Simulators — Statevector vs Shot-Based

qc/programming qc/qiskit

Two fundamentally different ways to run a circuit without real hardware.

Statevector simulation

Computes the exact amplitudes directly — no sampling, no shot noise, the mathematical ground truth.

from qiskit.quantum_info import Statevector
from qiskit import QuantumCircuit
 
qc = QuantumCircuit(1)
qc.h(0)
Statevector(qc).probabilities()   # array([0.5, 0.5]) — exact, not estimated

Key insight: this only works because the simulator can see amplitudes directly — something no real device can ever give you (see Measurement and Collapse). It also doesn’t scale: representing $n$ qubits exactly needs $2^n$ complex amplitudes, so this is a debugging/learning tool for small circuits, not a path to simulating utility-scale circuits. Concretely: exact statevector simulation becomes infeasible beyond roughly 30 qubits, and 50 qubits alone would need on the order of 8 petabytes of RAM. Simulating noisy circuits is worse still — density-matrix simulation (see Density Matrix) scales as $4^n$, strictly worse than statevector’s already-brutal $2^n$, since $\rho$ is a $2^n\times 2^n$ matrix ($4^n$ entries) where $|\psi ⟩$ is just a $2^n$-entry vector.

Shot-based simulation

AerSimulator simulates individual measurement shots the way real hardware actually behaves — you get counts, not exact probabilities, with statistical noise from finite sampling even when the simulator itself is otherwise “clean” (noiseless).

from qiskit_aer import AerSimulator
from qiskit import QuantumCircuit, transpile
 
qc = QuantumCircuit(1, 1)
qc.h(0)
qc.measure(0, 0)
 
sim = AerSimulator()
counts = sim.run(transpile(qc, sim), shots=1000).result().get_counts()
# e.g. {'0': 512, '1': 488} — sampling noise even though the simulator has zero hardware noise

Adding realistic noise

AerSimulator.from_backend(backend) builds a shot-based simulator informed by a real (or fake) backend’s actual calibration data — basis gates, coupling map, measured error rates — see Backend Properties for the full breakdown of what that data contains.

Fake backends (e.g. FakeTorino, used in Heavy-Hex Topology) package up a real device’s calibration snapshot without needing live hardware access — useful for realistic testing without consuming QPU time or waiting in a queue.

Official reference: Qiskit Aer documentation.

Related

• Measurement and Collapse
• Backend Properties
• Heavy-Hex Topology
• The Primitives Family — local primitives wrap these same two simulation modes
• Density Matrix — the noisy-simulation object, and why it scales even worse

Self-Check

• Why does statevector simulation give you “ground truth” while shot-based simulation still has noise even with zero hardware error?
• Why doesn’t statevector simulation scale to large circuits?
• What’s the point of a fake backend like FakeTorino if it’s still just a simulator?
• Why does density-matrix (noisy) simulation scale as $4^n$ instead of $2^n$?