Time-adaptive phase estimation
arxiv(2024)
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 1.42 above the Heisenberg limit, which is the lowest value we know of
for sequential phase estimation. 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.
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