Factoring integers with sublinear resources on a superconducting quantum processor

• URL: http://arxiv.org/abs/2212.12372v1
• Date: Fri, 23 Dec 2022 14:45:02 GMT
• Title: Factoring integers with sublinear resources on a superconducting quantum processor
• Authors: Bao Yan, Ziqi Tan, Shijie Wei, Haocong Jiang, Weilong Wang, Hong Wang, Lan Luo, Qianheng Duan, Yiting Liu, Wenhao Shi, Yangyang Fei, Xiangdong Meng, Yu Han, Zheng Shan, Jiachen Chen, Xuhao Zhu, Chuanyu Zhang, Feitong Jin, Hekang Li, Chao Song, Zhen Wang, Zhi Ma, H. Wang, Gui-Lu Long
• Abstract summary: Shor's algorithm has seriously challenged information security based on public key cryptosystems. To break the widely used RSA-2048 scheme, one needs millions of physical qubits, which is far beyond current technical capabilities. We report a universal quantum algorithm for integer factorization by combining the classical lattice reduction with a quantum approximate optimization algorithm.
• Score: 11.96383198580683
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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