Bloch Sphere
<h1>Quantum Measurement</h1>
<p>
<strong>Quantum Measurement</strong> is the process of observing a qubit to determine its state.
When a qubit is measured, its quantum state collapses into one of the classical states
<strong>|0⟩</strong> or <strong>|1⟩</strong>.
</p>
<p>
Before measurement, a qubit may exist in <strong>superposition</strong>, meaning it represents
multiple states simultaneously. However, once measured, the qubit collapses to a single outcome.
</p>
<img class="img-fluid" src="/static/images/bloch_sphere.png"
alt="Quantum Measurement Collapse" width="500">
<hr>
<h2>Understanding Measurement</h2>
<p>
A qubit in superposition can be written as:
</p>
<pre>
|ψ⟩ = α|0⟩ + β|1⟩
</pre>
<p>
Where:
</p>
<ul>
<li><strong>α</strong> is the probability amplitude for state |0⟩</li>
<li><strong>β</strong> is the probability amplitude for state |1⟩</li>
</ul>
<p>
The probability of measuring each state is determined by:
</p>
<pre>
Probability(0) = |α|²
Probability(1) = |β|²
</pre>
<p>
After measurement, the qubit collapses to the measured state.
</p>
<hr>
<h2>Measurement in Quantum Circuits</h2>
<p>
In quantum circuit diagrams, measurement is represented by a
<strong>meter symbol</strong>.
</p>
<img class="img-fluid" src="/static/images/bloch_sphere.png"
alt="Quantum Measurement Symbol" width="450">
<p>
The measurement operation converts the quantum state into a classical bit.
</p>
<hr>
<h2>Example Measurement Outcomes</h2>
<table border="1" cellpadding="10">
<tr>
<th>Quantum State</th>
<th>Measurement Result</th>
</tr>
<tr>
<td>|0⟩</td>
<td>0</td>
</tr>
<tr>
<td>|1⟩</td>
<td>1</td>
</tr>
<tr>
<td>(|0⟩ + |1⟩)/√2</td>
<td>50% chance of 0, 50% chance of 1</td>
</tr>
</table>
<hr>
<h2>Measurement in Qiskit</h2>
<p>
In Qiskit, measurement is used to convert qubits into classical bits
so the result can be observed.
</p>
<pre><code class="language-python">
from qiskit import QuantumCircuit
# Create a quantum circuit
qc = QuantumCircuit(1,1)
# Create superposition
qc.h(0)
# Measure qubit
qc.measure(0,0)
print(qc)
</code></pre>
<hr>
<h2>Why Measurement is Important</h2>
<p>
Measurement is essential because it allows us to extract useful information
from a quantum system.
</p>
<ul>
<li>Converts quantum information into classical data</li>
<li>Determines the final result of a quantum algorithm</li>
<li>Collapses superposition states</li>
</ul>
<hr>
<h2>Measurement in Quantum Algorithms</h2>
<p>
Quantum algorithms typically perform many gate operations before a final measurement.
The algorithm manipulates probability amplitudes so that the correct result
has the highest probability when measured.
</p>
<hr>
<h2>Conclusion</h2>
<p>
Quantum measurement is the bridge between the quantum world and classical computing.
Although qubits can exist in superposition, measurement forces the system into
a definite state, allowing quantum computations to produce observable results.
</p>