Quantum error correcting codes are expected to play a crucial role in making quantum computers resilient against environmental noise. Recent years have seen the first experimental demonstrations of this idea with more advances expected in the near future. At the same time, quantum error correction has fundamental connections to important aspects of modern condensed matter physics, particularly to exotic quantum phases of matter, exhibiting so-called topological order. Within quantum error correction, an important current direction involves the study of so-called "low density parity check" (LDPC) codes, which use certain kinds of spatially non-local interactions between quantum bits to achieve qualitatively better results than more conventional error correcting schemes; at the same time, the newest generation of quantum devices have developed capabilities needed to realize such non-local interactions. The resarch of the PhD candidate will contribute to the development of such quantum LDPC codes, developing new codes, decoding algorithms and ways of manipulating the encoded quantum information. At the same time, it will explore the connections between these codes and questions in quantum many-body physics, such as the possibility of realizing novel exotic quantum states with the help of non-local interactions.