Optimal Low-Depth Quantum Signal-Processing Phase Estimation
<|reference_start|>Optimal Low-Depth Quantum Signal-Processing Phase Estimation: 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 an unprecedented 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.<|reference_end|>
@article{dong2024optimal,
    title={Optimal Low-Depth Quantum Signal-Processing Phase Estimation},
    author={Yulong Dong, Jonathan A. Gross, Murphy Yuezhen Niu},
    journal={arXiv preprint arXiv:2407.01583},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.01583},
    primaryClass={quant-ph cs.LG cs.NA math.NA physics.data-an}
}