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

Yonggang Peng

doi:10.3788/LOP220821

Journals >Laser & Optoelectronics Progress >Volume 60 >Issue 7 >Page 0727002 > Article

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

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

Yonggang Peng^*

Author Affiliations

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

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DOI: 10.3788/LOP220821 Cite this Article Set citation alerts

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

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

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Evolution of Q1, Q2, and Q3 with execution time when initial quantum state is 000

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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	$Y_{3}$	$U_{23}$	${\bar{Y}}_{3}$	$Y_{2}$	$I_{12}$	${\bar{Y}}_{2}$	${\bar{U}}_{23}$	$U_{13}$
$J_{12}^{z}$	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 1. Toffoli gate NMR pulse sequence parameter values

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

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

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

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