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.

中文翻译：

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随机电路块编码矩阵和量子LINPACK基准的提议

LINPACK 基准报告了计算机求解具有密集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 年列表首次亮相以来，LINPACK 基准已经被用来定义 TOP500 超级计算机的列表。我们建议一个类似的基准，称为量子 LINPACK 基准，可以用于衡量量子计算机的整机性能。量子 LINPACK 基准测试的成功应被视为量子计算机执行解决线性代数问题（例如线性方程组）的有用任务的最低要求。我们提出了一种称为随机电路块编码矩阵 (RACBEM) 的输入模型，它是量子设置中密集随机矩阵的适当推广。RACBEM 模型可以高效地在量子计算机上实现，并且可以设计为最佳地适应任何给定的量子架构，并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。RACBEM 模型可用于执行与许多物理应用相关的各种线性代数任务，例如计算光谱测量、由哈密顿模拟生成的时间序列以及能量的热平均。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。RACBEM 模型可用于执行与许多物理应用相关的各种线性代数任务，例如计算光谱测量、由哈密顿模拟生成的时间序列以及能量的热平均。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。