Combining Our Learnings So Far: Basis Rotation & Probability Amplitude Calculations

Let's step by step solve a problem to solidify our understanding of Quantum calculations

Photograph of Ocelot, the first-generation quantum chip developed by the AWS Center for Quantum Computing that promises to reduce quantum error correction by up to 90% and accelerate the development of real-world quantum computing applications (Source: AWS; The Wall Street Journal)

Here’s a problem statement:

Given a spin-up electron (qubit) in the standard basis (0° orientation), we need to measure it using a measuring apparatus rotated by 120° and find the probability of obtaining spin-up in the new rotated basis.

Let’s solve it using what we learned from the last lesson.

We are given a spin-up electron (qubit) in the standard basis: