Fast parallel circuits for the quantum Fourier transform
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Synthesis and optimization of reversible circuits—a survey
ACM Computing Surveys (CSUR)
Quantum phase estimation with arbitrary constant-precision phase shift operators
Quantum Information & Computation
Selecting efficient phase estimation with constant-precision phase shift operators
Quantum Information Processing
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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.