Qiskit

Introduction

https://quantum-computing.ibm.com/

https://quantum-computing.ibm.com/challenges/fall-2020

https://quantum-computing.ibm.com/jupyter/user/IBMQuantumChallenge2020/week-1/ex_1a_en.ipynb

Theory

Installation

Installation https://qiskit.org/documentation/install.html

conda create -n qiskit python=3
conda activate qiskit
pip install qiskit _OR_ pip install qiskit[visualization]

Setting Up Qiskit

https://qiskit.org/textbook/ch-states/representing-qubit-states.html

qc = QuantumCircuit(1)  # Create a quantum circuit with one qubit
initial_state = [0,1]   # Define initial_state as |1>
qc.initialize(initial_state, 0) # Apply initialisation operation to the 0th qubit
qc.draw('text')  # Let's view our circuit (text drawing is required for the 'Initialize' gate due to a known bug in qiskit)
result = execute(qc,backend).result() # Do the simulation, returning the result
out_state = result.get_statevector()
print(out_state) # Display the output state vector

qc.measure_all()
qc.draw()
result = execute(qc,backend).result()
counts = result.get_counts()
plot_histogram(counts)

Take superposition as initial state

initial_state = [1/sqrt(2), 1j/sqrt(2)]  # Define state |q>

The Bloch Sphere

from qiskit_textbook.widgets import plot_bloch_vector_spherical
coords = [pi/2,0,1] # [Theta, Phi, Radius]
plot_bloch_vector_spherical(coords) # Bloch Vector with spherical coordinates

Quantum Gates

Pauli X gate. $\sigma _{x}=X={\begin{bmatrix}0&1\\1&0\end{bmatrix}}=|0\rangle \langle 1|+|1\rangle \langle 0|$

Pauli Y gate $\sigma _{y}=Y={\begin{bmatrix}0&-i\\i&0\end{bmatrix}}=-i|0\rangle \langle 1|+i|1\rangle \langle 0|$

Pauli Z gate $\sigma _{z}=Z={\begin{bmatrix}1&0\\0&-1\end{bmatrix}}=|0\rangle \langle 0|-|1\rangle \langle 1|$

qc = QuantumCircuit(1)
qc.x(0)
#qc.y(0) # Y-gate on qubit 0
#qc.z(0) # Z-gate on qubit 0
qc.draw('mpl')
# Let's see the result
backend = Aer.get_backend('statevector_simulator')
out = execute(qc,backend).result().get_statevector()
plot_bloch_multivector(out)

Exercises

Week 1

Week 2

Week 3