single_systems_problem_set.ipynb

Kernel: Python 3

Single Systems - Problem Set

Problem 1

Quick quiz

Which one of these is a valid probability vector?

1. $\begin{pmatrix} \sqrt{2}\\\\ 1 - \sqrt{2} \end{pmatrix}$

2. $\begin{pmatrix} 0.3 \\\\ 0.3 \end{pmatrix}$

3. $\begin{pmatrix} 0 \\\\ 1 \\\\ 0 \end{pmatrix}$

Problem 2

Quick quiz

Which one of these is matrices is unitary?

1. $\begin{pmatrix} 1 & 0 \\\\ 1 & 0 \end{pmatrix}$

2. $\begin{pmatrix} 0 & \frac{1}{2} \\\\ \frac{-i}{2} & 0 \end{pmatrix}$

3. $\begin{pmatrix} 1 & 0 \\\\ 0 & i \end{pmatrix}$

Problem 3

Using Qiskit, create a QuantumCircuit that represents the following state:

$|\beta_{01} \rangle = \frac{1}{\sqrt2}(|00\rangle + |10\rangle)$

from qiskit import *

# Start your work here.
# We've provided the circuit that is shown above
# Your circuit MUST be named qc

qc = QuantumCircuit(2)

qc.draw()

Problem 4

Using Qiskit, create a QuantumCircuit that represents the following state:

$|\beta_{10} \rangle = \frac{1}{\sqrt2}(|00\rangle - |11\rangle)$

from qiskit import *

# Start your work here.
# We've provided the circuit that is shown above
# Your circuit MUST be named qc

qc = QuantumCircuit(2)

qc.draw()

Problem 5

Using Qiskit, create a QuantumCircuit that represents the following state:

$|\beta_{11} \rangle = \frac{1}{\sqrt2}(|01\rangle - |10\rangle)$

from qiskit import *

# Start your work here.
# We've provided the circuit that is shown above
# Your circuit MUST be named qc

qc = QuantumCircuit(2)

qc.draw()