Time-adaptive phase estimation

TL;DR

This paper introduces adaptive Bayesian phase estimation techniques that optimize control parameters based on prior knowledge, achieving near-optimal performance and robustness in noisy quantum systems for calibrating quantum gates.

Contribution

It presents novel adaptive Bayesian methods for phase estimation that incorporate prior knowledge and noise robustness, improving calibration accuracy in quantum computing.

Findings

Achieves near-Heisenberg limit performance with classical strategies.

Demonstrates robustness of estimates against unmodeled noise.

Provides a framework for optimizing control parameters based on information gain.

Abstract

Phase estimation is known to be a robust method for single-qubit gate calibration in quantum computers, while Bayesian estimation is widely used in devising optimal methods for learning in quantum systems. We present Bayesian phase estimation methods that adaptively choose a control phase and the time of coherent evolution based on prior phase knowledge. In the presence of noise, we find near-optimal performance with respect to known theoretical bounds, and demonstrate some robustness of the estimates to noise that is not accounted for in the model of the estimator, making the methods suitable for calibrating operations in quantum computers. We determine the utility of control parameter values using functions of the prior probability of the phase that quantify expected knowledge gain either in terms of expected narrowing of the posterior or expected information gain. In particular, we find that by maximising the rate of expected gain we obtain phase estimates having standard deviation a factor of 1.43 larger than the Heisenberg limit using a classical sequential strategy. The methods provide optimal solutions accounting for available prior knowledge and experimental imperfections with minimal effort from the user. The effect of many types of noise can be specified in the model of the measurement probabilities, and the rate of knowledge gain can easily be adjusted to account for times included in the measurement sequence other than the coherent evolution leading to the unknown phase, such as times required for state preparation or readout.