| （英） |
The discovery of Shor's algorithm for integer factorization has revealed the potential vulnerability of current cryptographic systems to future decryption. Consequently, to accurately estimate the timeframe for decryption, it is essential to evaluate the factorization capabilities of current quantum hardware. While experiments with Shor's algorithm on actual quantum devices have been conducted, circuit simplifications have hindered precise assessments. Moreover, among various proposed circuit constructions, it remains unclear which is most efficient for factoring small integers. In this study, we aim to identify the most efficient circuit constructions and its computational resources for factoring small integers, such as $N=21$, to assess the factorization capabilities of current quantum devices. Firstly, we propose a more efficient circuit for one of the circuit components, namely the quantum read-only memory(QROM). Subsequently, we compare the computational resources required for factoring $N=21$ using different circuit constructions. The results indicate that factorizing $N=21$ requires a quantum circuit with 24 qubits and a cx depth of 8187, making experimental implementation on current NISQ devices challenging. |