Selecting Efficient Phase Estimation With Constant-Precision Phase Shift Operators

TL;DR

This paper compares three phase estimation methods using constant-precision phase shift operators, focusing on their gate costs and measurement efficiency, revealing trade-offs and improvements over existing approaches.

Contribution

It introduces the Arbitrary Constant-Precision Approach (ACPA) and analyzes its gate efficiency and measurement reduction compared to Kitaev's and faster phase estimation methods.

Findings

ACPA minimizes elementary gate count with a factor of 14 reduction over Kitaev's method.

Faster phase estimation reduces the number of measurements with a logarithmic factor.

The reduction factors increase with higher precision requirements.

Abstract

We investigate the cost of three phase estimation procedures that require only constant-precision phase shift operators. The cost is in terms of the number of elementary gates, not just the number of measurements. Faster phase estimation requires the minimal number of measurements with a \log * factor of reduction when the required precision n is large. The arbitrary constant-precision approach (ACPA) requires the minimal number of elementary gates with a minimal factor of 14 of reduction in comparison to Kitaev's approach. The reduction factor increases as the precision gets higher in ACPA. Kitaev's approach is with a reduction factor of 14 in comparison to the faster phase estimation in terms of elementary gate counts.