Quantum Computing Basics

calendarDec 12, 2024 · 1 min read · quantum quantum-computing qubits quantum-gates  ·
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Qubit

Superposition of $|0\rangle$ and $|1\rangle$:

$$ |\psi\rangle = \alpha|0\rangle + \beta|1\rangle $$

Where $|\alpha|^2 + |\beta|^2 = 1$

Quantum Gates

Pauli-X (NOT)

$$ X = \begin{pmatrix} 0 & 1 \ 1 & 0 \end{pmatrix} $$

Hadamard

$$ H = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \ 1 & -1 \end{pmatrix} $$

Creates superposition: $H|0\rangle = \frac{|0\rangle + |1\rangle}{\sqrt{2}}$

CNOT (Controlled-NOT)

$$ CNOT = \begin{pmatrix} 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 0 & 1 \ 0 & 0 & 1 & 0 \end{pmatrix} $$

Python (Qiskit)

 1from qiskit import QuantumCircuit, execute, Aer
 2
 3# Create circuit
 4qc = QuantumCircuit(2, 2)
 5
 6# Apply gates
 7qc.h(0)  # Hadamard on qubit 0
 8qc.cx(0, 1)  # CNOT: control=0, target=1
 9
10# Measure
11qc.measure([0, 1], [0, 1])
12
13# Simulate
14backend = Aer.get_backend('qasm_simulator')
15job = execute(qc, backend, shots=1000)
16result = job.result()
17counts = result.get_counts()
18print(counts)

Further Reading

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