Yulong Dong

Yulong Dong, Jonathan Gross, Murphy Yuezhen Niu

Leveraging quantum effects in metrology such as entanglement and coherence allows one to measure parameters with enhanced sensitivity. However, time-dependent noise can disrupt such Heisenberg-limited amplification. We propose a quantum-metrology method based on the quantum-signal-processing framework to overcome these realistic noise-induced limitations in practical quantum metrology. Our algorithm separates the gate parameter $\varphi$~(single-qubit Z phase) that is susceptible to time-dependent error from the target gate parameter $θ$~(swap-angle between |10> and |01> states) that is largely free of time-dependent error. Our method achieves an accuracy of $10^{-4}$ radians in standard deviation for learning $θ$ in superconducting-qubit experiments, outperforming existing alternative schemes by two orders of magnitude. We also demonstrate the increased robustness in learning time-dependent gate parameters through fast Fourier transformation and sequential phase difference. We show both theoretically and numerically that there is an interesting transition of the optimal metrology variance scaling as a function of circuit depth $d$ from the pre-asymptotic regime $d \ll 1/θ$ to Heisenberg limit $d \to \infty$. Remarkably, in the pre-asymptotic regime our method's estimation variance on time-sensitive parameter $\varphi$ scales faster than the asymptotic Heisenberg limit as a function of depth, $\text{Var}(\hat{\varphi})\approx 1/d^4$. Our work is the first quantum-signal-processing algorithm that demonstrates practical application in laboratory quantum computers.

Yulong Dong, Christopher Kang, Murphy Yuezhen Niu

Analog quantum simulators can directly emulate time-dependent Hamiltonian dynamics, enabling the exploration of diverse physical phenomena such as phase transitions, quench dynamics, and non-equilibrium processes. Realizing accurate analog simulations requires high-fidelity time-dependent pulse control, yet existing calibration schemes are tailored to digital gate characterization and cannot be readily extended to learn continuous pulse trajectories. We present a characterization algorithm for in situ learning of pulse trajectories by extending the Quantum Signal Processing (QSP) framework to analyze time-dependent pulses. By combining QSP with a logical-level analog-digital mapping paradigm, our method reconstructs a smooth pulse directly from queries of the time-ordered propagator, without requiring mid-circuit measurements or additional evolution. Unlike conventional Trotterization-based methods, our approach avoids unscalable performance degradation arising from accumulated local truncation errors as the logical-level segmentation increases. Through rigorous theoretical analysis and extensive numerical simulations, we demonstrate that our method achieves high accuracy with strong efficiency and robustness against SPAM as well as depolarizing errors, providing a lightweight and optimal validation protocol for analog quantum simulators capable of detecting major hardware faults.

Zikang Jia, Suying Liu, Yulong Dong

Quantum phase estimation is a central primitive in quantum algorithms and sensing, where performance is governed by the sensitivity of measurement signals to the target parameter. While existing methods have developed increasingly sophisticated inference and adaptive design strategies, the signal family used for phase learning is often largely pre-specified. Here we propose a programmable signal design framework for quantum phase estimation based on quantum signal processing, which enables the measurement signal to be tailored to the current uncertainty region. We cast phase estimation as a max-min optimization problem over admissible signals and introduce a sensitivity efficiency parameter that quantifies information gain per query depth. The resulting iterative algorithm combines optimized quantum signal transformations with structured classical inference, retaining Heisenberg-limited scaling while improving sensitivity efficiency and practical resource prefactors. Numerical results show reduced estimation variance compared with standard protocols such as robust phase estimation. Our framework also extends to Hamiltonian eigenvalue estimation in higher dimensions and establishes a quantum-classical co-design paradigm through programmable signal shaping.

Yulong Dong, Jonathan A. Gross, Murphy Yuezhen Niu

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.