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On the complexity of unitary transformations. (English. Russian original) Zbl 1088.68609
Discrete Math. Appl. 13, No. 6, 601-606 (2003); translation from Diskretn. Mat. 15, No. 4, 113-118 (2003).
Summary: In this paper, we suggest a method to derive lower bounds for the complexity of nonbranching programs whose elementary operations are unitary transformations over two complex numbers. This method provides us with estimates of the form $$\Omega(n \log n)$$ for unitary operators $$\mathbb C^n\to\mathbb C^n$$, in particular, for the Fourier and Walsh transformations. For $$n = 2^k$$ we find precise values of the complexity of those transformations.
##### MSC:
 68Q25 Analysis of algorithms and problem complexity 68N01 General topics in the theory of software 68Q05 Models of computation (Turing machines, etc.) (MSC2010)
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##### References:
 [1] J. E. Savage, The Complexity of Computing. Wiley, New York, 1976. · Zbl 0391.68025 [2] A. M. Steane, Quantum computing. Rept. Prog. Phys. (1998) 61, 117-173.
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