Nonstabilizerness, also known as magic, quantifies the number of non-Clifford operations needed to prepare a quantum state. As typical measures either involve minimization procedures or computational cost exponential in qubits $N$, it is notoriously hard characterize for many-body states. In this paper, we show that nonstabilizerness, quantified by recently introduced stabilizer R\'enyi entropi...

An orthonormal wavelet system in R, d ∈ N, is a countable collection of functions {ψ j,k}, j ∈ Z, k ∈ Z, ` = 1, . . . , L, of the form ψ j,k(x) = | deta|−j/2ψ`(a−jx− k) ≡ (Daj Tk ψ)(x) that is an orthonormal basis for L2(Rd), where a ∈ GLd(R) is an expanding matrix. The first such system to be discovered (almost one hundred years ago) is the Haar system for which L = d = 1, ψ1(x) = ψ(x) = χ[0,1...

There is an apparent renewed interest in application of the Haar wavelet transform in switching theory and logic design.1–6 In particular, the discrete Haar transform appears very interesting for its wavelets-like properties and fast calculation algorithms. The applications have been found in circuit synthesis, verification and testing.1–9 For applications of the Haar transform in logic design,...