Refining Quantum Phase Estimation Precision Conditions on Unitaries for Many-Electron Systems

TL;DR

This paper analyzes how approximate controlled-unitaries affect the precision of quantum phase estimation in many-electron systems, deriving conditions to optimize accuracy and applying them to Trotterization.

Contribution

It derives unified conditions on unitaries necessary for precise quantum phase estimation, improving bounds and providing formal analysis with numerical examples.

Findings

Derived first-order and unified conditions on unitaries for QPE precision.

Applied conditions to Trotterization, yielding tighter bounds.

Numerical results on H2 molecule illustrate the theoretical insights.

Abstract

Beyond ground state energy estimation, quantum phase estimation (QPE) applied to many-electron systems has the potential to output an approximation of the ground state, enabling in a second step an evaluation of observables other than the energy. We here focus on the impact of approximate controlled-unitaries implementations on QPE precision. After recalling the role of the QPE free parameters, we derive first-order and unified conditions on the unitaries that are necessary to control the QPE energy estimation precision together with the QPE output state precision, important in case we want to leverage the full potential of QPE. We apply these conditions to a Trotterization case, leading to tighter or more general bounds than in previous works. The main results in this article are formal. First numerical illustrations on the H2 molecule provide useful insights.