Magic Class and the Convolution Group
8 February 2024
Introduce concept of magic class to categorize quantum states
Construct efficient convolution group coarse-graining procedure
Relate circuit and convolution magic classes
Characterize classes by symmetries and entropy
Simplified magic classification of quantum convolution states
We introduce a classification of quantum states based on their 'magic' or non-stabilizerness, which measures usefulness for quantum computation. We propose an iterative coarse-graining procedure called the convolution group to extract this magic. States fall into equivalence classes based on symmetries and entropy at the fixed points of this coarse-graining flow. This connects to circuit-based classification, providing insight into quantum phases of matter.
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