How to Simulate Quantum Circuits Using Qiskit

Qiskit is an open-source quantum computing framework developed by IBM.

It allows you to:

Build quantum circuits

Simulate them locally

Visualize results

Run circuits on real quantum hardware

This guide focuses on simulation, which is the best way to learn quantum computing without needing real quantum hardware.

🔹 1. Install Qiskit

Install using pip:

pip install qiskit

Optionally, install visualization dependencies:

pip install qiskit[visualization]

🔹 2. Build Your First Quantum Circuit

Import the required libraries:

from qiskit import QuantumCircuit

Create a simple circuit with 2 qubits and 2 classical bits:

qc = QuantumCircuit(2, 2)

# Add operations

qc.h(0)         # Apply Hadamard gate on qubit 0

qc.cx(0, 1)     # Apply CNOT between qubit 0 (control) and qubit 1 (target)

qc.measure([0,1], [0,1])   # Measure both qubits

qc.draw()

🔹 3. Simulate Using Qiskit's Aer Simulator

Qiskit includes Aer, a high-performance simulator framework.

Import Aer and execute:

from qiskit import Aer, execute

simulator = Aer.get_backend('qasm_simulator')

result = execute(qc, backend=simulator, shots=1024).result()

counts = result.get_counts()

print(counts)

Expected output (approx):

{'00': 512, '11': 512}

This indicates the Bell state: qubits collapse to 00 or 11 with equal probability.

🔹 4. Using the Statevector Simulator

The statevector simulator shows the exact quantum state (complex amplitudes).

Example:

from qiskit.quantum_info import Statevector

state = Statevector.from_instruction(qc.remove_final_measurements(inplace=False))

print(state)

This prints something like:

Statevector([0.707+0.j, 0.+0.j, 0.+0.j, 0.707+0.j])

Meaning |00⟩ and |11⟩ have equal amplitude.

🔹 5. Simulate Without Measurement (to see amplitudes)

If your circuit contains measurements, remove them:

qc2 = qc.remove_final_measurements(inplace=False)

Then:

state = Statevector.from_instruction(qc2)

🔹 6. Visualize Results

Qiskit provides built-in plotting tools:

Plot counts (histogram):

from qiskit.visualization import plot_histogram

plot_histogram(counts)

Draw the circuit:

qc.draw('mpl')

🔹 7. Advanced: Using the AerSimulator (new API)

Qiskit Aer also provides the modern API:

from qiskit_aer import AerSimulator

sim = AerSimulator()

result = sim.run(qc).result()

counts = result.get_counts()

🔹 8. Simulating Noise (Realistic Hardware Behavior)

Quantum hardware has errors, so Qiskit allows adding noise models.

Example:

from qiskit_aer.noise import NoiseModel

noise_model = NoiseModel.from_backend(Aer.get_backend('qasm_simulator'))

result = execute(qc, backend=simulator, noise_model=noise_model).result()

You can also create custom noise models:

depolarizing noise

readout noise

gate errors

🔹 9. Simulating Larger Circuits

You can scale simulations up to:

20–30 qubits easily on a laptop

32+ qubits depending on memory (statevectors require 2ⁿ amplitudes)

For larger circuits, use:

Aer’s GPU simulators

IBM Cloud's high-performance simulators

🔹 10. Running on Real Quantum Hardware (Optional)

Once you master simulation:

from qiskit import IBMQ

IBMQ.load_account()

provider = IBMQ.get_provider(hub='ibm-q')

backend = provider.get_backend('ibmq_quito')

result = execute(qc, backend=backend).result()

⭐ Summary

Task Simulator

Outcome probabilities qasm_simulator

Exact amplitudes statevector_simulator

Density matrices density_matrix_simulator

Noise simulation AerSimulator + noise model

GPU simulation Aer GPU backend

⭐ Want More?

I can also provide:

✅ A full beginner project with Qiskit

✅ Simulation of a quantum algorithm (Grover, QFT, QPE)

✅ A guide to noise models

✅ A tutorial on Bloch sphere visualization

✅ Side-by-side comparison of simulators

Learn Quantum Computing Training in Hyderabad

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Step-by-Step Tutorial: Implementing Grover’s Algorithm

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November 25, 2025

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