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Quantum Lab

An interactive quantum mechanics learning platform and cryostat wiring co-design tool. From plain-language intuition to formal mathematics.

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The most famous experiment in physics
No detectorNo detector: amplitudes can interfere
0 hits

Interactive 3D double-slit demonstration with a source, two slits, and a detector screen. The controls let you fire particles, toggle a detector, and compare an interference pattern with the detector-on washout pattern.

Predict before reveal
What changes when a detector watches the slits?
Predict before reveal
What changes when a detector watches the slits?
Read the stage

Amplitude is not a water wave. It is the underlying quantity quantum mechanics adds before it turns the result into probability.

With no detector, the two slit alternatives remain part of one coherent state, so their amplitudes reinforce in some places and cancel in others.

Turn the detector on, and the screen no longer receives one shared interference pattern. It receives the sum of two separate which-path contributions.

What to notice
One hit looks random. The full pattern does not.
The detector changes what can interfere, not the particles.
Toggle the detector to compare quantum vs classical behavior.

One phenomenon. Two outcomes depending on whether the path is watched. That single contrast is the doorway into everything that follows.

Chapter 1Chapter 2Chapter 3Chapter 4Chapter 5
Narrative arc
Chapter 1
The mystery
Chapter 2
The language of quantum states
Chapter 3
From waves to qubits
Chapter 4
Why quantum computing works
Chapter 5
Beyond the first surprise
Chapter 1

What you just saw

The pattern is not random noise. It is the visible trace of amplitudes combining before measurement turns them into probabilities.

Chapter frame
One sentence: measurement changes what can interfere. The detector does not simply watch the same pattern appear. It changes the experimental situation so the two slit alternatives no longer contribute coherently to one shared screen pattern.

The stripes matter because they are structured. A single hit looks random. The accumulated pattern does not.

The wave-like part is about amplitude, not tiny water ripples moving through space. Quantum mechanics adds amplitudes, and only later turns them into measurable probabilities.

When which-path information becomes available, interference is lost. The pattern is still lawful, but the law changes from "add the amplitudes together" to "add the separate path probabilities."

No detector

Bright and dark bands appear because the amplitudes add before measurement.

Detector on

Two broader lobes remain because the paths no longer interfere coherently.

1
See It

Watch a detector screen go from alternating bright and dark bands to two smoother lobes. The eye already sees the rule change before the symbols appear.

2
Touch It

Fire particles, switch the detector on, and let the screen refill. The experiment answers the question directly.

3
Understand It

Measurement is not a late-stage camera pointed at a fixed story. It changes which alternatives remain coherent enough to interfere.

4
Formalize It

Without path information:P(x)∝∣ψ1​(x)+ψ2​(x)∣2

With path information:P(x)∝∣ψ1​(x)∣2+∣ψ2​(x)∣2

Takeaway: The first great quantum lesson is this: what you measure is not the same thing as the state that was evolving before the measurement.
Chapter 2

The language of quantum states

Once the double-slit experiment feels real, the vocabulary stops feeling arbitrary. A quantum state is a recipe for amplitudes. Probabilities are what you see only after measurement.

Chapter frame
Learn the layers in order: intuition first, then amplitude, then probability, then the compact formal language that keeps those layers straight.

State

A quantum state is a compact description of what can happen next. It is not the same thing as the result you will read out on one measurement.

Anchor
state
result

Amplitude

Amplitudes are the quantities quantum mechanics adds together. They can cancel or reinforce because they have both size and phase.

Anchor
+

Probability

Probabilities are what you get only after turning amplitudes into measurable chances. They are the end of the story, not the beginning.

Anchor

Phase

Phase can be invisible in one basis and decisive in the next. Quantum computing works by shaping those relative phases deliberately.

Anchor
The four things to remember

These are the anchors that keep the subject intuitive even once the notation becomes more precise.

A state is not a result

The state tells you what outcomes are possible and how they relate. One measurement gives one ordinary result.

Anchor

Amplitudes are not probabilities

You add amplitudes first. Only then do you square their magnitudes into probabilities.

Anchor

Phase is hidden but important

Two states can share the same immediate histogram and still behave differently after another coherent step.

Anchor

Parts can look random while the whole is structured

That is why entanglement feels strange: the pair can be well-defined even when each single qubit does not carry its own full description.

Anchor
Amplitude vs probability

Some differences are invisible now but decisive later.

Slide the relative phase between the two amplitudes. In the computational basis the immediate measurement statistics stay 50/50. Apply one more interference step, and the hidden phase becomes visible.

Relative phase visual
Amplitude for |0⟩
phase 0
Amplitude for |1⟩
phase 0
The lengths stay the same, so the direct measurement chances stay balanced. The angle changes, and that angle is exactly the part that later interference reads out.
Measure now
P(0)50%
P(1)50%
After one more transform
P(0)100%
P(1)0%
Immediate probabilities can look identical even when the quantum state has changed. The difference is stored in relative phase, and another coherent transform can expose it.
1
See It

Two state arrows can have the same length and different phase. The immediate histogram can stay unchanged.

2
Touch It

Move the phase slider. Watch the "measure now" panel stay flat while the "after interference" panel swings.

3
Understand It

This is why amplitude matters more deeply than raw probability. Phase is not decorative. It is the part of the state that future interference reads.

4
Formalize It

∣ψ⟩=α∣0⟩+β∣1⟩

P(0)=∣α∣2,P(1)=∣β∣2

Compact equation
∣ψ⟩=α∣0⟩+βeiϕ∣1⟩

The magnitudes of α and β control the immediate measurement chances. The relative phase φ can stay hidden now and still decide what happens after the next coherent transform.

Chapter 3

From waves to qubits

A qubit is not all of quantum mechanics, but it is a beautifully compressed piece of it. The same logic from the double-slit experiment survives: superposition, measurement, and phase-sensitive interference.

Chapter frame
The qubit is what happens when you keep the full quantum logic but focus it into the smallest useful state space.

The full wavefunction can describe many possibilities across space. A qubit keeps only two basis states, |0⟩ and |1⟩, but the core rules stay intact. You still have amplitudes. You still have phase. You still have measurement.

Bloch sphere bridge

A qubit is a compact map of one quantum state space.

The Bloch sphere does not replace the full wavefunction. It compresses one qubit into a geometry where amplitude balance and relative phase become visible at a glance. Apply a few gates and watch the state move.

Loading sphere...
Think of the sphere as a compass for one qubit. Up versus down tracks measurement in the computational basis; motion around the equator tracks phase-sensitive superpositions.
Current state
P(0)
100%
Relative phase
0
Gate trail
start in |0⟩
H changes the balance between basis states. Z and S mostly rotate relative phase. X swaps north and south.
Balance
|0⟩ amplitude weight100%
|1⟩ amplitude weight0%
Readout in Z basis
North pole tendency100%
Equator phase relevance0%
North versus south tracks computational-basis measurement. Motion around the equator tracks phase-sensitive superpositions. H moves probability structure; Z and S mostly rotate hidden phase.
1
See It

The north and south poles show basis certainty. The equator shows balanced superpositions where phase matters most.

2
Touch It

Apply H, X, Z, and S. Each move has a clean geometric meaning, which makes the abstract state feel concrete.

3
Understand It

The Bloch sphere is a reasoning tool. It turns hidden amplitude relationships into a navigable map of one-qubit behavior.

4
Formalize It

∣ψ⟩=cos2θ​∣0⟩+eiϕsin2θ​∣1⟩

θ sets the balance. φ sets the relative phase.

Chapter 4

Why quantum computing works

Quantum speedups do not come from reading many classical answers out of one measurement. They come from evolving amplitudes so useful possibilities interfere constructively and useless ones interfere destructively.

Chapter frame
The double-slit experiment is already a tiny quantum computation: prepare alternatives, let phase accumulate, and read out the interference pattern.
Phase becomes visible

Interference is controlled by phase relationships.

Prepare a superposition, add a relative phase, then apply one more coherent transform. The second transform converts that hidden phase into visible constructive and destructive interference.

Gate sequence
1
H

Prepare an equal superposition.

2
P(180°)

Change relative phase without changing the immediate 50/50 readout.

3
H

Convert the phase difference into interference at the output.

This is where algorithms begin: by steering phase so desired paths reinforce while undesired paths cancel.
Immediately before the final H
P(0)50%
P(1)50%
After interference
Constructive branch0%
Suppressed branch100%
Quantum advantage is not “reading many answers at once.” The useful move is evolving amplitudes so phase relationships amplify promising outcomes and suppress the rest.
Misconception
A quantum computer does not just try every answer and read them all out.
Each run still ends in one ordinary measurement result. The power comes earlier, while amplitudes are evolving. Algorithms are designed so relative phase steers interference toward good answers and away from bad ones.
1
See It

A middle step can look invisible in the measurement basis. The final transform exposes the hidden difference.

2
Touch It

Change the phase shift and watch the final probabilities flow between the constructive and suppressed branches.

3
Understand It

This is the algorithmic center of the subject: phase relationships become visible only after the right interference step.

4
Formalize It

P(0)=cos22ϕ​,P(1)=sin22ϕ​

Different φ means different interference, even when the earlier histogram looked unchanged.

Algorithm bridge
HP(ϕ)H∣0⟩⟹P(0)=cos22ϕ​

The specific gate names are less important than the pattern: prepare coherence, sculpt phase, then use one more coherent step to convert that hidden structure into a measurable advantage.

Chapter 5

Beyond the first surprise

The double-slit experiment is the doorway, not the whole house. Beyond it lie entanglement, spin, tunneling, and the real hardware that keeps quantum states alive long enough to matter.

Chapter frame
Each topic below is a doorway, not an encyclopedia entry. The goal is traction and a clear next step.
Entanglement teaser

The whole system can be sharp even when the parts are not.

Measure a Bell pair repeatedly. Each side looks random on its own, but the joint outcomes stay structured. That is the signature move: the pair has a well-defined state that the parts do not carry independently.

Pair readout
0
0
Left qubit
Right qubit
Sample count: 0. Each local panel looks random over time, but the pair keeps landing on the correlated strings.
Local views
Left: 00%
Left: 10%
Right: 00%
Right: 10%
Joint outcomes
000%
010%
100%
110%
This is the conceptual foothold for entanglement: separate readouts can look maximally uncertain while the joint state remains highly organized.
1
See It

The pair keeps landing on correlated outcomes even while each single qubit looks random when viewed alone.

2
Touch It

Sample the Bell pair repeatedly. The local panels drift toward 50/50, but the joint panel keeps only the allowed strings.

3
Understand It

Entanglement means the whole system carries structure that the parts do not separately contain.

4
Formalize It

∣Φ+⟩=2​∣00⟩+∣11⟩​

The state is definite as a pair, not as two independent local descriptions.

Spin

Measurement depends on the axis you ask.

Prepare a state aligned with the X axis. Measure along X, and the result is definite. Measure along Z or Y, and the same state looks balanced again.

+ along Z50%
- along Z50%
Tunneling

Quantum amplitude leaks through barriers.

Classically, a too-high barrier stops the particle cold. Quantum mechanically, the wavefunction penetrates the barrier and leaves a nonzero transmission chance on the far side.

Transmission chance: 20%
Hardware relevance

These ideas live inside real machines.

Qubits need controlled electromagnetic environments, extreme cooling, and careful signal routing. The math is not just elegant. It is the operating language of the device.

Cryostat Studio

Follow the physics down to the refrigerator: stages, wiring, thermal budgets, and the hardware side of coherence.

Open Cryostat Studio
Continue Learning

Go deeper with structured lessons.

You have seen the intuition. The lessons page gives you the precise framework — formulas, worked explanations, misconception checks, and self-test questions for every topic you just explored interactively.

Open structured lessonsTry it in Circuit LabSee the real hardware
Structured lessons
Formulas and precision

Twelve lessons covering states, operators, gates, interference, and entanglement — each with LaTeX formulas and academic references.

Circuit Lab
Build and verify

Load an example, step through the circuit, and compare the Bloch sphere with the histogram to verify what you learned.

Hardware bridge
Cryostat Studio

See where real quantum devices live: staged cooling, signal routing, and the physical environment that keeps qubits coherent.

Selected references
Young’s double-slit

The conceptual doorway: interference makes the mystery concrete before the formalism arrives.

Feynman on amplitudes

The path-integral viewpoint makes the add-then-square logic emotionally and mathematically precise.

Nielsen & Chuang

The canonical bridge from states and phase to qubits, gates, interference, and entanglement.

Modern hardware references

Real devices make coherence, phase control, readout, and cryogenic engineering operational rather than abstract.