Shot

A shot is one complete execution of a quantum circuit: state preparation, gate application, and measurement, producing a single classical bitstring as output. Because quantum measurement is inherently probabilistic (Born rule), a single shot gives only one sample from the output distribution. To reconstruct the probability distribution or estimate expectation values, the circuit must be repeated for many shots.

Why multiple shots are necessary

Consider a single qubit prepared in the state $|\psi\rangle = \frac{1}{\sqrt{2}}|0\rangle + \frac{1}{\sqrt{2}}|1\rangle$. Each shot yields either 0 or 1, each with probability 50%. A single shot tells you nothing about the probabilities. With $N$ shots, the estimated probability of measuring $|0\rangle$ is:

$\hat{p}_0 = \frac{n_0}{N}$

where $n_0$ is the number of shots that returned 0. The statistical uncertainty on this estimate is:

$\sigma(\hat{p}_0) = \sqrt{\frac{p_0(1-p_0)}{N}} \approx \frac{1}{2\sqrt{N}}$

To estimate a probability to within $\pm 1\%$, you need roughly $N = 10{,}000$ shots. To estimate an expectation value $\langle O \rangle$ with observable variance $\text{Var}(O)$ to precision $\epsilon$, the required number of shots scales as:

$N = \frac{\text{Var}(O)}{\epsilon^2}$

Shots in practice

When running circuits on IBM Quantum or other cloud platforms, the number of shots is a parameter you specify:

from qiskit_ibm_runtime import SamplerV2 as Sampler

sampler = Sampler(backend)
job = sampler.run([circuit], shots=4096)
result = job.result()

Common shot counts range from 1,000 to 100,000 depending on the required precision. More shots improve statistical accuracy but increase execution time and cost (cloud providers often charge per shot or per job).

Shot noise

The statistical fluctuation from finite sampling is called shot noise. It is a fundamental limit: even on a perfect noiseless quantum computer, results from a finite number of shots have sampling uncertainty. Shot noise is distinct from hardware noise (gate errors, decoherence, readout errors), though both contribute to uncertainty in the final result.

For variational algorithms like VQE, shot noise directly impacts the accuracy of gradient estimates, which affects the convergence of the classical optimizer. Choosing the right shot budget is an optimization problem itself: too few shots give noisy gradients that slow convergence, too many shots waste quantum resources on unnecessary precision.

Shots vs. circuit repetitions

On some hardware platforms, a single job submission executes all shots sequentially on the same physical qubits. On others, shots may be batched or interleaved with calibration. The assumption is that each shot is an independent, identically prepared execution of the circuit. In practice, slow drifts in qubit parameters can introduce correlations between shots taken far apart in time.

Why it matters for learners

The shot count is one of the most practical parameters in quantum computing. Understanding the relationship between shots, statistical precision, and execution cost helps you design experiments efficiently. It also reinforces that quantum computation is fundamentally probabilistic: the useful output is a distribution, not a single answer, and extracting information from that distribution requires careful statistical reasoning.

See also

• Measurement
• Born Rule
• Shot Noise
• Expectation Value
• Readout Error