Pricing…Open Lab
Foundations · after Superposition · ~7 min

What measurement actually gives you

One measurement gives you one plain bit: a 0 or a 1. You never see an amplitude or a chance directly, and afterward the qubit is left in the state that matches the bit you read. To see the odds, you run the same circuit many times. The bar chart then settles toward the squared sizes of the amplitudes.

Measuring a qubit gives you one ordinary bit. That is all. You never see an amplitude (the number that says how strongly the qubit leans toward an answer). You never see a chance or a superposition either. You see a 0 or a 1. Afterward, the qubit sits in the state that matches what you read.

So where do all the charts and error bars come from? They come from running the circuit again, many times. Each run is called a shot.

This lesson shows it with a loaded coin. We set up a qubit so that the chance of 0 is exactly 2/3 and the chance of 1 is exactly 1/3. We write that as P(0) = 2/3 and P(1) = 1/3.

What does a loaded coin look like?

RY(1.2310) sets the amplitudes to √(2/3) and √(1/3). About two thirds of shots read 0 and one third read 1. At 1,024 shots, expect it to be off by up to about ±1.5 percentage points.standby
12q0|0⟩RY
press run to acquire
|0⟩|1⟩
——
counts: sampledamplitudes: statevector, exactengine: in-browser

Where does the 2/3 come from?

RY(θ) is a gate that rotates the qubit by an angle θ (theta). It takes |0⟩ to cos(θ/2)|0⟩ + sin(θ/2)|1⟩. Here the angle is θ = 1.2310 radians. We picked it so that cos²(θ/2) = 2/3.

Let's check it. Half the angle is 1.2310 ÷ 2 ≈ 0.6155. The cosine of 0.6155 is about 0.8165. Square that: 0.8165 × 0.8165 ≈ 0.667, which is 2/3. The rest, 1 − 2/3 = 1/3, goes to the answer 1.

The angle works like a dimmer switch, not an on/off switch. You can turn it to any spot you like, so you can make a coin with any bias you want.

Now notice how little one shot tells you. Say this circuit gives you one 0. A fair coin could give that. So could a 99-to-1 coin. So could a qubit that was |0⟩ the whole time. You can only tell them apart by repeating. That is why every run panel on this site shows counts over many shots. It never shows one magic answer.

Can you reproduce a run exactly?

In the simulator, yes. Each run here uses a seeded random number maker. A seed is a starting number that fixes the whole sequence of "random" results, like the number that sets up a shuffle in a card game app. The panel shows the seed. The same circuit, shot count, and seed give the exact same shot-by-shot results. That makes simulator results easy to debug and share. Try it in the Lab.

On hardware, no. A real measurement has no seed you can fix. Only the overall odds repeat. Even those drift a little from one tuning session to the next, as the device's error rates change. This is a real difference between a simulator and hardware, not a small detail.

What does this look like on real hardware?

On real devices, measuring is a physical step of its own. In a short circuit it is usually the step most likely to go wrong. On superconducting chips, readout gets the bit wrong about 1% of the time. That is roughly ten times the error of a single-qubit gate. It takes about a microsecond (a millionth of a second). Trapped-ion readout is slower but more accurate. Makers report this as readout fidelity (how often the bit is read correctly) or as assignment error. You can find it for each device on the QPU pages and compare platforms on the comparison view.

More shots smooth out random noise. They do not fix a steady bias in the readout. Picture a bathroom scale that always reads 2 pounds heavy. Weighing yourself 100 times won't fix that. In the same way, if 1s are often misread as 0s, more shots just settle on the wrong odds. That is why hardware results are often corrected afterward with measurement-error mitigation. The noise-free simulator on this site does not need that step.

Primary sources & further reading