Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by a binary tree, we construct an explicit quantum algorithm for an important three-dimensional subspace of the parameter space that runs in polynomial time to sample from the process once. The corresponding naive Markov chain algorithm does not produce the correct probability distribution and an explicit classical calculation of the full distribution requires exponentially many operations. However, the problem can be reduced to a system of two qubits with repeated measurements, shedding light on a quantum-inspired efficient classical algorithm.

中文翻译：

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一种有效地从干扰二叉树中采样的量子算法

量子计算机提供了一个机会，可以从概率分布中有效采样，这些概率分布包括幅度之间的非平凡干扰效应。通过使用一个简单的过程（其中所有可能的状态历史可以由二叉树指定），我们为参数空间的重要三维子空间构造了一个显式量子算法，该空间在多项式时间内运行以从该过程中采样一次。相应的朴素的马尔可夫链算法无法产生正确的概率分布，并且对整个分布进行显式经典计算需要成倍地增加运算量。但是，该问题可以简化为两个具有重复测量的量子比特的系统，从而避免了量子激发的高效经典算法的麻烦。