5 Questions to Build Your Muscle in Linear Algebra for Quantum Computing

Strengthen your linear algebra skills by solving these questions by hand.

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Here are 5 questions to strengthen your linear algebra skills and make you a better quantum engineer.

Solve them by hand and share their solutions in the community chat.

1

Given the following matrix U:

1. Prove that U is a unitary matrix.

2. Next, apply U to the state |0> and express the resulting state in Dirac notation and vector form.

3. Finally, compute the measurement probabilities in the computational basis.

2

Given the following matrix A:

1. Prove that it is Hermitian

2. Find its eigenvalues and orthonormal eigenvectors

3

Given two quantum states as follows:

1. Compute their inner product

2. Compute their Fidelity

4

Given two matrices A and B:

• Compute the commutator [A,B] = AB − BA

• Check if A and B commute.

5

For the given matrix M:

• Compute M † M

• Find the eigenvalues of M † M

• Determine the singular values of M.

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