Optimal Low-Depth Quantum Signal-Processing Phase Estimation
This addresses the challenge of achieving Heisenberg-limited amplification in quantum computing for two-qubit gate learning, though it appears incremental as it builds on existing quantum signal-processing frameworks.
The paper tackles the problem of quantum parameter estimation hindered by decoherence and time-dependent errors, introducing Quantum Signal-Processing Phase Estimation algorithms that achieve optimal performance with a standard deviation accuracy of 10^{-4} radians in superconducting two-qubit experiments, representing up to two orders of magnitude improvement over existing methods.
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 Cramér-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.