The learnability of quantum states
The learnability of quantum states
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DOI：
10.1098/rspa.2007.0113
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发表时间：
2007-12-08
影响因子：
3.5
通讯作者：
Aaronson, Scott
中科院分区：
文献类型：
--
作者：
Aaronson, Scott
传统的量子态层析成像需要随着量子位数n呈指数增长的测量数量。但是，使用计算学习理论的思想，我们表明，在统计环境中，人们可以做得更好。特别是，为了预测从任意概率分布中提取的大多数测量结果，只需要一些随n线性增长的样本测量。这个定理的概念含义是量子态，尽管是指数长的向量，但在学习理论的意义上是“合理的”。该定理在量子计算中也有两个应用：第一，量子单向通信协议的新模拟;第二，使用可信的经典建议来验证不可信的量子建议。
Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n. But using ideas from computational learning theory, we show that one can do exponentially better in a statistical setting. In particular, to predict the outcomes of most measurements drawn from an arbitrary probability distribution, one needs only a number of sample measurements that grows linearly with n. This theorem has the conceptual implication that quantum states, despite being exponentially long vectors, are nevertheless 'reasonable' in a learning theory sense. The theorem also has two applications to quantum computing: first, a new simulation of quantum one-way communication protocols and second, the use of trusted classical advice to verify untrusted quantum advice.