Optimal Pulse Sequence of Quantum Controlled Not-Gates via Nuclear Magnetic Resonance Realization

Peng Yonggang

doi:10.3788/LOP202158.0127002

Laser & Optoelectronics Progress, Volume. 58, Issue 1, 127002(2021)

Optimal Pulse Sequence of Quantum Controlled Not-Gates via Nuclear Magnetic Resonance Realization

Peng Yonggang^*

Department of Applied Physics, College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210003, China

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Figures & Tables(12)

Fig. 1. Q₁and Q₂versus time step obtained by executing ${C_{CNOT}}_{1} |11〉$ when k=1

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Fig. 2. Q₁and Q₂versus time step obtained by executing ${C_{CNOT}}_{2} |11〉$ when k=1

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Fig. 3. Q₁and Q₂versus time step obtained by executing ${C_{CNOT}}_{3} |11〉$ when k=1

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Fig. 4. Q₁and Q₂versus time step obtained by executing ${C_{CNOT}}_{4} |11〉$ when k=1

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Fig. 5. Q₁and Q₂versus time step obtained by executing ${C_{CNOT}}_{1} |11〉$ when k=32

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Fig. 6. Q₁and Q₂versus time step obtained by executing ${C_{CNOT}}_{2} |11〉$ when k=32

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Fig. 7. Q₁and Q₂versus time step obtained by executing ${C_{CNOT}}_{3} |11〉$ when k=32

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Fig. 8. Q₁and Q₂ versus time step obtained by executing ${C_{CNOT}}_{4} |11〉$ when k=32

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Table 1. Parameters $J$ ,
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Table 1. Parameters $J$ ,
Parameter $Y_{1}$ $X_{1}^{'}$ ${\bar{Y}}_{1}$ $X_{2}^{'}$ ${\bar{Y}}_{2}$ $I_{12}^{'}$ $Y_{2}$
$J_{12}^{z}$ -4.3×10^-7 -4.3×10^-7 -4.3×10^-7 -4.3×10^-7 -4.3×10^-7 -4.3×10^-7 -4.3×10^-7
$h_{1}^{z}$ 1 1 1 1 1 1 1
$h_{2}^{z}$ 0.25 0.25 0.25 0.25 0.25 0.25 0.25
${\tilde{h}}_{1}^{x}$ 3.125×10^-2 5.596×10^-2 -3.125×10^-2 4.451×10^-2 -7.812×10^-3 0 7.812×10^-3
${\tilde{h}}_{2}^{x}$ 7.812×10^-3 1.399×10^-2 -7.813×10^-3 1.113×10^-2 -1.953×10^-3 0 1.953×10^-3
$f_{1}^{x}$ 1.00 1.00 1.00 0.25 0.25 0 0.25
$f_{2}^{x}$ 1.00 1.00 1.00 0.25 0.25 0 0.25
${\tilde{h}}_{1}^{y}$ 3.125×10^-2 5.595×10^-2 -3.125×10^-2 4.451×10^-2 -7.812×10^-3 0 7.812×10^-3
${\tilde{h}}_{2}^{y}$ 7.812×10^-3 1.398×10^-2 -7.812×10^-3 1.112×10^-2 -1.953×10^-3 0 1.953×10^-3
$f_{1}^{y}$ 1.00 1.00 1.00 0.25 0.25 0 0.25
$f_{2}^{y}$ 1.00 1.00 1.00 0.25 0.25 0 0.25

Table 2. Parameter execution time of NMR pulse sequence under different operation when k =1 unit:
4
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Table 2. Parameter execution time of NMR pulse sequence under different operation when k =1 unit: $4 Operation Y_{1} X_{1}^{'} {\bar{Y}}_{1} X_{2}^{'} {\bar{Y}}_{2} I_{12}^{'} Y_{2} Value 8.00 8.00 8.00 128.00 128 1.16×10 6 128.00Table 3. Execution time, time step and number of execution steps of NMR pulse sequence under different operation when k =1 unit: View table Table 3. Execution time, time step and number of execution steps of NMR pulse sequence under different operation when k =1 unit: Parameter Y_{1} X_{1}^{'} {\bar{Y}}_{1} X_{2}^{'} {\bar{Y}}_{2} I_{12}^{'} Y_{2} τ δ m 8 8.00×10 -2 100 8 8.00×10 -2 100 8 8.00×10 -2 100 128 1.28 100 128 1.28 100 1.162×10 6 1.162×10 61 128 1.28 100Table 4. Expectation values of Q 1 and Q 2 under four different operation when k =1,2,4,8,32 View table Table 4. Expectation values of Q 1 and Q 2 under four different operation when k =1,2,4,8,32 Operation k =1 k =2 k =4 k =8 k =32 Q 1 Q 2 Q 1 Q 2 Q 1 Q 2 Q 1 Q 2 Q 1 Q 2 {C_{CNOT}}_{1} |11〉 0.999 0 1.000 0 1.000 0 1.000 0 1.000 0 {C_{CNOT}}_{2} |11〉 0.745 0 0.931 0 0.982 0 0.996 0 1.000 0 {C_{CNOT}}_{3} |11〉 0.744 0 0.931 0 0.982 0 0.996 0 1.000 0 {C_{CNOT}}_{4} |11〉 0.729 0 0.927 0 0.981 0 0.995 0 1.000 0Tools Get Citation Copy Citation Text Peng Yonggang. Optimal Pulse Sequence of Quantum Controlled Not-Gates via Nuclear Magnetic Resonance Realization[J]. Laser & Optoelectronics Progress, 2021, 58(1): 127002 Download Citation EndNote(RIS) BibTex Plain Text Share Set citation alerts for article Save article for my favoritesSet citation alerts for the article Cancel ConfirmPaper Information Category: Quantum Optics Received: Apr. 27, 2020 Accepted: -- Published Online: Jan. 28, 2021 The Author Email: Yonggang Peng (pengyg@njupt.edu.cn) DOI: 10.3788/LOP202158.0127002Topics laser devices and laser physics Lasers and Laser Optics Laser physics laser manufacturing Instrumentation, Measurement and MetrologyAbout CLP About Us Privacy Policy Products Service Journals Articles Conferences News For Advertisers Quick Link Chinese Laser Press CLP online library SIOM SPIE Cambridge University Press Optica Publishing Group OE SHOW COS Share CLP © Copyright 2018-2021 | Chinese Laser Press. All Rights Reserved 沪ICP备15018463号-20 document.write(unescape("%3Cspan id='cnzz_stat_icon_1280142344'%3E%3C/span%3E%3Cscript src='https://v1.cnzz.com/z_stat.php%3Fid%3D1280142344%26show%3Dpic' type='text/javascript'%3E%3C/script%3E"));$

Table 4. Expectation values of Q₁and Q₂ under four different operation when k=1,2,4,8,32

Table 4. Expectation values of Q₁and Q₂ under four different operation when k=1,2,4,8,32

Table 3. Execution time, time step and number of execution steps of NMR pulse sequence under different operation when k =1 unit: ParameterY1X1'Y¯1X2'Y¯2I12'Y2τδm88.00×10-210088.00×10-210088.00×10-21001281.281001281.281001.162×1061.162×10611281.28100

Table 4. Expectation values of Q1 and Q2 under four different operation when k=1,2,4,8,32

Table 4. Expectation values of Q1 and Q2 under four different operation when k=1,2,4,8,32

Table 4. Expectation values of Q₁and Q₂ under four different operation when k=1,2,4,8,32

Table 4. Expectation values of Q₁and Q₂ under four different operation when k=1,2,4,8,32