Portfolio · measurement-and-sampling
Measurement and sampling
Measurement desk
Measurement turns amplitudes into recorded outcomes. Sampling repeats that step. The measurement desk treats the shot count as part of the result, whether the shots come from a simulator or a device.
The Born rule
For a state written in the computational basis, the probability of a bit string is the squared modulus of its amplitude. One measurement returns one string. It does not return the amplitude. A second measurement on a fresh copy of the state can return a different string.
The quantum circuit model must say which qubits are read and in which basis. The computation desk’s gate list ends at that declaration. Everything after it is statistics.
Estimates, not single shots
An expectation value is the average of a function of many shots. The spread of that average shrinks as the number of shots grows, typically like one over the square root of the count. The desk will not quote a cost, a probability, or a comparison without that count.
Exact state-vector simulation probabilities can be used to check a sampler on a small circuit. They are not a substitute for the sampler once the method is tensor-network contraction or a device. Device shots also include noise and error, so the estimate and the ideal probability are different objects.
Finding from this desk
The desk’s finding is that a circuit does not return a state. It returns samples. Any published number is an estimate from those samples, with a count attached, or it is not a result.