Running Quantum Circuits on Simulators: A Practical Guide

Table of Contents

1. Introduction
2. What Is a Quantum Simulator?
3. Why Use Simulators?
4. Types of Simulators in Qiskit
5. Installing Required Packages
6. QASM Simulator Overview
7. Statevector Simulator Overview
8. Unitary Simulator Overview
9. Building a Sample Circuit
10. Running on QASM Simulator
11. Retrieving and Analyzing Counts
12. Running on Statevector Simulator
13. Understanding the Wavefunction Output
14. Using the Unitary Simulator
15. Noise Models and Noisy Simulation
16. Custom Noise Channel Integration
17. Using the Density Matrix Simulator
18. Comparison: Simulator vs Real Device
19. Best Practices for Simulator Use
20. Conclusion

1. Introduction

Quantum simulators allow you to test, verify, and analyze quantum circuits without needing physical quantum hardware. They are essential for prototyping algorithms and debugging.

2. What Is a Quantum Simulator?

A quantum simulator is a classical program that emulates the behavior of quantum systems. It reproduces expected quantum state evolution for validation and benchmarking.

3. Why Use Simulators?

• No access limits or queues
• Ideal for debugging and unit testing
• Enable visualization of quantum state evolution
• Easier parameter sweeping and experimentation

4. Types of Simulators in Qiskit

• QASM Simulator (for measurement outcomes)
• Statevector Simulator (for full quantum state)
• Unitary Simulator (for matrix of full circuit)
• Density Matrix Simulator (for mixed state simulation)
• Noise Model Simulators

5. Installing Required Packages

pip install qiskit

6. QASM Simulator Overview

from qiskit import Aer
backend = Aer.get_backend('qasm_simulator')

Simulates measurement with shot-based outcomes.

7. Statevector Simulator Overview

backend = Aer.get_backend('statevector_simulator')

Gives the complete quantum state as a vector.

8. Unitary Simulator Overview

backend = Aer.get_backend('unitary_simulator')

Returns the circuit’s full unitary transformation matrix.

9. Building a Sample Circuit

from qiskit import QuantumCircuit
qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1)

10. Running on QASM Simulator

from qiskit import execute
job = execute(qc, backend, shots=1024)
counts = job.result().get_counts()
print(counts)

11. Retrieving and Analyzing Counts

from qiskit.visualization import plot_histogram
plot_histogram(counts)

12. Running on Statevector Simulator

backend = Aer.get_backend('statevector_simulator')
result = execute(qc, backend).result()
state = result.get_statevector()
print(state)

13. Understanding the Wavefunction Output

The result is a list of amplitudes for each basis state, e.g.:

[0.707+0.j, 0.+0.j, 0.+0.j, 0.707+0.j]

corresponds to \( rac{1}{\sqrt{2}}(|00
angle + |11
angle) \)

14. Using the Unitary Simulator

backend = Aer.get_backend('unitary_simulator')
unitary = execute(qc, backend).result().get_unitary()
print(unitary)

15. Noise Models and Noisy Simulation

from qiskit.providers.aer.noise import NoiseModel
noise_model = NoiseModel.from_backend(backend)

Add noise to QASM simulations.

16. Custom Noise Channel Integration

You can apply:

• Bit-flip
• Phase damping
• Depolarizing noise

from qiskit.providers.aer.noise.errors import pauli_error

17. Using the Density Matrix Simulator

backend = Aer.get_backend('density_matrix_simulator')

Returns a matrix describing the mixed quantum state.

18. Comparison: Simulator vs Real Device

19. Best Practices for Simulator Use

• Always test circuits on simulators before submitting to hardware
• Use statevector/unitary outputs for debugging
• Employ noise models to emulate real hardware

20. Conclusion

Quantum simulators are an essential part of the development lifecycle in quantum computing. Qiskit provides multiple simulators to test circuits, analyze errors, and accelerate learning in a zero-cost, low-friction environment.