The computational power of normalizer circuits over in nite and black-box groups
نویسندگان
چکیده
Normalizer circuits [3, 4] are a family of quantum circuits which generalize Cli ord circuits [5 8] to Hilbert spaces associated with arbitrary nite abelian groups G = Zd1 × · · · × Zdn . Normalizer circuits are composed of normalizer gates. Important examples are quantum Fourier transforms (QFTs), which play a central role in quantum algorithms, such as Shor's [9]. Refs. [3, 4] showed that normalizer circuits of arbitrary size can be e ciently classically simulated, thereby serving as example-families of quantum computations that fail to harness the power of QFTs to achieve achieve exponential quantum speed-ups. In this work we generalize the normalizer circuit framework in two ways [1] [2] and characterize the computational power of these generalizations. In summary our results are as follows:
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