基于量子数据存取机的t深度优化量子搜索

IF 5.6 2区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY
Jung Jun Park, Kyunghyun Baek, Myungshik Kim, Hyunchul Nha, Jaewan Kim, Jeongho Bang
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引用次数: 1

摘要

量子搜索算法利用量子叠加原理将查询复杂度二次降低,具有显著的优势。然而,到目前为止,实际的架构如何访问和处理量子叠加状态下的数据库在很大程度上尚未被探索;数据的量子态被简单地假设为通过黑箱操作(即所谓的量子预言)来准备和访问,即使这个过程如果设计不当,可能会对量子查询的优势产生不利影响。本文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),并给出了量子搜索算法的通用架构。在有效的量子纠错码中,我们分析了由逻辑量子比特组成的容错量子计算(FTQC)算法的运行时。具体来说,我们引入了一个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,如T(即π/8旋转)门,已知在FTQC中实现成本最高。我们的分析表明,对于N搜索数据,QDAM模型可以构造出T深度复杂度的对数增长,即O(logN)增长。进一步分析表明,我们的qdam嵌入式量子搜索需要O(√N × logN)运行时成本。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加快经典方法的速度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
T-depth-optimized Quantum Search with Quantum Data-access Machine
Abstract 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 quantum 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.
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来源期刊
Quantum Science and Technology
Quantum Science and Technology Materials Science-Materials Science (miscellaneous)
CiteScore
11.20
自引率
3.00%
发文量
133
期刊介绍: Driven by advances in technology and experimental capability, the last decade has seen the emergence of quantum technology: a new praxis for controlling the quantum world. It is now possible to engineer complex, multi-component systems that merge the once distinct fields of quantum optics and condensed matter physics. Quantum Science and Technology is a new multidisciplinary, electronic-only journal, devoted to publishing research of the highest quality and impact covering theoretical and experimental advances in the fundamental science and application of all quantum-enabled technologies.
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