代写COMP 4114 QUANTUM COMPUTING 2024代写C/C++程序
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COMP 4114
October 1, 2024
Solve the problems below. Your answers should be detailed, complete, precise, concise and clear. Write the solutions on your own and acknowl- edge your sources in case you used“library”material. Look in the course webpage on how to avoid plagiarism and for submission details. Exercises marked with a (★) are usually more challenging and may involve mate- rial not covered in class and some of the exercises may require material that will be covered in forthcoming lectures. It is preferred that you type your work using your favourite software package but you submit only in pdf. At the discretion of the TA a 5% bonus will be added for carefully typed and rigorously explained work. Two excellent and free packages are LATEX for typesetting mathematics (add in the preamble the packages “braket”and“kpfonts”), Ipe (for drawing pictures), and qcircuit to plot quantum circuits.
Assignment AQ2
1 [10 pts] October 1, 2024
Consider the two Pauli matrices calculate the tensor products σ1 σ2 and σ2 σ1 . Give details of your answers.
2 [10 pts] October 1, 2024
Consider the three Pauli matrices
Show that for all i,j ∈ {1, 2, 3},
where δi,j = 1, if i = j, and = 0,otherwise.
3 [10 pts] October 1, 2024
Give a pair among the set of three vectors
which form. an orthonormal basis. How many such pairs exist? Show details and justify your work.
4 [5 pts] October 1, 2024
Calculate the commutators [σ1, σ2], [σ2, σ3], [σ3, σ1]. Show your work.
5 [5 pts] October 1, 2024
Consider the matrices and compute their eigen-
values using the characteristic polynomial equation det(M - zI) = 0, for M = A and M = B separately.
6 [10 pts] (★) October 1, 2024
Prove or disprove: Is it true that if [A, B] = [A, C] = 0 then [B, C] = 0, for 2 × 2 Hermitian matrices A,B,C, where 0 is the 2 × 2 zero matrix? Hint: Use as A the identity matrix.