基于QAOA的亚线性因子分解算法的缺陷
Pitfalls of the sublinear QAOA-based factorization algorithm
AI总结：
本文针对Yan等人提出的基于亚线性量子资源的因子分解算法，指出其未系统分析利用Schnorr格方法的经典部分计算复杂度，通过示例说明需补充资源分析。
摘要：
量子计算设备被认为在解决素数因子分解问题方面能力强大，而该问题是广泛部署的公钥密码工具的核心。然而，Shor量子因子分解算法的实现需要与数字规模线性增长的大量资源；考虑到量子纠错所需的开销，据估算，在8小时内分解2048位RSA密钥需要2000万个（含噪声的）物理量子比特。Yan等人近期的一项提案声称可以用亚线性量子资源解决因子分解问题。我们在研究中表明，该提案缺乏对算法经典部分计算复杂度的系统分析，这部分算法利用了Schnorr基于格的方法。我们提供了若干示例，说明对这一拟议的量子因子分解算法有必要开展额外的资源分析。
英文摘要：
Quantum computing devices are believed to be powerful in solving the prime factorization problem, which is at the heart of widely deployed public-key cryptographic tools. However, the implementation of Shor's quantum factorization algorithm requires significant resources scaling linearly with the number size; taking into account an overhead that is required for quantum error correction the estimation is that 20 millions of (noisy) physical qubits are required for factoring 2048-bit RSA key in 8 hours. Recent proposal by Yan et al. claims a possibility of solving the factorization problem with sublinear quantum resources. As we demonstrate in our work, this proposal lacks systematic analysis of the computational complexity of the classical part of the algorithm, which exploits the Schnorr's lattice-based approach. We provide several examples illustrating the need in additional resource analysis for the proposed quantum factorization algorithm.
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