Harnessing Bayesian Optimisation for Quantum Information Processing

Achieving precise control over quantum systems has groundbreaking ap-plications, such as simulating complex quantum systems, or implementing quantum algorithms with an improved efficiency over classical algorithms. Quantum computing has been under development for the last decades, re-sulting in the so-called Noisy Intermediate-Scale Quantum (NISQ) devices with about 50 qubits. While these devices are built with the purpose of achieving practical advantages over classical processors, they are vulnerable to noise sources. In order to account for error sources, one needs to im-plement Quantum Error Correction (QEC) techniques. These techniques protect quantum information by encoding a logical qubit into several phys-ical ones. For the implementation of NISQ devices and QEC techniques, it is vital to keep improving the quantum operations and states involved. Here we develop calibration protocols based on the application of Bayesian inference. We show their advantages compared to the more traditional frequentist approaches, such as their ability to maximise the information gained with each measurement, or their straightforward automation. In our first line of research, we develop a Bayesian protocol for the correction of unwanted phases appearing in the experimental preparation of Steane code states. This protocol requires 13 times less measurements than the frequentist approach. In our second line of research, we develop a proto-col for locking a laser to the qubit transition frequency in a trapped-ion architecture. This calibration is vital, since the correct implementation of single-qubit gates depends on it. In our final line of research, we study the Mølmer-Sørensen entangling gate, used in trapped-ion systems. First we introduce the calibration parameters, and derive a semianalytical model of the effects of one of them, for which there was no previous analytical understanding. Finally, we develop a Bayesian protocol for the calibration of these parameters, which was successfully implemented and tested in an experimental trapped-ion quantum processor