Quantum Volume for Measurement-based Quantum Processors

Defining metrics for near-term quantum computing processors has been an integral part of quantum hardware research and development efforts. Such quantitative characteristics are not only useful for reporting the progress and comparing different quantum platforms but also essential for identifying the bottlenecks and designing a technology roadmap. Most metrics, such as the quantum volume (QV), were originally introduced for circuit-based quantum computers and were not immediately applicable to measurement-based quantum computing (MBQC) units. In this talk, I introduce a framework to map physical noises and imperfections in MBQC processes to logical errors in equivalent quantum circuits, thereby enabling the well-known metrics to characterize MBQC. I further explain our framework in the case of a continuous-variable cluster state based on the Gottesman-Kitaev-Preskill (GKP) encoding as a near-term candidate for photonic quantum computing, derive the effective logical gate error channels, and calculate the QV in terms of the GKP squeezing and photon loss rate.