Fast Signal Transforms for Quantum
نویسنده
چکیده
We present the discrete Fourier transform as a basic primitive in the treatment of controlled quantum systems. Based on the complexity model for quantum circuits the Fourier transform of size 2 n surprisingly can be realised with O(n 2) elementary operations which is an exponential speedup compared to the classical case. This is the reason for its presence in almost all known quantum algorithms among which Shor's algorithm for factoring is the most prominent example. We show how recent results in the theory of signal processing (for a classical computer) can be applied to obtain fast quantum algorithms for various discrete signal transforms. As an example we derive a quantum circuit implementing the discrete cosine transform DCTIV(8) eeciently.
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