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<p>As one of the fundamental quantum circuits widely used today, the quantum modular exponentiation circuit has been applied in various quantum algorithms, including Shor’s algorithm. However, due to the limitations of quantum computers in the noisy intermediate-scale quantum (NISQ) era, excessive circuit depth and high quantum cost can lead to significant noise accumulation, thereby increasing the likelihood of computational errors. Consequently, reducing both circuit depth and quantum cost is essential. To address these issues, this work proposes two modular exponentiation circuits based on the V gate, with further improvements introduced through the use of zero resets. Comparative analysis shows that both proposed circuits achieve reductions in circuit depth and quantum cost within their respective domains, while preserving general applicability. Furthermore, by relaxing the constraint of circuit reversibility, the improved designs achieve an additional two to three fold reduction in circuit depth and quantum cost. Finally, the correctness of the proposed circuits was verified through experimental implementation using the Qiskit package in Python.</p>

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Construction and optimization of quantum modular exponentiation circuits based on the V gate

  • 期刊论文

  • 发表日期：

    2025年11月3日

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  • Xinglan Zhang,
  • Xiaojun Rong,
  • Zheng Li

摘要

As one of the fundamental quantum circuits widely used today, the quantum modular exponentiation circuit has been applied in various quantum algorithms, including Shor’s algorithm. However, due to the limitations of quantum computers in the noisy intermediate-scale quantum (NISQ) era, excessive circuit depth and high quantum cost can lead to significant noise accumulation, thereby increasing the likelihood of computational errors. Consequently, reducing both circuit depth and quantum cost is essential. To address these issues, this work proposes two modular exponentiation circuits based on the V gate, with further improvements introduced through the use of zero resets. Comparative analysis shows that both proposed circuits achieve reductions in circuit depth and quantum cost within their respective domains, while preserving general applicability. Furthermore, by relaxing the constraint of circuit reversibility, the improved designs achieve an additional two to three fold reduction in circuit depth and quantum cost. Finally, the correctness of the proposed circuits was verified through experimental implementation using the Qiskit package in Python.