Quantum verification of NP problems with single photons and linear optics

Aonan Zhang; Hao Zhan; Junjie Liao; Kaimin Zheng; Tao Jiang; Minghao Mi; Penghui Yao; Lijian Zhang

doi:10.1038/s41377-021-00608-4

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Quantum verification of NP problems with single photons and linear optics

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- Quantum verification of NP problems with single photons and linear optics
- Quantum verification of NP problems with single photons and linear optics
- LSA 2021年10卷第9期页码：1750-1760
- Affiliations：
  
  1.National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation (Ministry of Education) and College of Engineering and Applied Sciences, Nanjing University, 210093, Nanjing, China
  2.Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 210093, Nanjing, China
  3.State Key Laboratory for Novel Software Technology, Nanjing University, 210093, Nanjing, China
- Author bio：
  
  Penghui Yao (pyao@nju.edu.cn)
  Lijian Zhang (lijian.zhang@nju.edu.cn)
- Funds：
- DOI：10.1038/s41377-021-00608-4
  中图分类号：
- 纸质出版日期：2021-09-30，
  
  网络出版日期：2021-08-18，
  
  收稿日期：2021-01-19，
  
  修回日期：2021-07-22，
  
  录用日期：2021-07-30
- Accepted：
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Quantum verification of NP problems with single photons and linear optics[J]. LSA, 2021,10(9):1750-1760.

Zhang, A. et al. Quantum verification of NP problems with single photons and linear optics. Light: Science & Applications, 10, 1750-1760 (2021).
Quantum verification of NP problems with single photons and linear optics[J]. LSA, 2021,10(9):1750-1760. DOI： 10.1038/s41377-021-00608-4.

Zhang, A. et al. Quantum verification of NP problems with single photons and linear optics. Light: Science & Applications, 10, 1750-1760 (2021). DOI： 10.1038/s41377-021-00608-4.

摘要

Abstract

Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) is a complexity class containing many important but intractable problems like the satisfiability of potentially conflict constraints (SAT). According to the well-founded exponential time hypothesis

verifying an SAT instance of size

requires generally the complete solution in an

(

)-bit proof. In contrast

quantum verification algorithms

which encode the solution into quantum bits rather than classical bit strings

can perform the verification task with quadratically reduced information about the solution in

$$\tilde O(\sqrt n)$$

qubits. Here we realize the quantum verification machine of SAT with single photons and linear optics. By using tunable optical setups

we efficiently verify satisfiable and unsatisfiable SAT instances and achieve a clear completeness-soundness gap even in the presence of experimental imperfections. The protocol requires only unentangled photons

linear operations on multiple modes and at most two-photon joint measurements. These features make the protocol suitable for photonic realization and scalable to large problem sizes with the advances in high-dimensional quantum information manipulation and large scale linear-optical systems. Our results open an essentially new route toward quantum advantages and extend the computational capability of optical quantum computing.

关键词

Keywords

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