Random circuit block-encoded matrix and a proposal of quantum LINPACK benchmark
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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 gauge the performance of future quantum computers. 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. The task of the quantum LINPACK benchmark can also be difficult for classical computers, and its success can pave the way for achieving quantum advantage. Besides solving linear systems, the RACBEM model can be used to perform a variety of linear algebra tasks, 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 that such tasks can be only steps away from Google's quantum supremacy test.
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