The lecture slides are available here.

In this lecture, we explore the concept of circle notation in quantum computing. It begins by highlighting the fundamental difference between classical bits, which have binary states (0 and 1), and qubits, which can exist in superpositions of states before measurement. The visualization of these qubit states in circle notation is introduced, emphasizing the importance of understanding amplitude magnitude and relative phase.

The size of the circles directly relates to measurement probabilities, with larger circles indicating higher probabilities. The relative phase, represented by the rotation of circles, is discussed, and it's noted that only the relative phase matters in quantum computations.

While the relative phase of a single qubit doesn't directly affect measurements, it plays a crucial role in multi-qubit quantum computations, offering computational advantages. The lecture concludes by suggesting ways to implement circle notation, emphasizing the accessibility of qubit states as complex numbers with magnitude and phase.