Optimal Low-Depth Quantum Signal-Processing Phase Estimation

• URL: http://arxiv.org/abs/2407.01583v1
• Date: Mon, 17 Jun 2024 10:33:52 GMT
• Title: Optimal Low-Depth Quantum Signal-Processing Phase Estimation
• Authors: Yulong Dong, Jonathan A. Gross, Murphy Yuezhen Niu,
• Abstract summary: We introduce Quantum Signal-Processing Phase Estimation algorithms that are robust against challenges and achieve optimal performance. Our approach achieves an unprecedented standard deviation accuracy of $10-4$ radians for estimating unwanted swap angles in superconducting two-qubit experiments. Our results are rigorously validated against the quantum Fisher information, confirming our protocol's ability to achieve unmatched precision for two-qubit gate learning.
• Score: 0.029541734875307393
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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.

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