DiVincenzo criterion #5 from Chap. 18 states that the qubit lifetimes should be long compared to the duration of the algorithm. However, quantum systems are fragile. Unwanted external perturbations from the environment (e.g., electromagnetic waves, thermal excitations, charge, etc.) can interact with the quantum system, such that the system becomes entangled with the environment. Quantum computing presents two conflicting requirements: qubits should be isolated from the environment for long qubit lifetimes (DiVincenzo criterion #5), while also possessing good addressability (DiVincenzo criterion #2 and #4). We need to be able to address qubits without letting the noisy environment leak into the system. Due to the difficulty of this challenge, present day quantum algorithms have been demonstrated with only a few 10s of qubits. We need a way of correcting errors, known as quantum error correction (QEC).