Measurement and Running on a Simulator

Statevector gives exact probabilities, but that's only possible on a simulator that can peek at the math directly. Real quantum hardware (and a more realistic simulator) only ever gives you measurement outcomes, one bitstring per run. This lesson runs a circuit many times and looks at the resulting distribution.

Running with shots

from qiskit import QuantumCircuit
from qiskit_aer import AerSimulator

qc = QuantumCircuit(2, 2)
qc.h(0)
qc.cx(0, 1)
qc.measure([0, 1], [0, 1])

simulator = AerSimulator()
result = simulator.run(qc, shots=1024).result()
counts = result.get_counts()
print(counts)  # e.g. {'00': 512, '11': 512}

• AerSimulator() is a simulator that behaves like real hardware: it doesn't hand you the exact quantum state, only the outcome of measuring it, one shot at a time.
• shots=1024 runs the entire circuit 1024 times independently (each one a fresh superposition, fresh measurement), since a single measurement only ever gives you one bitstring, you need many repetitions to see the underlying probability distribution.
• result.get_counts() returns a dictionary mapping each observed bitstring to how many of the 1024 shots produced it.

Statistical noise

Run the code above a few times, the exact counts won't be identically 512/512 every time, maybe 498/526, this is expected: with a finite number of shots, you're estimating the true 50/50 probability, not measuring it exactly. More shots narrow that estimate, at the cost of more computation (or, on real hardware, more time and cost).

# fewer shots = noisier estimate of the true probabilities
result_small = simulator.run(qc, shots=10).result()
print(result_small.get_counts())  # could easily be lopsided, e.g. {'00': 7, '11': 3}