Nuclear-Magnetic-Resonance-Based Physical Realization of Quantum Toffoli Gate

Yonggang Peng

doi:10.3788/LOP220821

Laser & Optoelectronics Progress, Volume. 60, Issue 7, 0727002(2023)

Nuclear-Magnetic-Resonance-Based Physical Realization of Quantum Toffoli Gate

Yonggang Peng^*

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

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Figures & Tables(11)

Fig. 1. Quantum network for Toffoli gates using controlled NOT and phase shift gates

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Fig. 2. Evolution of $Q_{1}$ , $Q_{2}$ , and $Q_{3}$ with execution time when initial quantum state is $|000〉$

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Fig. 3. Evolution of $Q_{1}$ , $Q_{2}$ , and $Q_{3}$ with execution time when initial quantum state is $|001〉$

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Fig. 4. Evolution of $Q_{1}$ , $Q_{2}$ , and $Q_{3}$ with execution time when initial quantum state is $|010〉$

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Fig. 5. Evolution of $Q_{1}$ , $Q_{2}$ , and $Q_{3}$ with execution time when initial quantum state is $|011〉$

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Fig. 6. Evolution of $Q_{1}$ , $Q_{2}$ , and $Q_{3}$ with execution time when initial quantum state is $|100〉$

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Fig. 7. Evolution of $Q_{1}$ , $Q_{2}$ , and $Q_{3}$ with execution time when initial quantum state is $|101〉$

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Fig. 8. Evolution of $Q_{1}$ , $Q_{2}$ , and $Q_{3}$ with execution time when initial quantum state is $|110〉$

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Fig. 9. Evolution of $Q_{1}$ , $Q_{2}$ , and $Q_{3}$ with execution time when initial quantum state is $|111〉$

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Table 1. Toffoli gate NMR pulse sequence parameter values

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Table 1. Toffoli gate NMR pulse sequence parameter values

	$Y_{3}$	$U_{23}$	${\bar{Y}}_{3}$	$Y_{2}$	$I_{12}$	${\bar{Y}}_{2}$	${\bar{U}}_{23}$	$U_{13}$
$J_{12}^{z}$	0	$- 0.43 \times 10^{- 6}$	0	0	$- 0.43 \times 10^{- 6}$	0	$- 0.43 \times 10^{- 6}$	$- 0.43 \times 10^{- 6}$
$J_{23}^{z}$	0	$- 0.43 \times 10^{- 6}$	0	0	$- 0.43 \times 10^{- 6}$	0	$- 0.43 \times 10^{- 6}$	$- 0.43 \times 10^{- 6}$
$J_{13}^{z}$	0	$- 0.43 \times 10^{- 6}$	0	0	$- 0.43 \times 10^{- 6}$	0	$- 0.43 \times 10^{- 6}$	$- 0.43 \times 10^{- 6}$
${\tilde{h}}_{1}^{y}$	0.25	0	-0.25	0.25	0	-0.25	0	0
${\tilde{h}}_{2}^{y}$	0.25	0	-0.25	0.25	0	-0.25	0	0
${\tilde{h}}_{3}^{y}$	0.25	0	-0.25	0.25	0	-0.25	0	0
$h_{1}^{z}$	1	1	1	1	1	1	-1	1
$h_{2}^{z}$	1	1	1	1	1	1	-1	1
$h_{3}^{z}$	1	1	1	1	1	1	-1	1
$f_{1}^{x}$	1	0	1	1	0	1	0	0
$f_{2}^{x}$	1	0	1	1	0	1	0	0
$f_{3}^{x}$	1	0	1	1	0	1	0	0

Table 2. Execution time, time step, and number of time step of unitary transformation

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Table 2. Execution time, time step, and number of time step of unitary transformation

	${\bar{Y}}_{3}$	$U_{23}$	${\bar{Y}}_{3}$	$Y_{2}$	$I_{12}$	${\bar{U}}_{23}$	${\bar{Y}}_{2}$	${\bar{U}}_{13}$
$τ / s$	$1.58 \times 10^{- 7}$	$7.3 \times 10^{- 3}$	$1.58 \times 10^{- 7}$	$1.58 \times 10^{- 7}$	$1.46 \times 10^{- 2}$	$7.3 \times 10^{- 3}$	$1.58 \times 10^{- 7}$	$7.3 \times 10^{- 3}$
$δ / s$	$1.58 \times 10^{- 7}$	$7.3 \times 10^{- 3}$	$1.58 \times 10^{- 7}$	$1.58 \times 10^{- 7}$	$1.46 \times 10^{- 2}$	$7.3 \times 10^{- 3}$	$1.58 \times 10^{- 7}$	$7.3 \times 10^{- 3}$
$m$	1	1	1	1	1	1	1	1

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Yonggang Peng. Nuclear-Magnetic-Resonance-Based Physical Realization of Quantum Toffoli Gate[J]. Laser & Optoelectronics Progress, 2023, 60(7): 0727002

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Paper Information

Category: Quantum Optics

Received: Feb. 28, 2022

Accepted: Mar. 29, 2022

Published Online: May. 24, 2023

The Author Email: Yonggang Peng (pengyg@njyupt.edu.cn)

DOI:10.3788/LOP220821

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology