Resource analysis of quantum computing with noisy qubits for Shor's factoring algorithms

We decompose two implementations of Shor's algorithm for prime factorization into universal gate units at the logical level and predict the number of physical qubits and execution time when surface codes are used. Logical qubit encoding using a rotated surface code and logical qubits with all-to-all connectivity are assumed. We express the number of physical qubits and execution time in terms of the bit length of the number to be factorized and error rate of the physical quantum gate. We confirm the relationship between the number of qubits and the execution time by analyzing two algorithms using various bit lengths and physical gate error rates .

Automated summary

This study decomposes two implementations of Shor's algorithm for prime factorization into universal gate units at the logical level and predicts the number of physical qubits and execution time when surface codes are used. Assuming logical qubit encoding using a rotated surface code and logical qubits with all-to-all connectivity, the number of physical qubits and execution time are expressed in terms of the bit length of the number to be factorized and error rate of the physical quantum gate. By analyzing two algorithms with different bit lengths and physical gate error rates, the relationship between the number of qubits and the execution time is confirmed.