Autonomous Hamiltonian certification and changepoint detection

TL;DR

This paper introduces autonomous protocols for Hamiltonian certification and changepoint detection in quantum devices, enabling robust, self-monitoring calibration without external references or ancillary systems.

Contribution

It develops efficient, adaptive certification and changepoint detection methods using only single-qubit operations, suitable for noisy, multi-qubit quantum devices.

Findings

Certification distinguishes Hamiltonian differences with sample complexity $O(nM^2\,\ln(1/\delta)/\epsilon^2)$.

Changepoint detection achieves asymptotically optimal delay time $O(nM\ln(M\mathbb{E}_\infty[T])/\epsilon^2)$.

Protocols are robust to calibration issues and do not require trusted references or entangling operations.

Abstract

Modern quantum devices require high-precision Hamiltonian dynamics, but environmental noise can cause calibrated Hamiltonian parameters to drift over time, necessitating expensive recalibration. Detecting when recalibration is needed is challenging, especially since the very gates required for sophisticated verification protocols may themselves be miscalibrated. While cloud quantum computing services implement heuristic routines for triggering recalibration, the fundamental limits of optimal recalibration are not yet known. We develop efficient Hamiltonian certification and changepoint detection protocols in the autonomous setting, where we cannot rely on an external noiseless device and use only single-qubit gates and measurements, making the protocols robust to the calibration issues for multi-qubit operations they aim to detect. For unknown $n$-qubit Hamiltonians $H$ and $H_0$ with operator norm bounded by $M$, our certification protocol distinguishes whether $\|H-H_0\|_F\geq\epsilon$ or $\|H-H_0\|_F\leq O(\epsilon/\sqrt{n})$ with sample complexity $O(nM^2\ln(1/\delta)/\epsilon^2)$ and total evolution time $O(nM\ln(1/\delta)/\epsilon^2)$. We achieve this by evolving random stabilizer product states and performing adaptive single-qubit measurements based on a classically simulable hypothesis state. Extending this to continuous monitoring, we develop an online changepoint detection algorithm using the CUSUM procedure that achieves a detection delay time bound of $O(nM\ln(M\mathbb{E}_\infty[T])/\epsilon^2)$, matching the known asymptotically optimal scaling with respect to false alarm run time $\mathbb{E}_\infty[T]$. Our approach enables quantum devices to autonomously monitor their own calibration status without requiring ancillary systems, entangling operations, or a trusted reference device, offering a practical solution for robust quantum computing with contemporary noisy devices.