Programmable Signal Design for Quantum Phase Estimation via Quantum Signal Processing

TL;DR

This paper introduces a flexible quantum signal design framework for phase estimation that adapts signals based on current uncertainty, improving sensitivity and efficiency while maintaining optimal scaling.

Contribution

It presents a novel programmable signal design method using quantum signal processing, optimizing measurement signals for enhanced quantum phase estimation performance.

Findings

Reduced estimation variance compared to standard protocols

Maintains Heisenberg-limited scaling with improved sensitivity efficiency

Extends to higher-dimensional Hamiltonian eigenvalue estimation

Abstract

Quantum phase estimation is a central primitive in quantum algorithms and sensing, where performance is governed by the sensitivity of measurement signals to the target parameter. While existing methods have developed increasingly sophisticated inference and adaptive design strategies, the signal family used for phase learning is often largely pre-specified. Here we propose a programmable signal design framework for quantum phase estimation based on quantum signal processing, which enables the measurement signal to be tailored to the current uncertainty region. We cast phase estimation as a max-min optimization problem over admissible signals and introduce a sensitivity efficiency parameter that quantifies information gain per query depth. The resulting iterative algorithm combines optimized quantum signal transformations with structured classical inference, retaining Heisenberg-limited scaling while improving sensitivity efficiency and practical resource prefactors. Numerical results show reduced estimation variance compared with standard protocols such as robust phase estimation. Our framework also extends to Hamiltonian eigenvalue estimation in higher dimensions and establishes a quantum-classical co-design paradigm through programmable signal shaping.