While Quantum phase estimation (QPE) is at the core of many quantum
algorithms known to date, its physical implementation (algorithms based on
quantum Fourier transform (QFT)) is highly constrained by the requirement of
high-precision controlled phase shift operators, which remain difficult to
realize. In this paper, we introduce an alternative approach to approximately
implement QPE with arbitrary constant-precision controlled phase shift
operators.
The new quantum algorithm bridges the gap between QPE algorithms based on QFT
and Kitaev's original approach. For approximating the eigenphase precise to the
nth bit, Kitaev's original approach does not require any controlled phase shift
operator. In contrast, QPE algorithms based on QFT or approximate QFT require
controlled phase shift operators with precision of at least Pi/2n. The new
approach fills the gap and requires only arbitrary constant-precision
controlled phase shift operators. From a physical implementation viewpoint, the
new algorithm outperforms Kitaev's approach.Comment: 14 pages, 6 figures and 1 tabl
