Implementation of a many-qubit Grover search with trapped ultracold ions

Wan-Li Yang; Hua Wei; Chang-Yong Chen; Mang Feng

doi:10.1364/JOSAB.25.001720

Journal of the Optical Society of America B
Vol. 25,
Issue 10,
pp. 1720-1727
(2008)
•https://doi.org/10.1364/JOSAB.25.001720

Implementation of a many-qubit Grover search with trapped ultracold ions

Wan-Li Yang, Hua Wei, Chang-Yong Chen, and Mang Feng

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Wan-Li Yang, Hua Wei, Chang-Yong Chen, and Mang Feng, "Implementation of a many-qubit Grover search with trapped ultracold ions," J. Opt. Soc. Am. B 25, 1720-1727 (2008)

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Abstract

We propose a potentially practical scheme for realization of an n-qubit $(n > 2)$ conditional phase flip (CPF) gate and implementation of Grover’s search algorithm in an ion-trap system. We demonstrate, both analytically and numerically, that our scheme could be achieved efficiently to find a marked state with high fidelity and high success probability. We also show the merits of the proposal that the increase of the ion number can improve the fidelity and success probability of the CPF gate. The required operations for a Grover search are very close to the capabilities of current ion-trap techniques.

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Qubit number n	Number of							$\sum_{s = 2}^{n - 1} C_{s}^{(n)}$
Qubit number n	$α_{2}$	$α_{3}$	$α_{4}$	$α_{5}$	$α_{6}$	⋯	$α_{n - 1}$	$\sum_{s = 2}^{n - 1} C_{s}^{(n)}$
$n = 4$	3	1	0	0	0	0	0	4
$n = 5$	6	4	1	0	0	0	0	11
$n = 6$	10	10	5	1	0	0	0	26
$n = 7$	15	20	15	6	1	0	0	57

Regime	Parameter	Qubit number n
Regime	Parameter	$n = 2$	$n = 3$	$n = 4$	$n = 5$	$n = 6$	$n = 7$	$n = 8$
$Ω_{m} ⪡ η ν$	ν $(M H z ∕ 2 π)$	0.250	0.167	0.125	0.100	0.083	0.071	0.063
	$Ω_{m}$ $(k H z ∕ 2 π)$	2.500	1.670	1.250	1.000	0.830	0.710	0.630
	$t_{0}$ (ms)	19.14	28.71	38.29	47.86	57.43	67.00	76.57
$Ω_{m} ⪡ ν ∕ η$	$Ω_{m}$ $(M H z ∕ 2 π)$	0.125	0.084	0.063	0.050	0.042	0.036	0.032
	$t_{0}$ (ms)	0.383	0.574	0.766	0.957	1.148	1.340	1.531

Qubit number n	Number of							$\sum_{s = 2}^{n - 1} C_{s}^{(n)}$
Qubit number n	$α_{2}$	$α_{3}$	$α_{4}$	$α_{5}$	$α_{6}$	⋯	$α_{n - 1}$	$\sum_{s = 2}^{n - 1} C_{s}^{(n)}$
$n = 4$	3	1	0	0	0	0	0	4
$n = 5$	6	4	1	0	0	0	0	11
$n = 6$	10	10	5	1	0	0	0	26
$n = 7$	15	20	15	6	1	0	0	57

Regime	Parameter	Qubit number n
Regime	Parameter	$n = 2$	$n = 3$	$n = 4$	$n = 5$	$n = 6$	$n = 7$	$n = 8$
$Ω_{m} ⪡ η ν$	ν $(M H z ∕ 2 π)$	0.250	0.167	0.125	0.100	0.083	0.071	0.063
	$Ω_{m}$ $(k H z ∕ 2 π)$	2.500	1.670	1.250	1.000	0.830	0.710	0.630
	$t_{0}$ (ms)	19.14	28.71	38.29	47.86	57.43	67.00	76.57
$Ω_{m} ⪡ ν ∕ η$	$Ω_{m}$ $(M H z ∕ 2 π)$	0.125	0.084	0.063	0.050	0.042	0.036	0.032
	$t_{0}$ (ms)	0.383	0.574	0.766	0.957	1.148	1.340	1.531

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Journal of the Optical Society of America B