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Experimental realization of quantum algorithms for a linear system inspired by adiabatic quantum computing

Jingwei Wen, Xiangyu Kong, Shijie Wei, Bixue Wang, Tao Xin, and Guilu Long
Phys. Rev. A 99, 012320 – Published 14 January 2019
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  • INTRODUCTION
  • A BRIEF REVIEW OF THE THEORY
  • EXPERIMENTAL SETUPS AND RESULTS
  • CONCLUSION
  • ACKNOWLEDGMENTS
    • References

    Abstract

    Adiabatic quantum computation is of fundamental importance in the field of quantum computation as it offers an alternative approach to the gate-based model for the manipulation of quantum systems. Recently, an interesting work [arXiv:1805.10549] indicated that we can solve a linear equation system via an algorithm inspired by adiabatic quantum computing. Here we demonstrate the algorithm in a four-qubit nuclear magnetic resonance system by determining the solution of an eight-dimensional linear equation Ax=b. The result is by far the maximum-dimensional linear equation solution with a limited number of qubits in experiments, which include some ingenious simplifications. Our experiment provides the possibility of solving so many practical problems related to linear equations systems and has the potential applications in designing the future quantum algorithms.

    • Figure
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    • Received 26 June 2018

    DOI:https://doi.org/10.1103/PhysRevA.99.012320

    ©2019 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Adiabatic quantum optimizationMachine learningQuantum algorithmsQuantum information architectures & platforms
    1. Techniques
    Nuclear magnetic resonance
    Quantum Information, Science & Technology

    Authors & Affiliations

    Jingwei Wen1,*, Xiangyu Kong1,*, Shijie Wei2, Bixue Wang1, Tao Xin3,†, and Guilu Long1,4,5,‡

    • 1State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
    • 2IBM Research, Beijing 100094, China
    • 3Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
    • 4Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, People's Republic of China
    • 5Collaborative Innovation Center of Quantum Matter, Beijing 100084, China

    • *These authors contributed equally to this work.
    • †xint@sustc.edu.cn
    • ‡gllong@tsinghua.edu.cn

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    Issue

    Vol. 99, Iss. 1 — January 2019

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    Images

    • Figure 1
      Figure 1

      (a) Molecule structure of C13-labeled crotonic acid. C1–C4 are used as four qubits in the experiment, whereas all H1's are decoupled throughout the experiment. (b) Molecule parameters of the sample: the chemical shifts and J couplings (in hertz) are listed by the diagonal and off-diagonal elements, respectively. T2's(in seconds) are also shown at the bottom.

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    • Figure 2
      Figure 2

      Experimental results for the first algorithm. (a) (Energy and fidelity). The light and dark blue solid lines are theoretical values of the first-two energy levels of the time-dependent Hamiltonian, respectively. The solid points (black below) represent the experimental energy results, and the corresponding experimental fidelities are shown by the circle points above. (b) (Final solution). The real and imaginary parts of the theoretical (light blue bars) and experimental (dark blue bars) final quantum states of solution |x〉 are shown. The numbers labeled present the corresponding differences between experimental and theoretical values.

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    • Figure 3
      Figure 3

      Experimental results for the second algorithm. The solid lines are theoretical values of the energy spectrum of the time-dependent Hamiltonian. The light blue line is the middle level of the spectrum, and the other lines represent the closest eight energy levels. The black points represent experimental energy results in each step of our experiment.

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