y, Zhao H, Zhao Y, Zhou L, Zhu Q, Lu C Y, Peng C Z, Zhu X, Pan J W 2021 arXiv2106.14734[quant-ph]
[34]	Liu Y, Wang D, Xue S, Huang A, Fu X, Qiang X, Xu P, Huang H L, Deng M, Guo C, Yang X, Wu J 2020 Phys. Rev. A 101 052316 Google Scholar
[35]	Huang H L, Du Y, Gong M, Zhao Y, Wu Y, Wang C, Li S, Liang F, Lin J, Xu Y, Yang R, Liu T, Hsieh M H, Deng H, Rong H, Peng C Z, Lu C Y, Chen Y A, Tao D, Zhu X, Pan J W 2021 Phys. Rev. Appl. 16 024051
[36]	Liu J, Lim K H, Wood K L, Huang W, Guo C, Huang H L 2021 Sci. China-Phys. Mech. Astron. 64 290311 Google Scholar
[37]	Huang H L, Zhao Q, Ma X, Liu C, Su Z E, Wang X L, Li L, Liu N L, Sanders B C, Lu C Y, Pan J W 2017 Phys. Rev. Lett. 119 050503 Google Scholar
[38]	Huang H L, Bao W S, Li T, Li F G, Fu X Q, Zhang S, Zhang H L, Wang X 2017 Quantum Inf. Proc. 16 199 Google Scholar
[39]	Huang H L, nad Tan Li Y W Z, Li F G, Du Y T, Fu X Q, Zhang S, Wang X, Bao W S 2017 Front. Phys. 12 120305 Google Scholar
[40]	Abraham H, Akhalwaya I Y, Aleksandrowicz G, et al. 2019 Qiskit: An Open-source Framework for Quantum Computing

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基于辅助单比特测量的量子态读取算法