论文标题
基于创造复杂性的量子状态表征
Characterization of quantum states based on creation complexity
论文作者
论文摘要
量子状态的创建复杂性是从基本初始状态创建它所需的基本门的最小数量。量子状态的创建复杂性与量子电路的复杂性密切相关，这对于开发有效的量子算法至关重要，这些量子算法可以超越经典算法。到目前为止，尚未解决的一个主要问题是，可以使用许多基本门来创建哪些量子状态，这些门与量子数的数量缩放。在这项工作中，我们首先显示了完全通用的量子状态，这是指数级的（需要多个步骤，以指数尺度的量子数）来确定创建复杂性是否为多项式。然后，我们表明具有多项式创建复杂性的大型量子状态具有共同的系数特征，以便给定任何候选量子状态，我们可以设计一个有效的系数采样程序，以确定其是否属于该类别是否具有任意高成功概率。因此，获得了量子状态创造复杂性的部分知识，这对于设计涉及这种状态的量子电路和算法很有用。
The creation complexity of a quantum state is the minimum number of elementary gates required to create it from a basic initial state. The creation complexity of quantum states is closely related to the complexity of quantum circuits, which is crucial in developing efficient quantum algorithms that can outperform classical algorithms. A major question unanswered so far is what quantum states can be created with a number of elementary gates that scales polynomially with the number of qubits. In this work we first show for an entirely general quantum state it is exponentially hard (requires a number of steps that scales exponentially with the number of qubits) to determine if the creation complexity is polynomial. We then show it is possible for a large class of quantum states with polynomial creation complexity to have common coefficient features such that given any candidate quantum state we can design an efficient coefficient sampling procedure to determine if it belongs to the class or not with arbitrarily high success probability. Consequently partial knowledge of a quantum state's creation complexity is obtained, which can be useful for designing quantum circuits and algorithms involving such a state.
