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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.
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Keywords:
- quantum computing /
- quantum measurement /
- quantum state readout
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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Figure 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.
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
Figure 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
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[1] [2] [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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