Quantum Fourier Transform I

青木, 隆;AOKI, Takashi, Yusuke Maesaka, Mikio Nakahara

The spectral decomposition of an n-qubit quantum Fourier transform (QFT_n) is derived exactly. It is then applied to find the logarithm of a QFT_n gate. Hamiltonian which generates QFT_n in a single step is suggested.

Hiu Yung Wong

Hiu Yung Wong

Adriano Barenco, ARTUR K. EKERT, Kalle‐Antti Suominen +1 more

We discuss the advantages of using the approximate quantum Fourier transform (AQFT) in algorithms which involve periodicity estimations. We analyze quantum networks performing AQFT in the presence of decoherence and show that extensive approximations can be made before the accuracy of AQFT (as compared with regular quantum Fourier transform) is compromised. We show that for some computations an approximation may imply a better performance. \textcopyright{} 1996 The American Physical Society.

Hiu Yung Wong

Donny Cheung

It has previously been established that the logarithmic-depth approximate quantum Fourier transform (AQFT) provides a suitable replacement for the regular QFT in many quantum algorithms. Since the AQFT is less accurate by definition, polynomially many more applications of the AQFT are required to achieve the original accuracy. However, in many quantum algorithms, the smaller size of the AQFT circuit yields a net improvement over using the QFT. This paper presents a more thorough analysis of the AQFT circuit, which leads to the surprising conclusion that for sufficiently large input sizes, the difference between the QFT and the logarithmic-depth AQFT is negligible. In effect, the AQFT can be used as an direct replacement for the QFT, yielding improvements in any application which does not require exact quantum computation.