Quantum_cats

BIP, High performance shrodingers cat

Annotated beginner version

The most important concepts are:

Let's start completely from the beginning.

1. What is a qubit?

In a normal computer, a bit can be:

0
or
1

A qubit can be in a combination of both states at the same time.

We write:

|0⟩
|1⟩

for the two possible states.

---

2. What is a Quantum Circuit?

A quantum circuit is just a sequence of operations applied to qubits.

This line creates a circuit with 2 qubits:

qc = QuantumCircuit(2)

Initial state:

qubit 0 = |0⟩
qubit 1 = |0⟩

So:

|00⟩

means:

qubit0 = 0
qubit1 = 0

---

3. The Hadamard Gate (H)

qc.h(0)

applies a Hadamard gate to qubit 0.

Before:

|0⟩

After:

(|0⟩ + |1⟩)/√2

Meaning:

50% chance of measuring 0
50% chance of measuring 1

Visual idea:

Before H:

100% 0

After H:

50% 0
50% 1

So after:

qc.h(0)

the first qubit is random.

Current state:

(|00⟩ + |10⟩)/√2

---

4. The CNOT Gate (CX)

qc.cx(0, 1)

means:

Control = qubit 0
Target  = qubit 1

Rule:

If control = 1
    flip target

Examples:

00 → 00
01 → 01
10 → 11
11 → 10

---

Apply it to our state

Before CNOT:

(|00⟩ + |10⟩)/√2

Apply CNOT:

|00⟩ stays |00⟩
|10⟩ becomes |11⟩

Result:

(|00⟩ + |11⟩)/√2

This is called an entangled state.

---

5. What is Entanglement?

The qubits are now connected.

If you measure:

qubit0 = 0

you automatically know:

qubit1 = 0

If you measure:

qubit0 = 1

then:

qubit1 = 1

Possible outcomes:

00
11

Impossible outcomes:

01
10

---

6. Measurement

qc.measure_all()

Measurement converts quantum information into classical bits.

Before measurement:

(|00⟩ + |11⟩)/√2

After measurement:

50% → 00
50% → 11

---

7. The Sampler

sampler = StatevectorSampler()

The sampler runs the circuit many times.

One run gives only:

00

or

11

So we run it thousands of times.

---

8. Running 2200 shots

result = sampler.run([qc], shots=2200).result()

Here:

shots=2200

means:

Repeat the experiment 2200 times.

Example:

Run 1: 00
Run 2: 11
Run 3: 00
Run 4: 11
...

---

9. Counting Results

counts = result[0].data.meas.get_counts()

Possible output:

{
    '00': 1098,
    '11': 1102
}

Meaning:

00 appeared 1098 times
11 appeared 1102 times

which is approximately:

50%
50%

---

10. Printing

print(counts)

Output:

{'00': 1098, '11': 1102}

---

11. Histogram

plot_histogram(counts)

draws a graph.

Something like:

1100 |
     |        ████
1000 |        ████
     |        ████
 500 |
     |
   0 +----------------
       00      11

Because only:

00
11

can occur.

---

Complete Code Example

from qiskit import QuantumCircuit from qiskit.primitives import StatevectorSampler from qiskit.visualization import plot_histogram

Build a simple one-qubit circuit for beginners.

We create a single qubit and a matching classical bit to store the measurement:

QuantumCircuit(number of quantum bits, number of classical bits).

Each qubit starts in state |0⟩ and can be modified using quantum gates.

The number of classical bits is optional when using measure_all()

qc = QuantumCircuit(1, 1)

Apply a Hadamard gate to qubit 0.

This puts the qubit into a superposition of |0> and |1>.

This turns a definite state (|0>) into a 50/50 random state.

After measurement, the result has an equal chance of being 0 or 1.

qc.h(0)

Measure the qubit into the classical register.

After measurement, the state collapses to either 0 or 1.

qc.measure_all()

StatevectorSampler() is a Qiskit object that executes a quantum circuit and

returns simulated measurement results.

Execute the quantum circuit 2200 times (shots).

Each execution produces a measurement result (e.g., 0 or 1).

Running the circuit many times allows us to estimate the probability

distribution by counting how often each result occurs.

sampler = StatevectorSampler() result = sampler.run([qc], shots=2200).result()

Extract the counts from the result.

counts = result[0].data.meas.get_counts() print() print("Measurement counts:", counts) print()

Plot a histogram of the measured results.

This helps beginners see the distribution visually.

hist = plot_histogram(counts) hist.savefig("measurement_histogram.png") print("Histogram saved to measurement_histogram.png") print()