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Register a new userTesting the Robustness of Robust Phase Estimation
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The Robust Phase Estimation (RPE) protocol was designed to be an efficient and robust way to calibrate quantum operations. The robustness of RPE refers to its ability to estimate a single parameter, usually gate amplitude, even when other parameters are poorly calibrated or when the gate experiences significant errors. Here we demonstrate the robustness of RPE to errors that affect initialization, measurement, and gates. In each case, the error threshold at which RPE begins to fail matches quantitatively with theoretical bounds. We conclude that RPE is an effective and reliable tool for calibration of one-qubit rotations and that it is particularly useful for automated calibration routines and sensor tasks.
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We present an extension to the robust phase estimation protocol, which can identify incorrect results that would otherwise lie outside the expected statistical range. Robust phase estimation is increasingly a method of choice for applications such as estimating the effective process parameters of noisy hardware, but its robustness is dependent on the noise satisfying certain threshold assumptions. We provide consistency checks that can indicate when those thresholds have been violated, which can be difficult or impossible to test directly. We test these consistency checks for several common noise models, and identify two possible checks with high accuracy in locating the point in a robust phase estimation run at which further estimates should not be trusted. One of these checks may be chosen based on resource availability, or they can be used together in order to provide additional verification.
We study the generation of planar quantum squeezed (PQS) states by quantum non-demolition (QND) measurement of a cold ensemble of $^{87}$Rb atoms. Precise calibration of the QND measurement allows us to infer the conditional covariance matrix describing the $F_y$ and $F_z$ components of the PQS, revealing the dual squeezing characteristic of PQS. PQS states have been proposed for single-shot phase estimation without prior knowledge of the likely values of the phase. We show that for an arbitrary phase, the generated PQS gives a metrological advantage of at least 3.1 dB relative to classical states. The PQS also beats traditional squeezed states generated with the same QND resources, except for a narrow range of phase values. Using spin squeezing inequalities, we show that spin-spin entanglement is responsible for the metrological advantage.
Bayesian estimation approaches, which are capable of combining the information of experimental data from different likelihood functions to achieve high precisions, have been widely used in phase estimation via introducing a controllable auxiliary phase. Here, we present a non-adaptive Bayesian phase estimation (BPE) algorithms with an ingenious update rule of the auxiliary phase designed via active learning. Unlike adaptive BPE algorithms, the auxiliary phase in our algorithm is determined by a pre-established update rule with simple statistical analysis of a small batch of data, instead of complex calculations in every update trails. As the number of measurements for a same amount of Bayesian updates is significantly reduced via active learning, our algorithm can work as efficient as adaptive ones and shares the advantages (such as wide dynamic range and perfect noise robustness) of non-adaptive ones. Our algorithm is of promising applications in various practical quantum sensors such as atomic clocks and quantum magnetometers.
In this paper, we investigate the problem of estimating the phase of a coherent state in the presence of unavoidable noisy quantum states. These unwarranted quantum states are represented by outlier quantum states in this study. We first present a statistical framework of robust statistics in a quantum system to handle outlier quantum states. We then apply the method of M-estimators to suppress untrusted measurement outcomes due to outlier quantum states. Our proposal has the advantage over the classical methods in being systematic, easy to implement, and robust against occurrence of noisy states.
Efficiently estimating properties of large and strongly coupled quantum systems is a central focus in many-body physics and quantum information theory. While quantum computers promise speedups for many such tasks, near-term devices are prone to noise that will generally reduce the accuracy of such estimates. Here we show how to mitigate errors in the shadow estimation protocol recently proposed by Huang, Kueng, and Preskill. By adding an experimentally friendly calibration stage to the standard shadow estimation scheme, our robust shadow estimation algorithm can obtain an unbiased estimate of the classical shadow of a quantum system and hence extract many useful properties in a sample-efficient and noise-resilient manner given only minimal assumptions on the experimental conditions. We give rigorous bounds on the sample complexity of our protocol and demonstrate its performance with several numerical experiments.
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