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

Peng Yonggang

doi:10.3788/LOP202158.0127002

Journals >Laser & Optoelectronics Progress >Volume 58 >Issue 1 >Page 127002 > Article

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

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

Peng Yonggang^*

Author Affiliations

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

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DOI: 10.3788/LOP202158.0127002 Cite this Article Set citation alerts

Peng Yonggang. Optimal Pulse Sequence of Quantum Controlled Not-Gates via Nuclear Magnetic Resonance Realization[J]. Laser & Optoelectronics Progress, 2021, 58(1): 127002 Copy Citation Text

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Q1 and Q2 versus time step obtained by executing CCNOT111 when k=1

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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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 1. Parameters

J

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	1.16×10⁶	128.00

Table 2. Parameter execution time of NMR pulse sequence under different operation when k =1 unit:

4 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 3. Execution time, time step and number of execution steps of NMR pulse sequence under different operation when k =1 unit: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 0Table 4. Expectation values of Q 1 and Q 2 under four different operation when k =1,2,4,8,32Abstract Get PDF(in Chinese) Figures&Tables (12) Equations (0) References (16) Cited By (2) 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 Set citation alerts for the article Tools Share Set citation alerts for the article Save the article for my favorites Paper Information Category: Quantum Optics Received: Apr. 27, 2020 Accepted: -- Published Online:  Jan. 1, 2021 The Author Email: Yonggang Peng (pengyg@njupt.edu.cn) DOI: 10.3788/LOP202158.0127002 Recommended Topics laser devices and laser physics Lasers and Laser Optics Laser physics laser manufacturing Instrumentation, Measurement and MetrologySet citation alerts for the article Please enter your email address Cancel ConfirmAbout CLP About Us Privacy Policy Products & Service Journals News Articles Conferences For Advertisers Share CLP Quick Link Chinese Laser Press CLP online library SIOM SPIE Cambridge University Press Optica Publishing Group OE SHOW COS © 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"));$(function () {
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