This chapter examines quantum decoherence, a process by which quantum information is lost due to environmental interactions. Various noise channels, such as bit-flip, phase-flip, and depolarizing channels, are discussed to illustrate common errors in qubit states. The Kraus representation and Lindblad equation offer frameworks for modeling these interactions. Metrics such as T1 (relaxation time) and T2 (decoherence time) are introduced to measure qubit stability. Understanding decoherence mechanisms is critical for developing strategies to preserve quantum information, laying the groundwork for quantum error correction techniques and highlighting the challenges in creating reliable quantum systems.

Chapter 2 serves as a primer on quantum mechanics tailored for quantum computing. It reviews essential concepts such as quantum states, operators, superposition, entanglement, and the probabilistic nature of quantum measurements. This chapter focuses on two-level quantum systems (i.e. qubits). Mathematical formulations that are specific to quantum mechanics are introduced, such as Dirac (bra–ket) notation, the Bloch sphere, density matrices, and Kraus operators. This provides the reader with the necessary tools to understand quantum algorithms and the behaviour of quantum systems. The chapter concludes with a review of the quantum harmonic oscillator, a model to describe quantum systems that are complementary to qubits and used in some quantum computer implementations.