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一个T门使得分发学习变得更加困难
M Hinsche1, M Ioannou1, A Nietner1
1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.
Physical review letters
|June 30, 2023
概括
学习量子电路输出分布是复杂的. 虽然简单的克利福德电路是可以学习的,但添加T门或使用通用电路使它们在计算上变得困难,在机器学习中挑战量子优势要求.
科学领域:
- 量子计算是一种量子计算.
- 机器学习 机器学习
- 计算复杂性 计算复杂性
背景情况:
- 从样本中学习概率分布是自然科学的基础.
- 局部量子电路的输出分布对于量子优势建议和量子机器学习 (QML) 至关重要.
- 了解这些分布的可学习性是评估量子计算能力的关键.
研究的目的:
- 广泛描述局部量子电路产生的输出分布的可学习性.
- 在量子电路的背景下,将可学习性与可模拟性进行对比.
- 为了研究量子电路的生成和密度建模任务的硬度.
主要方法:
- 量子电路输出分布的理论分析.
- 复杂性理论论证以确定硬度结果.
- 克利福德电路与具有T门和通用电路的电路的学习能力的比较.
主要成果:
- 克利福德电路输出分布是可以有效地学习的.
- 引入单个T门使得密度建模对于深度d=n^{Ω(1) }的电路难以处理.
- 对于所有学习算法 (古典和量子) 来说,在深度d=n^{Ω(1) 的普遍量子电路的生成建模是很困难的.
- 即使是深度d=ω[log(n) ]克利福德电路对于统计查询算法来说也很难学习.
结论:
- 当地量子电路输出分布不能证明量子和经典生成模拟功率之间的分离.
- 这些发现提供了证据,证明了在概率模型任务中的实际量子优势.
- 学习量子分布的计算复杂性取决于电路结构和深度.
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