A Precise Error Bound for Quantum Phase Estimation

TL;DR

This paper derives an exact, symmetric error bound formula for quantum phase estimation, improving the accuracy of error probability calculations and aiding in the efficient design of quantum computers.

Contribution

It introduces a novel, exact error bound formula for quantum phase estimation by enforcing symmetry, surpassing previous approximate methods.

Findings

Exact error probability formula derived for quantum phase estimation

Formula validated through computer simulations

Reduces overestimation of qubits needed for reliability

Abstract

Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring symmetry in the error definitions, an exact formula can be found. This new approach may also have value in solving other related problems in quantum computing, where an expected error is calculated. Expressions for two special cases of the formula are also developed, in the limit as the number of qubits in the quantum computer approaches infinity and in the limit as the extra added qubits to improve reliability goes to infinity. It is found that this formula is useful in validating computer simulations of the phase estimation procedure and in avoiding the overestimation of the number of qubits required in order to achieve a given reliability. This formula thus brings improved precision in the design of quantum computers.