Proposed whole-machine benchmark that scores a device on solving linear systems built from random-circuit block-encoded matrices, in the spirit of classical computing's LINPACK.
The quantum LINPACK benchmark is a 2020 proposal by Yulong Dong and Lin Lin (UC Berkeley) to measure the whole-machine performance of a quantum computer on the task at the core of quantum linear algebra: solving a system of linear equations. The name nods to the classical LINPACK benchmark behind the TOP500 supercomputer ranking, though it shares no code or matrices with it: the analogy is the role, a linear-algebra task as the yardstick for a whole machine.
How it works
The key construction is the RAndom Circuit Block-Encoded Matrix (RACBEM): a random quantum circuit, built directly from the device’s native gates and topology, is reinterpreted as the block-encoding of a non-unitary matrix A. Using quantum singular value transformation, the device then applies an approximate inverse of A to an input state (solving A x = b), and the measured success probability of preparing the solution state is compared with the ideal noiseless value. Because the matrix comes from a hardware-efficient random circuit rather than a hand-built application instance, the test adapts to any architecture and scales in principle to any size. Dong and Lin demonstrated the protocol on IBM Q devices and simulators, and the paper was published as Phys. Rev. A 103, 062412 (2021). The random-circuit core makes it a cousin of Quantum Volume and cross-entropy benchmarking, but with the score tied to a linear-algebra task rather than to sampling statistics.
Strengths and limitations
The authors frame success as a minimal requirement: a machine that cannot invert random block-encoded matrices cannot be expected to run useful quantum linear-algebra workloads, while passing says little about real applications, since RACBEMs are synthetic rather than representative matrices. No single headline number analogous to LINPACK’s FLOPS was ever standardized. A naming caveat: RACBEM strictly names the input model, not the benchmark, though the reference repository carries that name and the two are often conflated.
It remains a paper proposal. The reference implementation has had no development since August 2020, and no adoption or reported device scores have surfaced through 2026.