关联规则挖掘量子算法的实验实现
Experimental implementation of quantum algorithm for association rules mining
摘要：
最近，一个量子算法在数据挖掘中的一个根本性的重要任务，关联规则挖掘（ARM），简称qARM，已被提出。值得注意的是，qARM在实现ARM的主要任务（即，从事务数据库中寻找频繁项集。在本文中，我们通过IBM量子计算平台，在真实的量子计算机和量子计算模拟器上实验性地实现了qARM。首先，我们为一个2 $\times$ 2事务数据库（即，一个涉及两个交易和两个项目的交易数据库），并在四个真正的五量子位IBM量子计算机以及模拟器上运行它。对于一个更大的4 $\times$ 4事务数据库，这将导致电路具有更多的量子位和更高的深度比目前可访问的IBM真正的量子设备可以处理，我们还构建了量子线路的qARM和执行他们的“aer\_simulator”单独。实验结果表明，两个事务数据库的频繁项集都能按要求成功地提取出来，验证了qARM的正确性和可行性。我们的工作可以作为一个基准，并提供原型实现qARM的大型交易数据库上的噪声中等规模的量子设备和通用容错量子计算机。
英文摘要：
Recently, a quantum algorithm for a fundamentally important task in data mining, association rules mining (ARM), called qARM for short, has been proposed. Notably, qARM achieves significant speedup over its classical counterpart for implementing the main task of ARM, i.e., finding frequent itemsets from a transaction database. In this paper, we experimentally implement qARM on both real quantum computers and a quantum computing simulator via the IBM quantum computing platform. In the first place, we design quantum circuits of qARM for a 2$\times$2 transaction database (i.e., a transaction database involving two transactions and two items), and run it on four real five-qubit IBM quantum computers as well as on the simulator. For a larger 4$\times$4 transaction database which would lead to circuits with more qubits and a higher depth than the currently accessible IBM real quantum devices can handle, we also construct the quantum circuits of qARM and execute them on "aer\_simulator" alone. Both experimental results show that all the frequent itemsets from the two transaction databases are successfully derived as desired, demonstrating the correctness and feasibility of qARM. Our work may serve as a benchmarking, and provide prototypes for implementing qARM for larger transaction databases on both noisy intermediate-scale quantum devices and universal fault-tolerant quantum computers.
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