Bell State Noise Simulation

This project is based on my bachelor’s monograph at Nangarhar University.

I used Qiskit Aer to compare a custom noise model with the FakeVigoV2 noise model. The aim was to see how the two models change the results of a Bell-state circuit.

Bell-State Circuit

The circuit prepares this Bell state:

|Φ+⟩ = (|00⟩ + |11⟩) / √2

It uses a Hadamard gate on the first qubit, followed by a CNOT gate.

Noise Models

I tested the circuit with two noise models:

• Custom model: uses T1, T2, depolarizing noise, and readout errors.
• FakeVigoV2 model: uses saved information from the FakeVigoV2 backend.

FakeVigoV2 is not a live IBM quantum computer. It is a fake backend made from saved device information.

Simulation

I ran each model 10 times with 10,000 shots in every run.

In my monograph, I used this value:

P(00) + P(11)

I called it Bell Measurement Fidelity, or BMF. It shows how often the circuit gives the expected |00⟩ and |11⟩ outcomes.

This value is not full quantum-state fidelity because it only checks the measurement results in the computational basis.

Results

Model	P(00) + P(11)	Standard Deviation	P(01) + P(10)
Custom model	0.8040	±0.0034	0.1960
FakeVigoV2 model	0.9018	±0.0030	0.0982

In this simulation, the FakeVigoV2 model gave more |00⟩ and |11⟩ results than the custom model.

Figure

The figure compares the results of both noise models.

Run the Code

Install the required packages:

pip install -r requirements.txt

Run the program:

python bell_state_analysis.py

For Google Colab, see HOW_TO_RUN.md.