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.
The striped pattern you saw is not random. It is direct evidence that quantum mechanics works differently from everyday physics. The key: possible paths combine before you observe the result.
A single particle lands in what looks like a random spot. But fire many particles, and the spots form a structured pattern of bright and dark stripes. That structure is the first clue that something deeper is going on.
The stripes are not caused by particles bumping into each other or by tiny water waves. They appear because quantum mechanics uses amplitudes -- numbers that can add together or cancel out -- to describe what happens. Only after the amplitudes combine does the result become a probability you can observe.
When the detector reveals which slit a particle used, the rules change. The amplitudes from both slits no longer combine. Instead, each slit contributes its own separate probability. The stripes disappear, and two broad lumps take their place.
Bright and dark bands form. The amplitudes from both paths combine, reinforcing in some places and canceling in others.
Two broad lumps appear -- one behind each slit. When the path is revealed, the amplitudes no longer combine.
Look at the screen with the detector off: alternating bright and dark bands. Now look with the detector on: the stripes are gone, replaced by two broad lumps. The difference is visible before you need any math.
Fire particles with the detector off and watch the pattern build. Then clear the screen, turn the detector on, and fire again. Compare the two results side by side.
The detector does not passively record a pattern that was already going to form. Revealing the path changes which possibilities can combine. That is why the pattern looks different. Measurement is not just observation -- it changes what happens.
These equations summarize what you just saw. Without the detector (amplitudes combine first, then you square):
With the detector (each path contributes its probability separately):
The first equation has a sum inside the squared brackets -- that is where interference lives. The second sums the squares separately -- no interference.
The double-slit experiment used three key ideas: states, amplitudes, and probabilities. This chapter defines each one clearly, then adds a fourth idea -- phase -- that explains why quantum mechanics is more than just fancy randomness.
A state is a complete description of a quantum system right now. It tells you what outcomes are possible and how likely they are. A state is not the same as a measurement result — the state is the recipe; the measurement result is one dish from that recipe.
An amplitude is a number that quantum mechanics assigns to each possible outcome. Amplitudes can add together or cancel each other out. You saw this in the double slit: the amplitudes from both paths combined to create the striped pattern.
A probability is the chance of getting a specific result when you actually measure. You get probabilities from amplitudes (by squaring them), not the other way around. Amplitudes come first; probabilities come at the end.
Phase is a property of an amplitude that controls how it combines with other amplitudes. Two states can have the same measurement probabilities right now, but different phases. That hidden difference can show up later when the states interact again.
Keep these four distinctions in mind. They prevent the most common confusions as you go deeper.
The state describes all the possibilities. A measurement gives you one actual outcome. Do not confuse the description of possibilities with the single thing you end up seeing.
Amplitudes combine first -- they can add up or cancel out. Probabilities only appear at the end, when you square the final amplitudes. This order matters.
Two states can give identical measurement results right now, yet behave completely differently after one more step. The difference is stored in their phase. The next interactive demo shows you exactly how.
You will see this in Chapter 5 with entanglement: each qubit by itself looks random, but the pair together follows a strict pattern. The whole system carries information that the parts do not carry separately.
Use the slider to change the phase. Watch what happens: the 'Measure now' panel stays at 50/50 no matter what. But the 'After one more step' panel changes dramatically. This is the key lesson about phase -- it can be invisible in one measurement but completely change what happens next.
Both amplitude arrows have the same length. The "Measure now" bars stay at 50/50. The only visible difference is the angle of the second arrow.
Drag the phase slider from 0° to 180°. The "Measure now" panel stays locked at 50/50. Now look at "After one more step" -- it swings from 100/0 to 0/100. That swing is caused entirely by the phase you changed.
This is why quantum states contain more information than probabilities alone. Phase is invisible in a single measurement but determines what happens when the state interacts again. Without phase, there would be no interference and no quantum computing.
The state of a qubit is written as:
The probability of measuring 0 is |α|², and the probability of measuring 1 is |β|². These probabilities do not tell you the phase. But the phase is still there, stored inside α and β.
The sizes of α and β set the probabilities you see when you measure right now. The phase angle φ is invisible in that measurement -- but it determines what happens after the next step. This is exactly what you saw in the interactive demo above.
A qubit is the simplest quantum system: it has just two possible measurement outcomes, 0 and 1. But it still has amplitudes, phase, and interference -- everything you learned in the double-slit experiment, packed into the smallest possible container.
In the double-slit experiment, the particle could land at many positions on the screen. A qubit is much simpler -- it has only two possible states, called and . Before measurement, a qubit can be in a superposition: a combination of and with amplitudes and phase. When you measure, you get either 0 or 1 -- just one outcome.
The Bloch sphere shows every possible state of a single qubit as a point on a sphere. The north pole is . The south pole is . Points on the equator are equal superpositions with different phases. Apply gates below and watch the qubit state move.
At the north pole, a measurement always gives 0. At the south pole, always 1. On the equator, measurement gives 0 or 1 with equal probability -- but the position around the equator shows the phase.
Try this sequence: start at (north pole), apply H (moves to equator), then apply Z (rotates phase -- the state moves around the equator but stays at 50/50). Then apply H again to return toward a pole. The final position depends on the phase.
The Bloch sphere turns an abstract quantum state into something you can see. Amplitude balance maps to position between the poles. Phase maps to position around the equator. Gates are movements on this sphere.
θ (theta) controls the position between the poles -- it sets the measurement probabilities. φ (phi) controls the position around the equator -- it sets the phase. Together, they specify any single-qubit state.
Quantum computers do not work by trying all answers at once and reading them out. They work by carefully controlling phase so that the right answer becomes more likely and wrong answers become less likely. The tool for this is interference.
This demo shows the three-step pattern behind every quantum algorithm. Step 1: create a superposition. Step 2: add a phase (invisible if you measure now). Step 3: apply one more gate, and the invisible phase turns into a visible change in probabilities. Drag the slider to change the phase and watch the result.
Create a 50/50 superposition of and .
Add a phase. If you measured right now, you would still see 50/50. The phase is hidden.
Apply one more H gate. This step combines the amplitudes again, and now the hidden phase controls the final probabilities.
It is tempting to think: "A quantum computer puts all possible answers into superposition and reads them all out." That sounds plausible, but it is wrong. Each measurement still gives one single result.
The real advantage happens before measurement. A quantum algorithm carefully adjusts the phases of different possibilities so that when the amplitudes combine, the right answer is amplified and the wrong answers are suppressed. The measurement at the end just reads out the winner.
The left panel stays at 50/50 no matter what phase you set. The right panel changes. The phase was there all along -- it just needed one more step to become visible.
Set the phase to 0° -- the final result is 100% in one outcome. Set it to 180° -- it flips completely to the other. Set it to 90° -- it is 50/50 again. The phase controls the final result with precision.
Every quantum algorithm follows this same pattern: prepare a superposition, apply operations that embed the answer in the phase, then use one more step to convert that phase into a high-probability measurement result.
The probability of measuring 0 depends entirely on the phase angle φ. At φ = 0, you always get 0. At φ = π (180°), you always get 1. The intermediate histogram told you nothing, but the phase was stored and the final step revealed it.
The pattern is: (1) create a superposition, (2) modify the phase, (3) use one more step to turn the phase difference into a probability difference. The specific gates may change, but this three-step structure is at the heart of most quantum algorithms.
The double-slit experiment introduced the core ideas: amplitudes, phase, and interference. This chapter goes further with three more topics and a look at the real machines that run quantum computations.
This demo samples from an entangled pair of qubits (called a Bell pair). Click 'Measure pair' to measure both qubits at once. Watch what happens: each qubit individually appears random (about 50/50). But look at the joint results -- you only ever see '00' or '11', never '01' or '10'. The two qubits are linked even though each one alone looks random.
The joint panel shows only "00" and "11". The individual panels each show roughly 50/50. The pattern exists in the pair, not in the parts.
Click "Measure pair" many times (or use "Auto sample"). Watch the individual panels approach 50/50 while the joint panel stays locked on "00" and "11".
Entanglement means the state of the pair cannot be described by giving each qubit its own separate state. The pair has a definite quantum state, but the individual qubits do not.
It is tempting to think one qubit "tells" the other what to do. But there is no signal between them. The correlation was built in when the pair was prepared. Entanglement does not allow faster-than-light communication.
This state cannot be written as "qubit A in some state" times "qubit B in some state." The two qubits are not independent. The state is only well-defined for the pair as a whole.
Spin is an intrinsic quantum property with only two possible measurement values: + or -. The result depends on which direction (axis) you measure along. This state points along X. Measure along X and you get a definite +. Measure along Z or Y and the same state gives 50/50.
In everyday physics, a ball without enough energy simply bounces back from a wall. In quantum mechanics, the amplitude does not drop to zero at the barrier. It gradually fades inside but some reaches the other side -- so there is a small but real chance of transmission. Drag the slider to increase the barrier height.
Qubits are fragile. Any uncontrolled interaction with the environment can destroy the phase relationships that make quantum computing work (this is called decoherence). Real quantum computers use extreme cooling, electromagnetic shielding, and precisely routed signal cables.
Explore the physical machine: cooling stages, signal wiring, and the engineering that keeps qubits alive long enough to compute.
Open Cryostat StudioThis page gave you the core ideas interactively. Seven structured modules take you from quantum foundations through theorems, algorithms, and hardware engineering — with experiments, formulas, and hands-on simulator practice at every step.
Structured modules covering quantum states, phase, entanglement, no-go theorems, cryogenic hardware, and system design. Each lesson has intuition, formulas, common mistakes, and checklists.
Place gates on qubits, run the circuit, and see the results in a histogram and on the Bloch sphere. Start with a pre-built example or build your own from scratch.
See the physical machine that keeps qubits working: a multi-stage refrigerator cooled near absolute zero, with carefully routed signal cables. Design wiring layouts in 3D.
The original experiment that started it all. A good starting point for deeper reading on interference.
Feynman's way of thinking about quantum mechanics: add up the amplitudes for all possible paths, then square to get the probability.
The standard textbook for quantum computing. Covers qubits, gates, entanglement, and algorithms in full mathematical detail.
Technical references on the physical machines: superconducting qubits, cryogenic engineering, and the challenge of keeping quantum states alive.