Noisy Circuits

GHZ circuit with noise applied per gate. All frameworks use their native noisy simulator.

TIP

qudit (stochastic) is a single shot — one Kraus branch sampled per gate. qudit (deterministic) applies the full Kraus sum, directly comparable to qiskit/cirq/etc. Multiply stochastic time by shot count to get equivalent accuracy.

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Depolarising

Amplitude Damping

Phase Damping

Notes:

qudit (stochastic) — Mode.NOISY, one Kraus branch sampled per gate. Constant time per shot, independent of noise strength. Scales to large $n$ because no full density matrix sum.
qudit (deterministic) — full Kraus sum $\sum_{k} E_{k} ρ E_{k}^{†}$ per channel application. Exact mixed state, directly comparable to qiskit/cirq. Cost scales as $O (K \cdot d^{2 n})$ .
qudit (mps) — stochastic shot on Apple Silicon GPU. Overhead dominates for small circuits.
All other frameworks compute the exact density matrix deterministically.

Noisy Circuits ​

Depolarising ​

Amplitude Damping ​

Phase Damping ​

Noisy Circuits

Depolarising

Amplitude Damping

Phase Damping