Page 1 of 4

[QC.BC-HW2-3] Quantum Computing and Blockchain Lecture Series - Homework 2-3

Participant ID

*

No Participant ID

I haven't received my Participant ID

First Name

*

Last Name

*

Main Email Address

*

Question 1

*

What is the magnitude of the vector v = (3, 4)?

Question 2

The sum of the vectors v = (1, 2) and w = (3, 4) is (a, b). Where a and b are:

a =

*

b =

*

Question 3

If we have vector v = (2, -1), then 5v is (a, b).

a =

*

b =

*

Question 4

What is the dot product of vectors a = (2, 3, 4) and b = (-1, 0, 2)?

*

Question 5

The vector v = (1, 0) expressed as a linear combination of the basis vectors x = (1, 0) and y = (0, 1) is on the format v = ax + by.

a =

*

b =

*

Question 6

In Dirac notation, the vector v = (2, 1) is represented as:

https://storage.tally.so/4c04fd34-9cf2-4676-8e35-520206f43eb3/q6.png

where

a =

*

b =

*

c =

*

d =

*

Question 7

The tensor product of |a⟩ = (1, 0) and |b⟩ = (0, 1) is:

https://storage.tally.so/074d2757-87f1-464e-b90a-ef70791672a8/Screenshot-2025-03-17-101530.png

j =

*

k =

*

l =

*

m =

*

Question 8

*

How is the superposition principle mathematically represented in quantum mechanics?

Question 8

A

As a scalar product.

B

As a matrix multiplication.

C

As a linear combination of quantum states.

D

As the cross product of two vectors.

Question 9

*

Which of the following best describes tensor products in quantum computing?

Question 9

A

Method for constructing multi-qubit systems

B

Describes multiplication of two states in the Hilbert space

C

Combines the wavefunction of two states

D

Only applies to classical vectors

Question 10

This arbitrary quantum gate K is used to put our qubit from ground state into an equal superposition state. Fill in the matrix representation of this quantum gate.

https://storage.tally.so/1378c933-f8e2-4787-bc34-a2829df9c98b/q10.png

a =

*

Question 10a

A

-1

B

0

C

1 / √2

D

1

E

-1 / √2

b =

*

Question 10b

A

1

B

-1 / √2

C

-1

D

1 / √2

E

0

Question 11

What is the probability that we measure a 0 on a qubit with this quantum state?

https://storage.tally.so/0a83e928-d4c5-4035-b2f1-88be0fe16764/q9.png

https://storage.tally.so/b7abe7ea-6ef2-4dc8-8a17-906f9d2112fd/q11.png

Note: Instead of using fractions, please enter the value as a decimal number.

*

Question 12

What are the amplitudes of a 2-qubit system on equal superposition?

https://storage.tally.so/ab9a4dd7-19fb-48d0-bfa0-e49b7e95983b/q12.png

Note: Instead of using fractions, please enter the value as a decimal number.

a =

*

b =

*

c =

*

d =

*