Quantum search algorithms offer a remarkable advantage of quadratic reduction in query complexity using quantum superposition principle. However, how an actual architecture may access and handle the database in a quantum superposed state has been largely unexplored so far; the quantum state of data was simply assumed to be prepared and accessed by a black-box operation—so-called oracle, even though this process, if not appropriately designed, may adversely diminish the quantum query advantage. Here, we introduce an efficient quantum data-access process, dubbed as quantum data-access machine (QDAM), and present a general architecture for quantum search algorithm. We analyze the runtime of our algorithm in view of the fault-tolerant quantum computation (FTQC) consisting of logical qubits within an effective quantum error correction code. Specifically, we introduce a measure involving two computational complexities, i.e. quantum query and T-depth complexities, which can be critical to assess performance since the logical non-Clifford gates, such as the T (i.e. π/8 rotation) gate, are known to be costliest to implement in FTQC. Our analysis shows that for N searching data, a QDAM model exhibiting a logarithmic, i.e. O(logN) , growth of the T-depth complexity can be constructed. Further analysis reveals that our QDAM-embedded quantum search requires O(N×logN) runtime cost. Our study thus demonstrates that the quantum data search algorithm can truly speed up over classical approaches with the logarithmic T-depth QDAM as a key component.

中文翻译：

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使用量子数据访问机进行 T 深度优化的量子搜索


量子搜索算法具有利用量子叠加原理二次降低查询复杂性的显着优势。然而，到目前为止，实际架构如何在量子叠加状态下访问和处理数据库在很大程度上尚未得到探索。数据的量子状态被简单地假设为通过黑盒操作（即所谓的预言机）准备和访问，尽管这个过程如果设计不当，可能会不利地削弱量子查询的优势。在这里，我们介绍了一种高效的量子数据访问过程，称为量子数据访问机（QDAM），并提出了量子搜索算法的通用架构。我们根据由有效量子纠错码内的逻辑量子位组成的容错量子计算（FTQC）来分析算法的运行时间。具体来说，我们引入了一种涉及两种计算复杂性的度量，即量子查询和 T 深度复杂性，这对于评估性能至关重要，因为逻辑非 Clifford 门，例如 T（即 π/8 旋转）门是已知的在 FTQC 中实施成本最高。我们的分析表明，对于 N 个搜索数据，可以构建呈现对数增长（即 O(logN)）的 T 深度复杂度增长的 QDAM 模型。进一步的分析表明，我们的 QDAM 嵌入式量子搜索需要 O(N×logN) 运行时间成本。因此，我们的研究表明，以对数 T 深度 QDAM 作为关键组件，量子数据搜索算法可以真正比经典方法加速。