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physics
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Interactive chapters from intuition to mastery
Structured Lessons
Eight modules with formulas and self-checks
Quantum Brain
Navigate lessons, laws, gates, devices, and tools
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Hands-on circuits that teach one idea each
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Circuit Lab
Build circuits, run them, and see the results
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Quick reference for all quantum gates
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Home/Quantum Physics/Lessons/Superposition
▶

Superposition

See what a qubit looks like before you measure it

beginner1 qubit·~1 min
The question

What does a qubit look like before you measure it?

Before you start

A qubit always starts in the ∣0⟩ state, which you can think of as a coin sitting heads-up on a table. In this experiment you will apply a single gate called the Hadamard (H) that puts the qubit into an equal mix of ∣0⟩ and ∣1⟩. This mixed state is called superposition.

What you will see

Before measurement, a qubit in superposition is not secretly 0 or secretly 1. It genuinely holds both possibilities at once, each with a probability amplitude. The Hadamard gate creates this by splitting the ∣0⟩ state into two equal branches. When you finally measure, each branch has a 50% chance of being the outcome you see. Run the experiment many times and watch the histogram settle toward a balanced split.

The circuit
Circuit
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q0H
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Step-by-step walkthrough
1

Apply Hadamard to qubit 0

The H gate transforms ∣0⟩ into an equal superposition of ∣0⟩ and ∣1⟩. Watch the Bloch sphere: the arrow moves from the north pole (pure ∣0⟩ to the equator, where it points along the +X direction. The histogram now shows equal weight on both outcomes.

2​∣0⟩+∣1⟩​=∣+⟩
What to notice
  • The Bloch sphere arrow moves from the north pole to the equator after the Hadamard gate.
  • The theory histogram shows equal weight on 0 and 1 for the active qubit.
  • Each individual shot still returns a single definite result, either 0 or 1.
  • Over many shots, the counts settle near a 50/50 split, confirming the equal probabilities.
Tempting but wrong

It is tempting to think superposition means the qubit reads out both 0 and 1 at the same time. That is not what happens. Each measurement returns one ordinary classical outcome. Superposition describes the probabilities before measurement, not the result after it.

Expected result

The active qubit produces 0 and 1 with roughly equal frequency. Over 1000 shots you should see counts near 500 for each outcome. Any untouched qubits stay in ∣0⟩.

Connection to the theory

This experiment is a hands-on companion to the Superposition and Measurement lesson. That lesson explains the mathematical framework (amplitudes, Born rule, state vectors) behind what you see here. After running this experiment, the formula ∣+⟩=(∣0⟩+∣1⟩)/2​ should feel concrete rather than abstract.

Read the full lesson →
Test your understanding

After applying H to |0⟩, you run a single measurement. What do you see?

▶ Load in simulator↗ Griffiths and Schroeter, Introduction to Quantum Mechanics↗ MIT OCW 8.04: lecture notes
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Interference
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