Optimal Low-Depth Quantum Signal-Processing Phase Estimation

TL;DR

This paper introduces robust low-depth quantum signal-processing algorithms for phase estimation that achieve near-optimal accuracy, outperforming existing methods, and are validated through theoretical and experimental results in superconducting qubits.

Contribution

The paper presents a novel quantum signal-processing phase estimation method that is robust against decoherence and errors, achieving optimal performance with low-depth circuits.

Findings

Achieves $10^{-4}$ radians accuracy in superconducting qubits.

Up to 100x improvement over previous methods.

Validated against quantum Fisher information for optimality.

Abstract

Quantum effects like entanglement and coherent amplification can be used to drastically enhance the accuracy of quantum parameter estimation beyond classical limits. However, challenges such as decoherence and time-dependent errors hinder Heisenberg-limited amplification. We introduce Quantum Signal-Processing Phase Estimation algorithms that are robust against these challenges and achieve optimal performance as dictated by the Cram\'{e}r-Rao bound. These algorithms use quantum signal transformation to decouple interdependent phase parameters into largely orthogonal ones, ensuring that time-dependent errors in one do not compromise the accuracy of learning the other. Combining provably optimal classical estimation with near-optimal quantum circuit design, our approach achieves a standard deviation accuracy of $10^{-4}$ radians for estimating unwanted swap angles in superconducting two-qubit experiments, using low-depth ($<10$) circuits. This represents up to two orders of magnitude improvement over existing methods. Theoretically and numerically, we demonstrate the optimality of our algorithm against time-dependent phase errors, observing that the variance of the time-sensitive parameter $\varphi$ scales faster than the asymptotic Heisenberg scaling in the small-depth regime. Our results are rigorously validated against the quantum Fisher information, confirming our protocol's ability to achieve unmatched precision for two-qubit gate learning.