Solving Systems of Linear Equations with a Superconducting Quantum Processor

  1. Yarui Zheng,
  2. Chao Song,
  3. Ming-Cheng Chen,
  4. Benxiang Xia,
  5. Wuxin Liu,
  6. Qiujiang Guo,
  7. Libo Zhang,
  8. Da Xu,
  9. Hui Deng,
  10. Keqiang Huang,
  11. Yulin Wu,
  12. Zhiguang Yan,
  13. Dongning Zheng,
  14. Li Lu,
  15. Jian-Wei Pan,
  16. H. Wang,
  17. Chao-Yang Lu,
  18. and Xiaobo Zhu
Superconducting quantum circuits are promising candidate for building scalable quantum computers. Here, we use a four-qubit superconducting quantum processor to solve a two-dimensional system of linear equations based on a quantum algorithm proposed by Harrow, Hassidim, and Lloyd [Phys. Rev. Lett. \textbf{103}, 150502 (2009)], which promises an exponential speedup over classical algorithms under certain circumstances. We benchmark the solver with quantum inputs and outputs, and characterize it by non-trace-preserving quantum process tomography, which yields a process fidelity of 0.837±0.006. Our results highlight the potential of superconducting quantum circuits for applications in solving large-scale linear systems, a ubiquitous task in science and engineering.
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