Researching | One-step implementation of Rydberg-antiblockade SWAP and controlled-SWAP gates with modified robustness

Journals >Photonics Research >Volume 9 >Issue 5 >Page 814 > Article

Photonics Research
Vol. 9, Issue 5, 814 (2021)

One-step implementation of Rydberg-antiblockade SWAP and controlled-SWAP gates with modified robustness

Jin-Lei Wu¹, Yan Wang¹, Jin-Xuan Han¹, Yu-Kun Feng¹, Shi-Lei Su², Yan Xia³, Yongyuan Jiang¹, and Jie Song^1、*

Author Affiliations

¹School of Physics, Harbin Institute of Technology, Harbin 150001, China

²School of Physics and Microelectronics, Zhengzhou University, Zhengzhou 450001, China

³Department of Physics, Fuzhou University, Fuzhou 350002, China

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DOI: 10.1364/PRJ.415795 Cite this Article Set citation alerts

Jin-Lei Wu, Yan Wang, Jin-Xuan Han, Yu-Kun Feng, Shi-Lei Su, Yan Xia, Yongyuan Jiang, Jie Song. One-step implementation of Rydberg-antiblockade SWAP and controlled-SWAP gates with modified robustness[J]. Photonics Research, 2021, 9(5): 814 Copy Citation Text

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Abstract

The prevalent fashion of executing Rydberg-mediated two- and multi-qubit quantum gates in neutral atomic systems is to pump Rydberg excitations using multistep piecewise pulses in the Rydberg blockade regime. Here, we propose to synthesize a

Λ

-type Rydberg antiblockade (RAB) of two neutral atoms using periodic fields, which facilitates one-step implementations of SWAP and controlled-SWAP (CSWAP) gates with the same gate time. Besides, the RAB condition is modified so as to circumvent the sensitivity of RAB-based gates to infidelity factors, including atomic decay, motional dephasing, and interatomic distance deviation. Our work makes up the absence of one-step schemes of Rydberg-mediated SWAP and CSWAP gates and may pave a way to enhance the robustness of RAB-based gates.

{\hat{H}}_{12} = {\hat{H}}_{1} \otimes {\hat{I}}_{2} + {\hat{I}}_{1} \otimes {\hat{H}}_{2} + V | r r ⟩ ⟨ r r |,

(1)

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{\hat{H}}_{j} = \sum_{k = 0}^{1} \frac{Ω_{k} (t)}{2} {| k ⟩}_{j} ⟨ r | + H .c.

(2)

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{\hat{H}}_{e} = [\frac{Ω_{e}}{2} (| 01 ⟩ ⟨ r r | + | 10 ⟩ ⟨ r r |) + H.c.] + δ^{'} | r r ⟩ ⟨ r r |,

(3)

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\dot{ρ} = i [ρ, {\hat{H}}_{Full}] - \frac{1}{2} \sum_{j = 1}^{N} \sum_{k = 0}^{2} ({\hat{L}}_{k}^{j †} {\hat{L}}_{k}^{j} ρ - 2 {\hat{L}}_{k}^{j} ρ {\hat{L}}_{k}^{j †} + ρ {\hat{L}}_{k}^{j †} {\hat{L}}_{k}^{j}),

(4)

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{\hat{H}}_{d d} = - \frac{Ω_{d d}}{2} (| 01 ⟩ + | 10 ⟩) (⟨ 01 | + ⟨ 10 |),

(5)

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{\hat{H}}_{12 c} = {\hat{H}}_{12} \otimes {\hat{I}}_{c} + {\hat{I}}_{1} \otimes {\hat{I}}_{2} \otimes {\hat{H}}_{c} + {\hat{I}}_{1} \otimes V_{2 c} {| r r ⟩}_{2 c} ⟨ r r | + V_{1 c} {| r ⟩}_{1} {⟨ r | \otimes {\hat{I}}_{2} \otimes | r ⟩}_{c} ⟨ r |,

(6)

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{\hat{H}}_{12 c}^{'} = {\hat{H}}_{e} \otimes {\hat{I}}_{c} + {\hat{I}}_{1} \otimes {\hat{I}}_{2} \otimes {\hat{H}}_{c} + (V_{1 c} + V_{2 c}) | r r r ⟩ ⟨ r r r |,

(7)

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{\hat{H}}_{eff} = {\hat{H}}_{e} \otimes {| 1 ⟩}_{c} ⟨ 1 |,

(8)

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{\hat{H}}_{0} = \frac{1}{2} [Ω_{0 m} \cos (ω_{0} t) (| 00 ⟩ ⟨ r 0 | + | 01 ⟩ ⟨ r 1 | + | 0 r ⟩ ⟨ r r | + | 00 ⟩ ⟨ 0 r | + | 10 ⟩ ⟨ 1 r | + | r 0 ⟩ ⟨ r r |) + Ω_{1 m} \cos (ω_{1} t) (| 10 ⟩ ⟨ r 0 | + | 11 ⟩ ⟨ r 1 | + | 1 r ⟩ ⟨ r r | + | 01 ⟩ ⟨ 0 r | + | 11 ⟩ ⟨ 1 r | + | r 1 ⟩ ⟨ r r |) + H .c .] + V | r r ⟩ ⟨ r r | .

(A1)

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{\hat{H}}_{1}^{'} = \frac{Ω_{0 m}}{4} {(e^{i ω_{0} t} + e^{- i ω_{0} t}) (| 00 ⟩ ⟨ r 0 | + | 01 ⟩ ⟨ r 1 | + | 00 ⟩ ⟨ 0 r | + | 10 ⟩ ⟨ 1 r |) + [e^{i (ω_{0} - δ) t} + e^{- i ω_{1} t}] (| 0 r ⟩ ⟨ r r | + | r 0 ⟩ ⟨ r r |)} + \frac{Ω_{1 m}}{4} {(e^{i ω_{1} t} + e^{- i ω_{1} t}) (| 10 ⟩ ⟨ r 0 | + | 11 ⟩ ⟨ r 1 | + | 01 ⟩ ⟨ 0 r | + | 11 ⟩ ⟨ 1 r |) + [e^{i ω_{0} t} + e^{- i (ω_{1} + δ) t}] (| 1 r ⟩ ⟨ r r | + | r 1 ⟩ ⟨ r r |)} + H .c .

(A2)

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\frac{Ω_{0 m}}{4} (e^{i ω_{0} t} + e^{- i ω_{0} t}) (| 00 ⟩ ⟨ r 0 | + | 00 ⟩ ⟨ 0 r |) + \frac{Ω_{1 m}}{4} (e^{i ω_{1} t} + e^{- i ω_{1} t}) (| 11 ⟩ ⟨ r 1 | + | 11 ⟩ ⟨ 1 r |) + H .c.

()

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{\hat{H}}_{1}^{'} ≃ [\frac{Ω_{0 m}}{4} (e^{i ω_{0} t} + e^{- i ω_{0} t}) | 01 ⟩ ⟨ r 1 | + \frac{Ω_{1 m}}{4} e^{i ω_{0} t} | r 1 ⟩ ⟨ r r |] + [\frac{Ω_{1 m}}{4} (e^{i ω_{1} t} + e^{- i ω_{1} t}) | 01 ⟩ ⟨ 0 r | + \frac{Ω_{0 m}}{4} e^{- i ω_{1} t} | 0 r ⟩ ⟨ r r |] + [\frac{Ω_{0 m}}{4} (e^{i ω_{0} t} + e^{- i ω_{0} t}) | 10 ⟩ ⟨ 1 r | + \frac{Ω_{1 m}}{4} e^{i ω_{0} t} | 1 r ⟩ ⟨ r r |] + [\frac{Ω_{1 m}}{4} (e^{i ω_{1} t} + e^{- i ω_{1} t}) | 10 ⟩ ⟨ r 0 | + \frac{Ω_{0 m}}{4} e^{- i ω_{0} t} | r 0 ⟩ ⟨ r r |] + \frac{Ω_{0 m}}{4} e^{i (ω_{0} - δ) t} (| 0 r ⟩ ⟨ r r | + | r 0 ⟩ ⟨ r r |) + \frac{Ω_{1 m}}{4} e^{- i (ω_{1} + δ) t} (| 1 r ⟩ ⟨ r r | + | r 1 ⟩ ⟨ r r |) + H .c .

(A3)

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{\hat{H}}_{e} = [\frac{Ω_{e}}{2} (| 01 ⟩ ⟨ r r | + | 10 ⟩ ⟨ r r |) + H .c .] + δ^{'} | r r ⟩ ⟨ r r |,

(A4)

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\bar{F} (ε, \hat{U}) = {\sum_{j = 1}^{4^{N}} tr [\hat{U} {\hat{u}}_{j}^{⏧} {\hat{U}}^{⏧} ε ({\hat{u}}_{j})] + l^{2}} / l^{2} (l + 1),

(B1)

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{\hat{H}}_{2}^{'} = \frac{Ω_{c m}}{4} (e^{i ω_{c} t} + e^{- i ω_{c} t}) (| 010 ⟩_{12 c} {⟨ 01 r | + | 100 ⟩}_{12 c} ⟨ 10 r | + {| r r 0 ⟩}_{12 c} ⟨ r r r |) + \frac{Ω_{e}}{2} {(| 010 ⟩}_{12 c} {⟨ r r 0 | + | 100 ⟩}_{12 c} ⟨ r r 0 | + {| 01 r ⟩}_{12 c} {⟨ r r r | + | 10 r ⟩}_{12 c} ⟨ r r r |) + H .c .

(C1)

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{\hat{H}}_{3}^{'} = \frac{Ω_{c m}}{4} [(e^{i ω_{c} t} + e^{- i ω_{c} t}) (| 010 ⟩_{12 c} {⟨ 01 r | + | 100 ⟩}_{12 c} ⟨ 10 r |) + (1 + e^{- 2 i ω_{c} t}) {| r r 0 ⟩}_{12 c} ⟨ r r r |] + \frac{Ω_{e}}{2} {(| 010 ⟩}_{12 c} ⟨ r r 0 | + {| 100 ⟩}_{12 c} {⟨ r r 0 | + | 01 r ⟩}_{12 c} {⟨ r r r | e^{- i ω_{c} t} + | 10 r ⟩}_{12 c} ⟨ r r r | e^{- i ω_{c} t}) + H .c .

(C2)

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{\hat{H}}_{3}^{''} = [\frac{Ω_{c m}}{4} {| r r 0 ⟩}_{12 c} ⟨ r r r | + \frac{Ω_{e}}{2} {(| 010 ⟩}_{12 c} {⟨ r r 0 | + | 100 ⟩}_{12 c} ⟨ r r 0 |) + H .c .] + Δ_{r r r} {| r r r ⟩}_{12 c} ⟨ r r r |,

(C3)

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{\hat{H}}_{4} = [\frac{Ω_{e}}{\sqrt{2}} {(| 010 ⟩}_{12 c} + {| 100 ⟩}_{12 c}) (⟨ ϕ_{0} | + ⟨ ϕ_{1} |) + H .c .] + \frac{Ω_{c m}}{4} \sum_{n = 0}^{1} {(- 1)}^{n} | ϕ_{n} ⟩ {⟨ ϕ_{n} | + δ^{'} | r r ⟩}_{12} ⟨ r r |,

(C4)

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{\hat{H}}_{5} = \frac{Ω_{e}}{\sqrt{2}} {(| 010 ⟩}_{12 c} + {| 100 ⟩}_{12 c}) [⟨ ϕ_{0} | e^{- i t (Ω_{c m} / 4 + δ^{'})} + ⟨ ϕ_{1} | e^{i t (Ω_{c m} / 4 - δ^{'})}] + H .c .

(C5)

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{\hat{H}}_{eff} = [\frac{Ω_{e}}{2} {(| 011 ⟩}_{12 c} + {| 101 ⟩}_{12 c}) ⟨ r r 1 | + H .c .] + δ^{'} {| r r 1 ⟩}_{12 c} ⟨ r r 1 |,

(C6)

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Jin-Lei Wu, Yan Wang, Jin-Xuan Han, Yu-Kun Feng, Shi-Lei Su, Yan Xia, Yongyuan Jiang, Jie Song. One-step implementation of Rydberg-antiblockade SWAP and controlled-SWAP gates with modified robustness[J]. Photonics Research, 2021, 9(5): 814

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