Reducing quantum resources for observable estimation with window-assisted coherent QPE

Quantum Phase Estimation (QPE) routines are known to fail probabilistically even with perfect gates and input states. This effect stems from an incompatibility of finite-sized quantum registers to capture a phase within QPE with phase angles of infinite precision, and the effect extend even beyond what would be reasonably expected from rounding. This effect can be partially mitigated by biasing the phase register with a window, or taper state, from classical signal processing. This paper focuses on how windowing a coherent QPE used as a subroutine can improve the accuracy of the overall algorithm. Specifically we study the quantum task of estimating observables where window-assisted coherent QPE is used as a subroutine to implement a reflection about an eigenstate. Quantum resource estimates show over 2-orders-of-magnitude reduction in Toffoli counts over the previous costed techniques -- also assisted by the use of improved block encoding techniques -- demonstrating an encouraging decrease in resources for quantum computation of molecular observables. Since QPE, as one of only a few quantum building blocks, appears as a subroutine in many algorithms; this analysis also provides a model for understanding how window functions propagate to an improved error in composite algorithms.