Bell State Experiment in IBM Quantum Composer – A Complete Step-by-Step Guide

Bell State Experiment in IBM Quantum Composer – A Complete Step-by-Step Guide

The Bell State experiment is one of the first experiments every quantum computing student performs. It demonstrates one of the most fascinating phenomena in quantum mechanics—quantum entanglement. In this experiment, two qubits become so strongly correlated that measuring one instantly determines the state of the other, regardless of the distance between them.

IBM Quantum Composer makes it possible to build and execute this experiment on both a simulator and real IBM quantum hardware without writing code. The standard Bell-state circuit uses a Hadamard (H) gate followed by a Controlled-NOT (CX) gate to create the entangled state Φ⁺ = (|00⟩ + |11⟩)/√2. 

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What is a Bell State?

A Bell State is the simplest example of quantum entanglement.

Unlike classical bits, which are either 0 or 1, quantum bits (qubits) can exist in multiple states simultaneously. When two qubits become entangled, they behave as one quantum system.

One of the four Bell states is

|\Phi^+\rangle=\frac{|00\rangle+|11\rangle}{\sqrt2}

This means:

There is a 50% probability of measuring 00

There is a 50% probability of measuring 11

You should never observe 01 or 10 in an ideal quantum computer

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Aim of the Experiment

To generate an entangled Bell State using IBM Quantum Composer and verify entanglement through measurements.

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Theory

Initially, both qubits are in the ground state.

|00⟩

The experiment consists of only two gates.

Step 1 – Apply Hadamard Gate

Apply the Hadamard gate to qubit q0.

The Hadamard gate creates a superposition.

Before:

|0⟩

After:

(|0⟩ + |1⟩)/√2

The complete two-qubit system becomes

(|00⟩ + |10⟩)/√2

Now the first qubit is simultaneously 0 and 1.

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Step 2 – Apply Controlled NOT Gate

Apply a CX gate.

Control Qubit:

q0

Target Qubit:

q1

The CX gate flips the target only when the control qubit is 1.

So,

|00⟩ → |00⟩

and

|10⟩ → |11⟩

Final state

(|00⟩ + |11⟩)/√2

This is the Bell State.

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Requirements

IBM Quantum Account

IBM Quantum Composer

You can launch Composer from the IBM Quantum Platform. [IBM Quantum Composer](https://quantum.cloud.ibm.com/composer?initial=N4IgdghgtgpiBcIBCMA2qAEBlALhHMGAWkQLQCyMEAzgK4BOMsYOGIANCAI41QIgB5AAoBRAHIBFAIJZyGAEwA6AAwBuADpgAlmADGqWgBNC67mi0AjAIyKdu0xrCaujAOYYuAbXkBdR7rcMXW8-TU1GahhWL2VQsAALD09YxwiopKs43QAPJNj2L0zHWBoGQhifDFIAPiDkuJK6RgzKmrqijhBjagCtAAccLQB7MH4QAF8gA&utm_source=chatgpt.com)

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Step-by-Step Procedure

Step 1

Login to IBM Quantum.

Open IBM Quantum Composer.

Create a new circuit.

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Step 2

Choose

2 Quantum Qubits

You should see

q0

q1

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Step 3

Leave both qubits in their initial state

|0⟩

|0⟩

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Step 4

From the gate library,

Drag the

H

gate

onto

q0

Circuit

q0 ──H────

q1 ───────

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Step 5

Now choose

CX Gate

Control

q0

Target

q1

Circuit

q0 ──H────■────

          │

q1 ───────X────

This is the complete Bell State circuit. 

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Step 6

Add measurement gates to both qubits.

q0 ──H────■────M

          │

q1 ───────X────M

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Step 7

Run on

Simulator

or

Real Quantum Hardware.

IBM recommends running multiple shots (for example, 1024) to observe the probability distribution. 

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Expected Results

Ideal measurement counts

Output Probability

00 50%

11 50%

01 0%

10 0%

Example

00 : 511

11 : 513

or

00 : 498

11 : 526

Small deviations occur because of statistical sampling and hardware noise.

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Why Don't We Get 01 or 10?

Because both qubits are entangled.

Whenever

First Qubit = 0

Second Qubit is also

0

Whenever

First Qubit = 1

Second Qubit becomes

1

They are perfectly correlated.

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State Evolution

Initial

|00⟩

↓

After H

(|00⟩ + |10⟩)/√2

↓

After CX

(|00⟩ + |11⟩)/√2

↓

Measurement

00

or

11

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Circuit Diagram

q0 ──H────■────M

          │

q1 ───────X────M

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Mathematical Derivation

Initial State

|00⟩

Apply Hadamard

H|0⟩

=

(|0⟩+|1⟩)/√2

Therefore

|00⟩

↓

(|00⟩+|10⟩)/√2

Apply Controlled NOT

CX|00⟩

=

|00⟩

CX|10⟩

=

|11⟩

Therefore

(|00⟩+|11⟩)/√2

which is the Bell State.

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Applications of Bell States

Quantum teleportation

Quantum cryptography (Quantum Key Distribution)

Superdense coding

Quantum communication

Quantum networking

Error correction

Quantum algorithms

Fundamental tests of quantum mechanics

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Advantages of IBM Quantum Composer

No programming required

Drag-and-drop circuit design

Run on simulators or real IBM quantum hardware

Visualize circuits and quantum states

Export to OpenQASM or Qiskit code automatically 

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Conclusion

The Bell State experiment is the foundation of quantum information science. By applying just two quantum gates—a Hadamard gate and a Controlled-NOT gate—you can create a maximally entangled pair of qubits. Running the circuit in IBM Quantum Composer demonstrates that measurements predominantly yield 00 and 11, illustrating the non-classical correlations that distinguish quantum computing from classical computing. This simple experiment forms the basis for many advanced quantum protocols, including teleportation, secure communication, and quantum algorithms.