Factoring integers with sublinear resources on a superconducting quantum processor

• Main Authors: Yan, Bao, Tan, Ziqi, Wei, Shijie, Jiang, Haocong, Wang, Weilong, Wang, Hong, Luo, Lan, Duan, Qianheng, Liu, Yiting, Shi, Wenhao, Fei, Yangyang, Meng, Xiangdong, Han, Yu, Shan, Zheng, Chen, Jiachen, Zhu, Xuhao, Zhang, Chuanyu, Jin, Feitong, Li, Hekang, Song, Chao, Wang, Zhen, Ma, Zhi, Wang, H, Long, Gui-Lu
• Format: Journal Article
• Language: English
• Published: 23.12.2022
• Subjects: Physics - Quantum Physics
• DOI: 10.48550/arxiv.2212.12372

Shor's algorithm has seriously challenged information security based on public key cryptosystems. However, to break the widely used RSA-2048 scheme, one needs millions of physical qubits, which is far beyond current technical capabilities. Here, we report a universal quantum algorithm for integer factorization by combining the classical lattice reduction with a quantum approximate optimization algorithm (QAOA). The number of qubits required is O(logN/loglog N), which is sublinear in the bit length of the integer $N$, making it the most qubit-saving factorization algorithm to date. We demonstrate the algorithm experimentally by factoring integers up to 48 bits with 10 superconducting qubits, the largest integer factored on a quantum device. We estimate that a quantum circuit with 372 physical qubits and a depth of thousands is necessary to challenge RSA-2048 using our algorithm. Our study shows great promise in expediting the application of current noisy quantum computers, and paves the way to factor large integers of realistic cryptographic significance.