Real-time Quantum Control of Qubits

Quantum computing relies on developing quantum devices that are robust against small and uncontrolled parameter variations in the Hamiltonian. One can apply feedback by estimating such uncontrolled variations in real time to stabilize quantum devices and improve their coherence. This task is important for many quantum platforms such as spins, superconducting circuits, trapped atoms, and others towards error suppression or correction. Semiconductor spin qubits are attractive due to their long coherence times, compact size, and potential large-scale integration with existing semiconductor technology. Until now however, spin qubits shine with high-fidelity operations of selected devices. Further scalability and reproducibility may require actively compensating for environmental fluctuations.

In this Thesis, we focus on real-time closed-loop feedback protocols to estimate uncontrolled fluctuations of the qubit Hamiltonian parameters, followed by enhancing the quality of qubit rotations. First, we coherently control a spin qubit with a low-latency quantum controller. The protocol uses a singlet-triplet spin qubit implemented in a gallium arsenide double quantum dot. We establish real-time feedback on both control axes and enhance the resulting quality factor of coherent spin rotations. Even with some components of the Hamiltonian purely governed by noise, we demonstrate noise-driven coherent control. As an application, we implement Hadamard rotations in the presence of two fluctuating control axes.

Next, we present a protocol for a physics-informed real-time Hamiltonian estimation. We estimate the fluctuating nuclear field gradient within the double dot on-the-fly by updating its probability distribution according to the Fokker-Planck equation. We further improve the physicsinformed protocol by adaptively choosing the free evolution time of the electrons singlet pair, based on the previous measurement outcomes. The protocol results in a ten-fold improvement of the estimation speed compared to former schemes.

Finally, we present an adaptive frequency binary search scheme for efficiently tracking lowfrequency fluctuations in a resonantly-driven qubit. In real time, we implement the Bayesian algorithm to estimate low-frequency magnetic flux noise in a flux-tunable transmon qubit, whose coherence and fidelity are improved. Furthermore, we show by gate set tomography that our frequency tracking protocol minimizes the amount of drift in the system.

Our approaches introduce closed-loop feedback schemes aimed at mitigating the effects of decoherence and extending the lifetime of quantum systems. This Thesis pushes the field towards integrating qubit hardware and control hardware, and implementing Bayesian estimation and optimization methods from computer science.