Integrated Quantum-Walk Structure and NAND Tree on a Photonic Chip

Yao Wang, Zi-Wei Cui, Yong-Heng Lu, Xiao-Ming Zhang, Jun Gao, Yi-Jun Chang, Man-Hong Yung, and Xian-Min Jin

Phys. Rev. Lett. 125, 160502 – Published 14 October 2020

Abstract

In the age of the post-Moore era, the next-generation computing model would be a hybrid architecture consisting of different physical components, such as photonic chips. In 2008, it was proposed that the solving of the NAND-tree problem can be sped up by quantum walk. This scheme is groundbreaking due to the universality of the NAND gate. However, experimental demonstration has not been achieved so far, mostly due to the challenge in preparing the propagating initial state. Here we propose an alternative solution by including a structure called a “quantum slide,” where a propagating Gaussian wave packet can be generated deterministically along a properly engineered chain. In our experimental demonstration, the optical NAND tree is capable of solving computational problems with a total of four input bits, based on the femtosecond laser 3D direct-writing technique on a photonic chip. These results remove one main roadblock to photonic NAND-tree computation, and the construction of a quantum slide may find other interesting applications in quantum information and quantum optics.

Received 19 June 2020
Accepted 8 September 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.160502

Physics Subject Headings (PhySH)

Integrated optics Quantum algorithms Quantum computation Quantum gates Quantum information processing Quantum networks Quantum protocols Quantum walks

NetworksQuantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Yao Wang ^1,2,*, Zi-Wei Cui ^3,4,*, Yong-Heng Lu^1,2, Xiao-Ming Zhang⁵, Jun Gao^1,2, Yi-Jun Chang^1,2, Man-Hong Yung ^3,4,6,7,†, and Xian-Min Jin ^1,2,3,4,‡

¹Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
²CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
³Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
⁴Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
⁵Department of Physics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong SAR, China
⁶Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
⁷Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China

^*These authors contributed equally to this work.
^†yung@sustech.edu.cn
^‡xianmin.jin@sjtu.edu.cn

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Issue

Vol. 125, Iss. 16 — 16 October 2020

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Images

Figure 1
Quantum NAND tree. The schematic of the tree structure with (a) one-layer branch and (b) two-layer branch. The site number in the last layer determines the number of input bits. The leaves on the last layer determine the input of the tree, if there is a leaf on the last layer, then the input of this site is one, and otherwise is zero. It is a NAND gate for each site on the layer besides the last layer. The logical value of the root presents the output result of the tree, which determines the evolution of the wave packet on the runway: the right-moving wave packet will back if the output result is zero, or go ahead if the output result is one.
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Figure 2
Quantum slide. (a) The relationship between the wave packet width $σ$ and the length of quantum slide $L_{qs}$ . The red dashed line gives the parameter adopted in experiment. (b) The sketch of quantum slide. Twenty sites are designed for the QS; the wave packet obtained by the QS process transmits to the runway consisting of 31 sites. The sites in QS are labeled from 1 to 20, while the sites in runway are labeled from 21 to 51. (c) The distribution of the coupling strengths. (d) Measured output distribution of photons with different evolution distance in the QS process. The red lines are the theoretical results, the green points present the measured values, and the black dashed lines are the fitting result of the experimental values.
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Figure 3
Measured result of one-layer NAND tree. (a) The sketch of one-layer NAND-tree structure in experiment. $S_{L}$ is the distribution amplitude summation of sites 21–35, $S_{R}$ represents the distribution amplitude summation of sites 37–51, $S_{C}$ is the distribution amplitude summation of sites in NAND-tree structure, and $S_{L C} = S_{L} + S_{C}$ . (b) The evolution result of $S_{R}$ and $S_{L C}$ . For the case of input [0 0], the $S_{R}$ goes larger than $S_{L C}$ with the increase of evolution distance, representing that the wave packet goes pass the site connecting the tree, while the result is contrary for the case of input [1 1]. (c) The measured result of one-layer NAND tree. The logic output is determined by the $L_{out}$ , which is obtained from the corresponding distributions of $S_{R}$ and $S_{L C}$ .
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Figure 4
Measured result of two-layer NAND tree. (a) The cross section micrograms of the NAND tree. There are six types of logical input for two-layer NAND tree. The insets show the dynamical result for the cases of input [0 0 0 0] and [0 0 1 1], respectively. For the case of input [0 1 0 1], the $S_{R}$ goes larger than $S_{L C}$ with the increase of evolution distance, representing that the wave packet goes past the site connecting the tree, while the result is contrary for the case of input [0 0 0 0]. (b) The measured logic output, $S_{R}$ and $S_{L C}$ of two-layer NAND tree. The four-bit input quantum NAND algorithm is well realized and the visibility of output result is stable.
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