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In this short note, we formulate a stabilizer formalism in the language of noncommutative graphs. The classes of noncommutative graphs we consider are obtained via unitary representations of finite groups and suitably chosen operators on finite-dimensional Hilbert spaces. This type of construction exhibits all the correctable errors by the stabilizer codes. Furthermore, in this framework, we generalize previous results in this area for determining when such noncommutative graphs have anticliques. [ABSTRACT FROM AUTHOR]

With the diverging improvements in CPU speeds and memory access latencies, detecting and removing memory access bottlenecks becomes increasingly important. In this work we present METRIC, a software framework for isolating and understanding such bottlenecks using partial access traces. METRIC extracts access traces from executing programs without special compiler or linker support. We make four primary contributions. First, we present a framework for extracting partial access traces based on dynamic binary rewriting of the executing application. Second, we introduce a novel algorithm for compressing these traces. The algorithm generates constant space representations for regular accesses occurring in nested loop structures. Third, we use these traces for offline incremental memory hierarchy simulation. We extract symbolic information from the application executable and use this to generate detailed source-code correlated statistics including per-reference metrics, cache evictor information, and stream metrics. Finally, we demonstrate how this information can be used to isolate and understand memory access inefficiencies. This illustrates a potential advantage of METRIC over compile-time analysis for sample codes, particularly when interprocedural analysis is required. [ABSTRACT FROM AUTHOR]