1. Introduction to Quantum Computing
Quantum computing leverages the principles of quantum mechanics to perform calculations that are infeasible for classical computers. Unlike classical bits, quantum computers use qubits which can exist in multiple states simultaneously through superposition.
Key Concept: Qubits are represented by quantum states that can be in a superposition: |ψ⟩ = α|0⟩ + β|1⟩
2. Understanding Quantum Bits
Unlike classical bits (0 or 1), qubits represent probabilities of states. This allows for parallel computation where multiple calculations happen simultaneously within the quantum state space.
from qiskit import QuantumCircuit, transpile from qiskit.visualization import plot_histogram qc = QuantumCircuit(1) qc.h(0) # Create superposition qc.measure_all()
3. Quantum Entanglement
When two qubits become entangled, their states become interdependent regardless of distance. This phenomenon allows for instantaneous information correlation between quantum systems.
Alice's qubit
Bob's qubit
4. Quantum Algorithm Examples
The Deutsch-Jozsa algorithm demonstrates the quantum speed advantage for specific problems. Let's implement a basic version using qiskit:
from qiskit import QuantumCircuit
def deutsch_jozsa(f):
qc = QuantumCircuit(2)
qc.h(0)
qc.h(1)
if f == 'constant':
pass
elif f == 'balanced':
qc.cx(0,1)
qc.h(0)
qc.measure_all()
return qc
circuit = deutsch_jozsa('balanced')