Summary
In a short amount of time, we have developed enough mathematics to explain superposition and its effects on measurement. We did this by introducing Euclidean vectors and the operations of addition and scalar multiplication upon them. Putting these operations together, we were able to get a definition for a linear combination and then apply that definition to what is termed superposition. In the end, we could use all of this to predict the probability of getting a zero or one when measuring a qubit.
In the next chapter, we will introduce the concept of a matrix and use it to manipulate qubits!
History (Optional)
Euclidean vectors are named after the Greek mathematician Euclid circa 300 BC. In his book, The Elements, he puts together postulates and theories from other Greek mathematicians, including Pythagoras, that defined Euclidean geometry. The book was a required textbook for math students for over 2,000 years.
Figure 1.13 – Euclid with other Greek mathematicians in Raphael's School of Athens
