Most concepts in Quantum mechanics aren’t intuitive and might not have macroscopic world alternatives to rely on.
For example, in the macroscopic world, observing a car does not alter its state, but in the quantum world, observing a particle does change it.
This is the reason why Quantum phenomena are best described using mathematics, rather than English.
If you’re new to this publication, I would highly recommend learning about Quantum Mechanics/ Computing from a mathematical lens.
This week, we will revisit the mathematics of Quantum Computing and solidify our understanding of it through 6 questions.
I would love it if you could solve these by hand. I will reveal detailed solutions to them in the next post on this publication.
Let’s begin!
Question 1: Normalization
A single qubit is in the state:
where α = 5/ 3 and β = 4(i)/ 5.
Verify if this is a valid quantum state by showing that it is normalized.
Question 2: Tensor Product of Qubits
Given two qubits in the following states:
Find the tensor product between these states and express the result in the computational basis.
Question 3: Inner Product of Qubits
Given two qubits in the following states:
Find their inner product and tell whether the two states are orthogonal.
Question 4: Probability Amplitudes in Quantum Measurement
Given a qubit in the following state:
If this qubit is measured in the computational basis, what is the probability of observing |0>?
Question 5: Eigenvalues of the Pauli-Y Operator
The Pauli-Y operator is defined as:
Find its eigenvalues and corresponding normalized eigenvectors.
Question 6: Measurement Probabilities in a Rotated Basis
Given a qubit in the following state:
If we measure it in the Hadamard basis, what is the probability of obtaining |+>?
