Scalable Multipartite Entanglement Created by Spin Exchange in an Optical Lattice

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Scalable Multipartite Entanglement Created by Spin Exchange in an Optical Lattice

Wei-Yong Zhang, Ming-Gen He, Hui Sun, Yong-Guang Zheng, Ying Liu, An Luo, Han-Yi Wang, Zi-Hang Zhu, Pei-Yue Qiu, Ying-Chao Shen, Xuan-Kai Wang, Wan Lin, Song-Tao Yu, Bin-Chen Li, Bo Xiao, Meng-Da Li, Yu-Meng Yang, Xiao Jiang, Han-Ning Dai, You Zhou, Xiongfeng Ma, Zhen-Sheng Yuan, and Jian-Wei Pan

Phys. Rev. Lett. 131, 073401 – Published 18 August 2023

See synopsis: Milestone for Optical-Lattice Quantum Computer

Abstract

Ultracold atoms in optical lattices form a competitive candidate for quantum computation owing to the excellent coherence properties, the highly parallel operations over spins, and the ultralow entropy achieved in qubit arrays. For this, a massive number of parallel entangled atom pairs have been realized in superlattices. However, the more formidable challenge is to scale up and detect multipartite entanglement, the basic resource for quantum computation, due to the lack of manipulations over local atomic spins in retroreflected bichromatic superlattices. In this Letter, we realize the functional building blocks in quantum-gate-based architecture by developing a cross-angle spin-dependent optical superlattice for implementing layers of quantum gates over moderately separated atoms incorporated with a quantum gas microscope for single-atom manipulation and detection. Bell states with a fidelity of 95.6(5)% and a lifetime of $2.20 \pm 0.13 s$ are prepared in parallel, and then connected to multipartite entangled states of one-dimensional ten-atom chains and two-dimensional plaquettes of $2 \times 4$ atoms. The multipartite entanglement is further verified with full bipartite nonseparability criteria. This offers a new platform toward scalable quantum computation and simulation.

Received 25 April 2023
Accepted 30 June 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.073401

Physics Subject Headings (PhySH)

Cold gases in optical lattices Entanglement in quantum gases Measurement-based quantum computing Quantum circuits Quantum gates

Atoms Bose gases

Bose-Hubbard model Cooling & trapping Optical lattices & traps

Atomic, Molecular & OpticalQuantum Information, Science & Technology

synopsis

Milestone for Optical-Lattice Quantum Computer

Published 18 August 2023

Quantum mechanically entangled groups of eight and ten ultracold atoms provide a critical demonstration for optical-lattice-based quantum processing.

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Authors & Affiliations

Wei-Yong Zhang ^1,2,*, Ming-Gen He^1,2,*, Hui Sun^1,2,*, Yong-Guang Zheng^1,2, Ying Liu^1,2, An Luo ^1,2, Han-Yi Wang^1,2, Zi-Hang Zhu^1,2, Pei-Yue Qiu^1,2, Ying-Chao Shen^1,2, Xuan-Kai Wang ^1,2, Wan Lin^1,2, Song-Tao Yu^1,2, Bin-Chen Li^1,2, Bo Xiao ^1,2, Meng-Da Li ^1,2, Yu-Meng Yang^1,2, Xiao Jiang^1,2, Han-Ning Dai ^1,2, You Zhou ^1,3, Xiongfeng Ma⁴, Zhen-Sheng Yuan^1,2,5, and Jian-Wei Pan^1,2,5

¹Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
²CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
³Key Laboratory for Information Science of Electromagnetic Waves (Ministry of Education), Fudan University, Shanghai 200433, China
⁴Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
⁵Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China

^*These authors contributed equally to this work.

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Vol. 131, Iss. 7 — 18 August 2023

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Images

Figure 1
Experimental setup and entanglement generation sketch. (a) Bar chart of the average occupation in the ROI as indicated in (b) after cooling atoms in the superlattice. (b) An exemplary fluorescence image of the atom array after cooling, with the marked ROI containing $18 \times 14$ lattice sites. (c) Simplified setups for cooling, entangling, and detecting the atoms in optical lattices (for details, refer to the Supplemental Material [28]). (d) Cartoon schematic of generating multipartite entanglement in optical lattices by parallel cascading the entangling gates to prepare isolated Bell pairs $① \to ② / ③$ and further connecting them to realize 1D entangled chains $② \to ④$ and 2D entangled plaquettes $③ \to ⑤ \to ⑥$ . (e) Measured occupation of the $| ↓ ⟩$ state in the driven Rabi oscillation via the Stern-Gerlach-type approach [28], indicating an exponential decay with a time constant of $τ_{Rabi} = 42.9 \pm 7.0 ms$ .
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Figure 2
Superexchange dynamics and Bell states. (a) The averaged occupancy $ρ_{| ↑, ↓ ⟩}$ (circles) of the $| ↑, ↓ ⟩$ state, showing the superexchange dynamics in isolated double wells within the ROI. The fitted curve (solid line) with a damped sinusoidal function gives the averaged exchange strength $J_{ex} = 20.5 \pm 0.1 Hz$ . (b) The averaged spin configurations were measured in the 49 plaquettes during the spin superexchange process in double wells. (c) Measured populations under $| + / - ⟩$ , $| ↺ / ↻ ⟩$ , and $| ↑ / ↓ ⟩$ basis for the prepared Bell states averaged within the ROI gives $P_{+, +} = 0.484 \pm 0.007$ , $P_{+, -} = 0.021 \pm 0.003$ , $P_{-, +} = 0.015 \pm 0.002$ , $P_{-, -} = 0.480 \pm 0.007$ , $P_{↺, ↺} = 0.488 \pm 0.010$ , $P_{↺, ↻} = 0.018 \pm 0.002$ , $P_{↻, ↺} = 0.020 \pm 0.003$ , $P_{↻, ↻} = 0.474 \pm 0.008$ , $P_{↑, ↑} = 0.010 \pm 0.001$ , $P_{↑, ↓} = 0.490 \pm 0.009$ , $P_{↓, ↑} = 0.496 \pm 0.009$ , $P_{↓, ↓} = 0.004 \pm 0.001$ . (d) The extracted parity oscillation contrast of the prepared Bell states after different holding times with a spin-echo $π$ pulse, fitted as an exponential decay with a time constant $τ = 2.20 \pm 0.13 s$ . Error bars denote the s.e.m.
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Figure 3
Ten-body entangled state. (a) Quantum circuit representation for preparing and measuring a ten-body entangled state. (b) Exemplary fluorescence images of the initial atom arrays (upper panel) and the prepared ten-atom entangled state (lower panel), detected with the Stern-Gerlach type measurement [28]. (c) For the target entangled state, theoretical values of these two-body correlations under the $σ_{x}$ and $σ_{z}$ basis are nonzero. (d) The theoretical values of these two-body correlations under the $σ_{x}$ and $σ_{z}$ basis are all zero for the target state. (e) The extracted results of observables $γ_{i, j}$ . The dashed-dot line represents the threshold for verifying full bipartite nonseparability. Since $γ_{1, 2} = 1.81 \pm 0.09$ , $γ_{3, 4} = 1.37 \pm 0.10$ , $γ_{5, 6} = 1.43 \pm 0.10$ , $γ_{7, 8} = 1.39 \pm 0.10$ , and $γ_{9, 10} = 1.76 \pm 0.09$ , we conclude that atoms 1 and 2, 3 and 4, 5 and 6, 7 and 8, and 9 and 10 are nonseparable, respectively. Moreover, since $γ_{1, 3} = 1.62 \pm 0.10$ , $γ_{3, 5} = 1.51 \pm 0.10$ , $γ_{5, 7} = 1.39 \pm 0.10$ , and $γ_{8, 10} = 1.57 \pm 0.10$ , we deduce that the ten-atom chain cannot be divided into any two separated partitions [28]. Error bars denote the s.e.m.
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Figure 4
2D four-body and eight-body entangled states. (a) A schematic sketch of fully spin-resolved detection in a 2D configuration is achieved via state-dependent atom transport in optical lattices. (b) Top: a 2D, four-body entangled state structure and the corresponding quantum circuit representation of state preparation and measurement. Bottom: measured spin correlations and observables for demonstrating four-body genuine multipartite entanglement. (c) Spatial structure of a 2D, eight-body entangled plaquette and the corresponding quantum circuit representation of state preparation and measurement. (d) Measured spin correlations for the first two measurement settings and corresponding observables. These measurements certify the nonseparability inside two individual chains, shown with solid brown marks. (e) Measured spin correlations for the last three measurement settings and corresponding observables. These measurements certify the nonseparability between the two chains, shown with solid brown marks. All the results presented are not corrected for detection errors. The solid red lines in the histograms represent the threshold for the full bipartite nonseparability. Error bars denote the s.e.m.
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