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Quantum boolean functions
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In this paper we introduce the study of quantum boolean functions, which are unitary operators f whose square is the identity: f^2 = I. We describe several generalisations of well-known results in the theory of boolean functions, including quantum property testing; a quantum version of the Goldreich-Levin algorithm for finding the large Fourier coefficients of boolean functions; and two quantum versions of a theorem of Friedgut, Kalai and Naor on the Fourier spectra of boolean functions. In order to obtain one of these generalisations, we prove a quantum extension of the hypercontractive inequality of Bonami, Gross and Beckner.
Forward citations
Cited by 2 Pith papers
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Reed-Muller Codes on CQ Channels via a New Correlation Bound for Quantum Observables
Reed-Muller codes achieve vanishing bit-error probability below Holevo capacity on binary-input symmetric classical-quantum channels.
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CNOT Oriented Synthesis for Small-Scale Boolean Functions Using Spatial Structures of Parallelotopes
SSHR uses parallelotopes (affine subspaces) in the Boolean hypercube to synthesize quantum oracles for <=8-bit functions and reports large CNOT reductions, but the provided construction does not uncompute its CNOTs.
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