import numpy as np from numpy import pi

Importing standard Qiskit libraries

from qiskit import QuantumCircuit, transpile, assemble, Aer from qiskit import IBMQ, execute from qiskit.quantum_info import Statevector from qiskit.visualization import plot_bloch_multivector from qiskit.visualization import plot_histogram from qiskit_textbook.problems import dj_problem_oracle

1. The goal is to reach the state |1>

def lab1_ex1(): qc = QuantumCircuit(1) qc.x(0) # Apply X gate to qubit 0 return qc

state = Statevector.from_instruction(lab1_ex1()) plot_bloch_multivector(state)

2. The goal is to reach the state |+> = sqrt(1/2) (|0> + |1>)

def lab1_ex2(): qc = QuantumCircuit(1) qc.h(0) # Apply Hadamard gate to qubit 0 return qc

state = Statevector.from_instruction(lab1_ex2()) plot_bloch_multivector(state)

3. Construct the Bell state |Ψ+> = sqrt(1/2) (|01> + |10>)

def lab1_ex5(): qc = QuantumCircuit(2, 2) qc.h(0) # Apply Hadamard gate to qubit 0 qc.cx(0, 1) # Apply CNOT gate with control qubit 0 and target qubit 1 return qc

qc = lab1_ex5() qc.draw() # we draw the circui