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Practical circuit optimization algorithm for quantum simulation based on template matching

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Abstract

We propose a circuit optimization algorithm that facilitates the implementation of various applications on noise intermediate-scale quantum (NISQ) devices. The algorithm is hardware-independent and reduces the overall circuit cost of Hamiltonian simulation, particularly by minimizing the number of CNOT gates. Our approach employs a sub-circuit synthesis scheme for intermediate representation and proposes the practical template matching algorithm (TM) for gate elimination to minimize CNOT counts. This algorithm demonstrates low complexity and enhances the circuit performance of Hamiltonian simulations. In our simulations, we benchmarked different algorithms across various Hamiltonian models to quantify and compare the benefits of our approach. Compared with advanced generic compilers and specific quantum compilers, the results obtained from simulating our algorithm show an average reduction of 1.5\(\times \) (up to 2.56\(\times \)) in CNOT counts, and 1.4\(\times \) (up to 3.1\(\times \)) in circuit depth. This improvement further advances the practical application of Hamiltonian simulation in the NISQ era.

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Data availability

The data and code that support the findings of this study are openly available at the following URL/:https://github.com/QUANTUM-AND-ML/QUANTUM-QuantumSimulation.git.

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Acknowledgements

This work was supported by the National Science Foundation of China (Nos. 61871111 and 61960206005), Jiangsu Key R &D Program Project (No. BE2023011-2), Jiangsu Funding Program for Excellent Postdoctoral Talent (No.2022ZB139), the Fundamental Research Funds for the Central Universities (2242022k60001), and the research fund of National Mobile Communications Research Lab. (2024A04), and the Opening Project of Key Laboratory of Medical Electronics and Digital Health of Zhejiang Province (No. MEDH202202).

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Authors and Affiliations

  1. National Mobile Communications Research Laboratory, Southeast University, Nanjing, 210096, China

    Yuxiang Liu, Zaichen Zhang & Yi Hu

  2. State Key Laboratory of Millimeter Waves, Southeast University, Nanjing, 210096, China

    Xutao Yu

  3. Purple Mountain Lab, Nanjing, 211111, China

    Zaichen Zhang & Xutao Yu

  4. Frontiers Science Center for Mobile Information Communication and Security, Southeast University, Nanjing, 210096, China

    Yuxiang Liu, Zaichen Zhang, Yi Hu & Xutao Yu

  5. Yangtze Delta Region Industrial Innovation Center of Quantum and Information Technology, Suzhou, 215133, China

    Tian Luan

  6. Key Laboratory of Medical Electronics and Digital Health of Zhejiang Province, Jiaxing University, Jiaxing, 314001, China

    Xianchao Zhang

  7. College of Artificial Intelligence, Nanjing Tech University, Nanjing, 211800, China

    Fanxu Meng

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  1. Yuxiang Liu
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Appendix A

Appendix A

Figure 20, 21, 22, 23, 24, 25, 26, 27 and 28 shows the proof of the equivalent circuits of Pauli intermediate representation (IR) using ZX-calculus, where \(\delta =2\theta \).

Fig. 20
figure 20

Equivalent circuit proof procedure for the two-local \(X\otimes X\) operator

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Fig. 21
figure 21

Equivalent circuit proof procedure for the two-local \(X\otimes Y\) operator

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Fig. 22
figure 22

Equivalent circuit proof procedure for the two-local \(X\otimes Z\) operator

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Fig. 23
figure 23

Equivalent circuit proof procedure for the two-local \(Y\otimes X\) operator

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Fig. 24
figure 24

Equivalent circuit proof procedure for the two-local \(Y\otimes Y\) operator

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Fig. 25
figure 25

Equivalent circuit proof procedure for the two-local \(Y\otimes Z\) operator

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Fig. 26
figure 26

Equivalent circuit proof procedure for the two-local \(Z\otimes X\) operator

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Fig. 27
figure 27

Equivalent circuit proof procedure for the two-local \(Z\otimes Y\) operator

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Fig. 28
figure 28

Equivalent circuit proof procedure for the two-local \(Z\otimes Z\) operator

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Liu, Y., Zhang, Z., Hu, Y. et al. Practical circuit optimization algorithm for quantum simulation based on template matching. Quantum Inf Process 23, 45 (2024). https://doi.org/10.1007/s11128-023-04252-2

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