Optimal Control Protocols for Quantum Memory Network Applications

Quantum networks play an indispensable role in quantum information tasks such as secure communications, enhanced quantum sensing, and distributed computing. In recent years several platforms are being developed for such tasks, witnessing breakthrough technological advancement in terms of fabrication techniques, precise control methods, and information transfer. Among the most mature and promising platforms are color centers in solids. These systems provide an optically active electronic spin and long-lived nuclear spins for information storage. The first part of this dissertation is concerned with error mechanisms in the control of electronic and nuclear spins. First, I will focus on control protocols for improved electron-spin rotations tailored to specific color centers in diamond. I will then discuss how to manipulate the entanglement between the electron and the always-coupled nuclear spin register. I will describe a general formalism to quantify and control the generation of en- tanglement in an arbitrarily large nuclear spin register. This formalism incorporates exactly the dynamics with unwanted nuclei, and quantifies the performance of entangling gates in the presence of unwanted residual entanglement links. Using experimental parameters from a well-characterized multinuclear spin register, I will show that preparation of multipartite entanglement in a single-shot is possible, which drastically reduces the total gate time of conventional protocols. Then, I will present a new formalism for describing all-way entanglement and show how to design gates that prepare GHZM states. I will show how to incorporate errors such as unwanted correlations, electronic dephasing errors or pulse control errors. The second part of this thesis focuses on the preparation of all-photonic graph states from a few quantum emitters. I will introduce heuristic algorithms that exploit graph theory concepts in order to reduce the entangling gate counts, and also discuss the role of locally equivalent graphs in the optimization of the generation circuits.