# Adaptive Bayesian phase estimation for quantum error correcting codes

## TL;DR

This paper introduces an adaptive Bayesian inference method for efficient phase estimation in multi-qubit quantum states, reducing resource requirements and improving state characterization in quantum computing experiments.

## Contribution

The paper presents a novel Bayesian inference approach that adaptively selects measurement bases and processes multiple observables simultaneously for quantum phase estimation.

## Key findings

- Reduces measurement resources compared to traditional methods
- Speeds up quantum state characterization
- Applicable across various quantum computing platforms

## Abstract

Realisation of experiments even on small and medium-scale quantum computers requires an optimisation of several parameters to achieve high-fidelity operations. As the size of the quantum register increases, the characterisation of quantum states becomes more difficult since the number of parameters to be measured grows as well and finding efficient observables in order to estimate the parameters of the model becomes a crucial task. Here we propose a method relying on application of Bayesian inference that can be used to determine systematic, unknown phase shifts of multi-qubit states. This method offers important advantages as compared to Ramsey-type protocols. First, application of Bayesian inference allows the selection of an adaptive basis for the measurements which yields the optimal amount of information about the phase shifts of the state. Secondly, this method can process the outcomes of different observables at the same time. This leads to a substantial decrease in the resources needed for the estimation of phases, speeding up the state characterisation and optimisation in experimental implementations. The proposed Bayesian inference method can be applied in various physical platforms that are currently used as quantum processors.