The query model (or black-box model) has attracted much attention from the communities of both classical and quantum computing. Usually, quantum advantages are revealed by presenting a quantum algorithm that has a better query complexity than its classical counterpart. In the history of quantum algorithms, the Deutsch algorithm and the Deutsch-Jozsa algorithm play a fundamental role and both are exact one-query quantum algorithms. This leads us to consider the problem: what functions can be computed by exact one-query quantum algorithms? This problem has been addressed in the literature for total Boolean functions and symmetric partial Boolean functions, but is still open for general partial Boolean functions. Thus, in this paper, we continue to characterize the computational power of exact one-query quantum algorithms for general partial Boolean functions. First, we present several necessary and sufficient conditions for a partial Boolean function to be computed by exact one-query quantum algorithms. Second, inspired by these conditions, we discover some new representative functions that can be computed by exact one-query quantum algorithms but have an essential difference from the already known ones. Specially, it is worth pointing out that before our work, the known functions that can be computed by exact one-query quantum algorithms are all symmetric functions and the quantum algorithm used is essentially the Deutsch-Jozsa algorithm, whereas the functions discovered in this paper are generally asymmetric and new algorithms to compute these functions are required. Thus, this expands the class of functions that can be computed by exact one-query quantum algorithms.

查询模型（或黑盒模型）引起了经典计算和量子计算界的广泛关注。通常，量子优势是通过提供比经典算法具有更好查询复杂性的量子算法来揭示的。在量子算法的历史上，Deutsch算法和Deutsch-Jozsa算法发挥着基础性的作用，都是精确的单查询量子算法。这让我们思考一个问题：哪些函数可以通过精确的单查询量子算法来计算？这个问题已经在全布尔函数和对称偏布尔函数的文献中得到解决，但对于一般的偏布尔函数仍然是开放的。因此，在本文中，我们继续表征一般部分布尔函数的精确单查询量子算法的计算能力。首先，我们提出了通过精确的单查询量子算法计算部分布尔函数的几个必要和充分条件。其次，受这些条件的启发，我们发现了一些新的代表性函数，这些函数可以通过精确的单查询量子算法计算，但与已知的函数有本质的区别。特别值得指出的是，在我们的工作之前，已知的可以通过精确单查询量子算法计算的函数都是对称函数，并且使用的量子算法本质上是Deutsch-Jozsa算法，而本文发现的函数通常是不对称的，需要新的算法来计算这些函数。因此，这扩展了可以通过精确的单查询量子算法计算的函数类别。