使用变量量子算法来解决LWE问题
Lihui Lv1,2, Bao Yan1,2, Hong Wang1,2
1State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China.
Entropy (Basel, Switzerland)
|July 8, 2023
概括
本研究引入了两种变量量子算法 (VQA) 来解决学习错误 (LWE) 问题. 实验表明,VQA增强了LWE的经典解决方案,这是量子计算的一个关键挑战.
科学领域:
- 量子计算是一种量子计算.
- 密码学 密码学 密码学 密码学
- 算法开发 算法开发
背景情况:
- 变量量子算法 (VQA) 是一种混合方法,适用于杂的中间尺度量子 (NISQ) 设备.
- 错误学习 (LWE) 问题是密码学和量子计算的一个基本挑战.
- 目前用于LWE的经典方法是计算密集型的,这激发了量子解决方案的探索.
研究的目的:
- 提出和评估两种基于VQA的新方法来解决LWE问题.
- 证明VQA在增强LWE的经典方法方面的潜力.
- 在NISQ设备上评估VQA对LWE的可行性.
主要方法:
- 将LWE问题缩小为边界距离解码 (BDD) 问题,使用量子近似优化算法 (QAOA) 解决.
- 将LWE问题缩小为唯一最短向量问题 (uSVP),使用变量量子自身解决器 (VQE) 解决.
- 基于VQE的方法对量子位需求的详细计算.
- 对两种拟议的VQA方法进行小规模实验验证.
主要成果:
- 两种拟议的VQA策略都在小规模实验中成功解决了LWE问题.
- 与纯粹的古典方法相比,VQA方法证明了解决方案质量的提高.
- 该研究提供了对LWE应用的VQE量子位资源需求的详细见解.
结论:
- 变量量子算法为解决NISQ硬件上的错误学习问题提供了一个有希望的途径.
- 在VQA框架内集成QAOA和VQE可以增强经典LWE解决能力.
- 在中等规模量子计算时代,VQA代表了推进加密解决方案的可行和有效策略.
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