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arXiv 2006.04010quant-phcs.NAmath.NA
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随机电路分组编码矩阵及量子LINPACK基准的提出

Random circuit block-encoded matrix and a proposal of quantum LINPACK benchmark

Yulong Dong, Lin Lin

摘要:

LINPACK基准测试报告了计算机求解具有稠密随机矩阵的线性方程组的性能。虽然这项任务的设计并没有直接考虑到实际应用,但自1993年首次发布以来,LINPACK基准一直用于定义TOP500超级计算机列表。我们建议使用一个类似的基准,称为量子LINPACK基准,可以用于测量量子计算机的整机性能。量子LINPACK基准测试的成功应该被视为量子计算机执行解决线性代数问题(如线性方程组)的有用任务的最低要求。我们提出了一个输入模型称为随机电路块编码矩阵(RACBEM),这是一个适当的推广密集随机矩阵的量子设置。RACBEM模型在量子计算机上实现是有效的,并且可以被设计为最佳地适应任何给定的量子架构,依赖于黑盒量子编译器。除了求解线性系统外,RACBEM模型还可用于执行与许多物理应用相关的各种线性代数任务,例如计算谱测量、由哈密顿模拟生成的时间序列以及能量的热平均值。我们在IBM Q量子设备和量子虚拟机上实现了这些线性代数运算,并展示了它们在解决科学计算问题方面的性能。

英文摘要:

The LINPACK benchmark reports the performance of a computer for solving a system of linear equations with dense random matrices. Although this task was not designed with a real application directly in mind, the LINPACK benchmark has been used to define the list of TOP500 supercomputers since the debut of the list in 1993. We propose that a similar benchmark, called the quantum LINPACK benchmark, could be used to measure the whole machine performance of quantum computers. The success of the quantum LINPACK benchmark should be viewed as the minimal requirement for a quantum computer to perform a useful task of solving linear algebra problems, such as linear systems of equations. We propose an input model called the RAndom Circuit Block-Encoded Matrix (RACBEM), which is a proper generalization of a dense random matrix in the quantum setting. The RACBEM model is efficient to be implemented on a quantum computer, and can be designed to optimally adapt to any given quantum architecture, with relying on a black-box quantum compiler. Besides solving linear systems, the RACBEM model can be used to perform a variety of linear algebra tasks relevant to many physical applications, such as computing spectral measures, time series generated by a Hamiltonian simulation, and thermal averages of the energy. We implement these linear algebra operations on IBM Q quantum devices as well as quantum virtual machines, and demonstrate their performance in solving scientific computing problems.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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