Quantum Phase Estimation with Arbitrary Constant-precision Phase Shift Operators

TL;DR

This paper presents a new quantum phase estimation algorithm that uses only constant-precision phase shift operators, making it more feasible for physical implementation while maintaining accuracy.

Contribution

It introduces an alternative QPE method that requires only arbitrary constant-precision controlled phase shifts, bridging existing approaches and improving physical implementability.

Findings

Requires only constant-precision phase shift operators

Bridges gap between QFT-based and Kitaev's approaches

Outperforms Kitaev's approach in physical implementation

Abstract

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.