Yulong Dong

Harnessing quantum effects in metrology, such as entanglement and coherence, enables enhanced sensitivity in measuring parameters. Despite this, decoherence and time-dependent errors can undermine Heisenberg-limited amplification. To navigate these challenges in realistic experiments for phase estimation of a two-level unitary gate, we introduce a suite of quantum metrology algorithms. These algorithms capitalize on the universality of quantum signal transformation to decouple two interdependent phase parameters into largely orthogonal ones, ensuring that time-dependent errors in one do not compromise the accuracy of learning the other. Our approach combines provably optimal classical estimation with nearly optimal quantum circuit design, achieving unparalleled accuracy of 10−4 radians in standard deviation for estimating extremely small angles in superconducting qubit experiments with low-depth (< 10) circuits. This accuracy surpasses existing alternatives by two orders of magnitude and is adaptable to ion trap gates. We prove both theoretically and numerically the optimality of our algorithm against time-dependent phase error in φ. Remarkably, in the low circuit depth limit, our method’s estimation variance on the time-sensitive parameter φ scales faster than the asymptotic Heisenberg limit as a function of depth, Var(φˆ) ∼ 1/d4. Crucially, our method’s efficacy is rigorously affirmed through an analysis against the quantum Fisher information, a feature lacking in prior art. This analysis underpins our protocol’s ability to achieve unmatched precision, leveraging quantum resources more effectively than has been possible before.