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SCIENTIA SINICA Physica, Mechanica & Astronomica, Volume 50 , Issue 9 : 090003(2020) https://doi.org/10.1360/SSPMA-2020-0158

Application of CS in weak signal quantum measurement and protein structure calculation

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  • ReceivedMay 3, 2020
  • AcceptedJun 15, 2020
  • PublishedAug 10, 2020
PACS numbers

Abstract


Funded by

国家自然科学基金(11675014)


Acknowledgment

感谢中国科学院国家空间科学中心翟光杰研究员、刘雪峰和姚旭日副研究员等仪器专项中所有合作者的帮助和支持, 感谢姚旭日副研究员对文章内容的讨论. 感谢张伟、韦仙、柴绪丹和靳晓鹏四位博士生为本文提供素材和整理资料.


References

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  • Figure 1

    (Color online) The picture (a) and schematic diagram (b) of the single photon imaging system.

  • Figure 2

    (Color online) The pseudo-color image of the “BIT” under extremely weak signal. The resolution is 1024×79, and the photon energy for imaging is 0.0387 nJ. There are 1.1006 count/s photons in average in each pixel on DMD.

  • Figure 3

    (Color online) The schematic diagram (a) and prototype equipment (b) for the measurement and imaging system of extremely weak signals.

  • Figure 4

    The schematic diagram on photon counting system.

  • Figure 5

    The reconstructed images of objects at different depths. (a) The reconstructed object “N” at depth of 1.98 m; (b) the reconstructed object “T” at depth of 2.13 m. Reprinted from ref. [39] with permission.

  • Figure 6

    The refined images after the refinement algorithm on Figure 5(a). (a) The refined image at photon counting rate 655 kHz; (b) the refined image at photon counting rate 536 kHz. Reprinted from ref. [39] with permission.

  • Figure 7

    The reconstructed 64×64 images from sparse sampling. (a) The number of “1” in each model is 1000; (b) the number of “1” in each model is 500; (c) the number of “1” in each model is 100; (d) the number of “1” in each model is 50. Reprinted from ref. [39] with permission.

  • Figure 8

    (Color online) The Krawtchouk moments and the reconstructed images of the Peppers and Cameraman at different sampling ratio (KM: Krawtchouk moment; RI: reconstructed image). (a) The image of Peppers; (b) the image of Cameraman. Reprinted from ref. [41] with permission.

  • Figure 9

    The reconstructed results of the interested region at different values of p1 and p2. (a) The original image; (b) p1=0.5, p2=0.5; (c) p1=0.2, p2=0.2; (d) p1=0.2, p2=0.8; (e) p1=0.9, p2=0.1; (f) p1=0.9, p2=0.9. Reprinted from ref. [41] with permission.

  • Figure 10

    (Color online) The schematic diagram of the Krawtchouk-SPI local region photon imaging experiment. Reprinted from ref. [41] with permission.

  • Figure 11

    The single pixel compress imaging experiment. (a) Images reconstructed with Fourier-SPI method; (b) images reconstructed with KM-SPI. Reprinted from ref. [41] with permission.

  • Figure 12

    The simulation result of the parallel compressd sensing with infrared light. (a) Perfect imaging results; (b) imperfect imaging results.

  • Figure 13

    The effects of the random 0, 1 masks and different H matrices on the recovered results under 2% noise. (a) The original image; (b) H matrix is 4×4; (c) H matrix is 6×6.

  • Figure 14

    The effects of the random −1-1 masks and different H matrices on the recovered result under 2% noise. (a) The original image; (b) H matrix is 2×2; (c) H matrix is 6×6.

  • Figure 15

    The simulation results on the simple objects. (a) The original image; (b) H matrix is 4×4; (c) H matrix is 6×6.

  • Figure 16

    (Color online) The simulation result of the dummy objects in real light path. (a) H matrix is 4×4; (b) H matrix is 5×5.

  • Figure 17

    The relation between fidelity and the number of sampling. Reprinted from ref. [45] with permission.

  • Figure 18

    (Color online) The reconstruction of the real part in density matrix, where the sampling ratio is (49×26)/(26)2≈0.7656. Reprinted from ref. [45] with permission.

  • Figure 19

    The reconstructions of the quantum state densities for different qubits. (a)–(c) The MSE values with sampling rate increasing, where the quantum states are GHZ state, Cluster state and W-state from left to right. (d)–(f) The reconstruction time cost with sampling rate increaing, where the quantum states are GHZ state, Cluster state and W-state from left to right. Reprinted from ref. [49] with permission.

  • Figure 20

    The reconstruction of the density matrix with different algorithms. (a), (b) The MSE values with number of qubits increasing, (a) is the GHZ state and (b) is the random states. (c), (d) The reconstruction time cost with number of qubits increaing, (c) is the GHZ state and (d) is the random states. The inset of panel (a) shows the MSE of 3, 4, 5, 6 qubits for Nesterov algorithm at sampling rates 0.3 and 0.6, respectively. The inset of panel (c) is the corresponding time cost. Reprinted from ref. [49] with permission.

  • Figure 21

    (Color online) The density matrix of the 2-qubit Schrödinger cat state (a) and the randomly generated density matrix (b). Reprinted from ref. [52] with permission.

  • Figure 22

    (Color online) The mean squared error (MSE) values at different number of replicas for the unknown quantum states. Reprinted from ref. [52] with permission.

  • Figure 23

    (Color online) The workflow of the NMR protein structure determination.

  • Figure 24

    (Color online) The set and the corresponding distance matrix with six points. (a) The set points; (b) the distance matrix.

  • Figure 25

    (Color online) The superimposition between the original PDB structure (red) and the reconstructed structure (blue) from the ideal distance data. (a) 2M5Z; (b) 1B4R; (c) 1G6J; (d) 2KT6; (e) 1CN7; (f) 2KTS; (g) 2K49; (h) 2KTE. Reprinted from ref. [53] with permission.

  • Figure 26

    (Color online) The superimposition of the original PDB structures (red) and structures estimated from triangle constraints (blue). (a) 2M5Z; (b) 1B4R; (c) 1G6J; (d) 2KT6; (e) 1CN7; (f) 2KTS; (g) 2K49; (h) 2KTE. Reprinted from ref. [53] with permission.

  • Figure 27

    (Color online) The superimposition of original PDB structure (red) and the structures from triangle constraints estimation (blue). (a) 1G6J; (b) 1B4R; (c) 2K62; (d) 1CN7; (e) 2K49; (f) 2L3O; (g) 2GJY; (h) 2K7H, (i) 2YT0; (j) 2L7B. Reprinted from ref. [54] with permission.

  • Figure 28

    (Color online) The comparison between the calculated structure and reference structure in Ramachandran plot and secondary structures, taking 1CN7 as an example. (a) The Ramachandran plot for the reconstructed structure; (b) the Ramachandran plot for the reference structure; (c) the comparison of secondary structure. Reprinted from ref. [54] with permission.

  • Figure 29

    (Color online) The plots of differences and accumulative distributions on TM-score/GDT-TS between the Riemannian structures and CYANA structures. (a) The TM-score differences between the Riemannian structures and CYANA structures; (b) the accumulative distributions of the TM-score for Riemannian structures and CYANA structures; (c) the GDT-TS differences between the Riemannian structures and CYANA structures; (d) the accumulative distributions of the GDT-TS for Riemannian structures and CYANA structures. Reprinted from ref. [56] with permission.

  • Figure 30

    (Color online) The RMSD differences between the Riemannian structures and CYANA structures. (a) The RMSD difference in well-defined region between the Riemannian structures and CYANA structures; (b) the accumulative distributions of the RMSD in well-defined region for Riemannian structures and CYANA structures; (c) the RMSD difference in all region between the Riemannian structures and CYANA structures; (d) the accumulative distributions of the RMSD in all region for Riemannian structures and CYANA structures. Reprinted from ref. [56] with permission.

  • Figure 31

    (Color online) The superimposition between the X-ray crystal structures (blue), CYANA structures (green) and reconstructed structures from Tr algorithm (magenta). (a) 1BVM; (b) 1TOF; (c) 2HFI; (d) 2K5P. Reprinted from ref. [56] with permission.

  • Figure 32

    (Color online) The RMSD comparison between the structures from matrix completion method and MODELLER method. Blue is from our method while red is from MODELLER. Reprinted from ref. [57] with permission.

  • Figure 33

    (Color online) The superimpositions for the structures recovered from MC and MODELLER methods with the corresponding NMR reference structure, respectively. The columns 1, 3 are from MC method, while columns 2, 4 are from MODELLER method. Reprinted from ref. [57] with permission.

  • Figure 34

    (Color online) The MPscore comparison between the structures from matrix completion method and MODELLER method. Blue is from our method, red is from MODELLER and green is the NMR structures from the PDB. Reprinted from ref. [57] with permission.

  • Table 1   The structure prediction results based on the ideal distances

    蛋白质

    描述

    原子数

    残基数

    采样率

    RMSD (Å)

    时间 (s)

    2M5Z

    Antimicrobial protein

    598

    44

    0.0673

    1.2×10−3

    7.36

    1B4R

    PKD domain1 from human polycystein-1

    1114

    80

    0.0449

    9.6×10−4

    10.77

    1G6J

    Ubiquitin

    1228

    76

    0.0407

    9.2×10−4

    15.33

    2KT6

    Outer membrane usher protein papC

    1283

    85

    0.0390

    2.1×10−3

    12.72

    1CN7

    Yeast ribosomal protein L30

    1648

    104

    0.0303

    1.3×10−3

    22.86

    2KTS

    Heat shock protein hs1J

    1784

    117

    0.0280

    3.4×10−4

    27.45

    2K49

    UPF0339 protein SO3888

    1823

    118

    0.0247

    6.7×10−4

    29.27

    2KTE

    Bacillus subtilis

    2380

    152

    0.0210

    1.0×10−3

    38.16

  • Table 2   The reconstructed structures from the triangle constraints estimation

    蛋白质

    描述

    原子数

    残基数

    采样率

    RMSD (Å)

    时间 (s)

    2M5Z

    Antimicrobial protein

    598

    44

    0.0673

    0.826

    17.36

    1B4R

    PKD domain1 from human polycystein-1

    1114

    80

    0.0449

    1.074

    41.63

    1G6J

    Ubiquitin

    1228

    76

    0.0407

    0.747

    56.55

    2KT6

    Outer membrane usher protein papC

    1283

    85

    0.0390

    0.818

    66.35

    1CN7

    Yeast ribosomal protein L30

    1648

    104

    0.0303

    0.786

    80.23

    2KTS

    Heat shock protein hs1J

    1784

    117

    0.0280

    1.668

    83.72

    2K49

    UPF0339 protein SO3888

    1823

    118

    0.0247

    0.887

    90.59

    2KTE

    Bacillus subtilis

    2380

    152

    0.0210

    1.320

    116.83

  • Table 3   The values of Ca RMSD and TM-score in well-defined region for 10 proteins

    蛋白质

    RMSD_well-defined (Å)

    TM-score

    1G6J

    0.99±0.13

    0.87±0.02

    1B4R

    1.57±0.16

    0.84±0.02

    2K62

    1.81±0.14

    0.86±0.02

    1CN7

    1.55±0.19

    0.78±0.02

    2K49

    1.55±0.14

    0.85±0.02

    2L3O

    2.08±0.23

    0.70±0.02

    2GJY

    1.64±0.12

    0.80±0.01

    2K7H

    1.96±0.20

    0.90±0.02

    2YT0

    0.92±0.09

    0.81±0.01

    2L7B

    2.25±0.19

    0.89±0.01

  • Table 4   The percentages (%) in the favored and disallowed regions in Ramachandran plots for the 10 proteins

    蛋白质

    Favorable (reference)

    Favorable (calculation)

    Disallowed (reference)

    Disallowed (calculation)

    1G6J

    92.23±2.40

    94.66±2.42

    0.63±0.91

    1.08±1.36

    1B4R

    83.14±1.87

    81.41±4.19

    3.91±1.14

    6.73±2.69

    2K62

    87.69±2.46

    88.25±1.82

    0.93±0.56

    2.64±1.15

    1CN7

    79.51±2.56

    85.49±3.39

    4.02±1.71

    3.14±1.51

    2K49

    94.57±1.66

    92.68±2.26

    0.30±0.42

    1.69±1.16

    2L3O

    74.18±2.02

    70.57±2.80

    8.86±1.85

    13.07±1.81

    2GJY

    75.99±3.12

    79.57±2.86

    7.29±1.96

    6.31±1.95

    2K7H

    97.29±1.08

    91.71±2.80

    1.10±0.24

    1.55±1.07

    2YT0

    85.55±2.76

    79.55±2.77

    1.15±0.56

    6.82±1.94

    2L7B

    75.69±1.58

    73.24±1.72

    6.41±1.19

    9.19±1.76

  • Table 5   The comparison of RMSD and MPscore between the structures from our method and the MODELLER method

    蛋白质

    方法

    缺失结构

    缺失结构RMSD (Å)

    已知结构RMSD (Å)

    MPscore

    1CTR

    本文方法

    75–80

    2.03±0.43

    0.23±0.02

    2.54±0.90

    MODELLER

    3.08±0.14

    0.10±0.01

    4.07±0.02

    2RKK

    本文方法

    65–75

    3.19±0.18

    0.18±0.05

    1.55±0.14

    MODELLER

    3.44±0.21

    0.57±0.01

    2.66±0.05

    2SAK

    本文方法

    1–15

    4.21±0.35

    0.14±0.01

    1.61±0.12

    MODELLER

    5.47±0.75

    0.03±0.01

    1.79±0.24

    1GSV

    本文方法

    1–3

    0.16±0.04

    0.13±0.01

    1.17±0.48

    MODELLER

    0.45±0.30

    0.05±0.05

    1.66±0.19

    5WLB

    本文方法

    31–37

    1.42±0.14

    0.15±0.01

    1.14±0.09

    MODELLER

    1.88±0.48

    0.05±0.01

    1.33±0.10

    2VRW

    本文方法

    178–184

    1.46±0.24

    0.11±0.01

    1.22±0.21

    MODELLER

    2.26±0.83

    0.01±0.01

    1.74±0.07

    3SD6

    本文方法

    67–69

    0.85±0.09

    0.01±0.00

    1.29±0.06

    MODELLER

    0.86±0.14

    0.04±0.01

    2.22±0.16

    1EY4

    本文方法

    1–5

    1.60±0.22

    0.14±0.01

    1.75±0.04

    MODELLER

    1.73±0.13

    0.05±0.02

    2.96±0.26

    本文方法

    142–149

    2.31±0.18

    MODELLER

    2.75±0.52

    2ZR4

    本文方法

    1–4

    1.01±0.27

    0.16±0.01

    1.46±0.07

    MODELLER

    0.98±0.38

    0.17±0.01

    2.02±0.10

    本文方法

    40–44

    0.81±0.17

    MODELLER

    1.25±0.18

    1AVS

    本文方法

    1–6

    1.25±0.24

    0.18±0.01

    1.64±0.09

    MODELLER

    3.32±0.72

    0.08±0.05

    3.03±0.64

    本文方法

    88–90

    0.38±0.09

    MODELLER

    0.12±0.06