论文标题
在超导量子处理器上以均方根资源的形式设定整数
Factoring integers with sublinear resources on a superconducting quantum processor
论文作者
论文摘要
Shor的算法已经严重挑战了基于公共密钥密码系统的信息安全性。但是，为了打破广泛使用的RSA-2048计划，需要数百万个物理量子位，这远远超出了当前的技术能力。在这里，我们通过将经典的晶格还原与量子近似优化算法（QAOA）相结合，报告了一种通用量子算法，用于整数分解。所需的量楼数为O（logn/loglog n），它在整数$ n $的位，使其成为迄今为止最频繁的分解算法。我们通过将多达48位的整数分解为10位超导量子位，这是量子设备上最大的整数。我们估计，使用我们的算法挑战RSA-2048的量子电路，具有372个物理Qubits和数千个深度是必要的。我们的研究表明，在加快当前嘈杂量子计算机的应用方面表现出了巨大的希望，并为考虑具有现实加密意义的大整数的方式铺平了道路。
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.
