What measurement actually gives you
One measurement gives one classical bit — you never observe an amplitude or a probability directly, and the qubit is left in the state matching the bit you read. Distributions exist only through repetition: run the same circuit many times and the histogram converges to the squared magnitudes of the amplitudes.
Measurement returns one classical bit per measured qubit — that is all. You never observe an amplitude, a probability, or a superposition; you observe a 0 or a 1, and the qubit afterwards sits in the state matching what you read. Everything statistical about quantum computing — histograms, probability estimates, error bars — comes from running the circuit again.
This lesson makes that concrete with a biased coin: a qubit prepared so that P(0) = 2/3 and P(1) = 1/3 exactly.
What does a biased coin look like?
Where does the 2/3 come from?
RY(θ) rotates the qubit, taking |0⟩ to cos(θ/2)|0⟩ + sin(θ/2)|1⟩. The angle here, θ = 1.2310 radians, was chosen so that cos²(θ/2) = 2/3. The angle is a continuous dial: amplitudes are analogue quantities, and you can prepare any bias you like.
Notice what a single shot tells you: almost nothing. One 0 from this circuit is indistinguishable from one 0 from a fair coin, a 99/1 coin, or a qubit that was |0⟩ all along. Telling those apart takes repetition — which is why every run panel on this site reports counts over many shots, never one oracle-like answer.
Can you reproduce a run exactly?
In the simulator, yes. Each run here is driven by a seeded pseudorandom generator, and the panel prints the seed. The same circuit, shot count, and seed reproduce the identical shot-by-shot sequence — which is what makes simulator results debuggable and shareable. Try it in the Lab.
On hardware, no. Physical measurement outcomes are not pseudorandom; there is no seed to fix. Only the statistics reproduce, and even those drift between calibration runs as the device's error rates move. That is a difference in kind between simulation and hardware, not an implementation detail.
What does this look like on real hardware?
On real devices, measurement is itself a physical operation — and typically the most error-prone step in a short circuit. Superconducting readout misassigns the bit on the order of 1% of the time, roughly ten times the error of a single-qubit gate, and takes about a microsecond; trapped-ion readout is slower but more accurate. Vendors quote this as readout fidelity or assignment error, listed per device on the QPU pages and comparable across platforms on the comparison view.
Repetition averages away statistical noise but not readout bias: if 1s are systematically misread as 0s, more shots just converge to the wrong distribution. That is why hardware results are often post-processed with measurement-error mitigation — a correction the noise-free simulator on this site does not need.