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13 votes
3 answers
2k views

Are there any quantum algorithms conjectured to give an exponential speedup for a non-oracle problem that don't use the Quantum Fourier Transform?

The Quantum Fourier Transform (QFT) subroutine seems ubiquitous in most quantum algorithms that are conjectured to give an exponential (or at least superpolynomial) speedup over the best classical ...
tparker's user avatar
  • 2,901
4 votes
0 answers
95 views

Simulation of algorithms with QFT on a classical computer

In paper The Quantum Fourier Transform Has Small Entanglement the authors showed that strong entanglement of qubits caused by QFT comes mainly from ordering the qubits. QFT itself prepares only weak ...
Martin Vesely's user avatar
24 votes
4 answers
2k views

Why can the Discrete Fourier Transform be implemented efficiently as a quantum circuit?

It is a well known result that the Discrete Fourier Transform (DFT) of $N=2^n$ numbers has complexity $\mathcal O(n2^n)$ with the best known algorithm, while performing the Fourier transform of the ...
glS's user avatar
  • 26.9k