Quantum higher-order Fourier analysis and the Clifford hierarchy
Abstract
Significance Quantum Fourier analysis is a powerful tool in mathematical physics. Here, we introduce quantum, higher-order Fourier analysis (q-HOFA). We explore some mathematical properties of this theory and show that it provides a way to quantify the complexity of unitary gates in quantum computation. This should provide a natural starting point for a more general study of q-HOFA.
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