Simulators, noise, T1/T2 and fake backends
Simulators compute what an ideal or noisy quantum computer would output. QubitLab offers four ideal methods and 68 noisy models of real IBM machines.
Simulation targets
| Target | Method | Limit | Use it for |
|---|---|---|---|
| ideal_statevector | Exact amplitudes; probabilities without shot noise. Memory 2ⁿ complex numbers. | 4 qubits | The reference every metric is compared against. |
| ideal_shots | Aer 'automatic' sampling: exact state, then random shots. | 4 qubits | Seeing statistical (shot) noise alone. |
| mps | Matrix product state: compresses weakly entangled states. | 4 qubits | Wide but shallow circuits, chains, low entanglement. |
| density_matrix | Tracks ρ (2ⁿ×2ⁿ) so mixed states and noise are exact. | 4 qubits | Studying decoherence precisely. |
| fake:<name> | AerSimulator built from a snapshot of a real backend: its coupling map, basis gates and calibrated noise. | 4 qubits | Predicting what hardware will do, for free. |
Noise: T1 and T2
Where does noise come from? A qubit is a tiny physical system (a superconducting circuit at 15 mK) that interacts with its environment. Two timescales summarize how fast it forgets:
A circuit of depth d with gate time τ takes about d·τ. Errors grow roughly like 1 − e^{−dτ/T2}, which is why depth matters so much. A CNOT takes ~300–500 ns, a √X ~30–60 ns, and readout ~1 µs.
Error channels
| Error channel | Model | Typical size |
|---|---|---|
| Depolarizing (gate error) | ρ → (1−p)ρ + p·I/2ⁿ | 1q: 2–5 ×10⁻⁴ · 2q: 3–10 ×10⁻³ |
| Thermal relaxation | T1, T2, gate duration | Depends on depth |
| Readout error | P(read 1 | was 0), P(read 0 | was 1) | 1–3 % per qubit |
Fake backends
Fake backends (FakeProviderForBackendV2) bundle a real device's snapshot: name, number of qubits, coupling map, basis gates, and calibration data (T1, T2, gate errors and durations, readout errors). AerSimulator.from_backend(...) turns that into a noise model, so fake_sherbrooke behaves like ibm_sherbrooke did on the snapshot day. Calibration changes daily on real hardware, so treat fake results as a forecast, not a measurement.
Shots and seeds
Shots and seed. More shots reduce statistical error as 1/√shots: 1024 shots give about ±1.5 % on a 50 % outcome, 4096 give ±0.8 %. Fixing a seed makes a simulation reproducible and lets QubitLab cache the result for 24 hours.