Backends Deep Dive

PRISM-Q does not have one simulation algorithm. It has eight, each optimal for a different class of circuit. This guide is the task-oriented companion to the architecture reference: it focuses on scaling and when to reach for each one. To select a backend in code, see Choosing a Backend. For which CPU and GPU architectures each backend supports, see the Capability and Support Matrix.

Scaling at a glance

Backend	Memory	Best for	Ceiling
Statevector	$O (2^{n})$	Dense general circuits	~28 qubits (RAM-bound)
Stabilizer	$O (n^{2})$	Clifford-only circuits	Thousands of qubits
Factored Stabilizer	$O (n^{2})$ per cluster	Clifford with independent blocks	Thousands of qubits
Sparse	$O (k)$ nonzero	Concentrated support	Large $n$ , small $k$
MPS	$O (n χ^{2})$	Low entanglement	Large $n$ , bounded $χ$
Product	$O (n)$	No entanglement	Unbounded
Tensor Network	order-dependent	Shallow / structured	$\leq 25$ prob qubits
Factored	$O (2^{n})$ worst case	Partially independent	Block-bound

Statevector

The default for dense circuits. Exact, fully general, and the fastest option whenever the state fits in RAM. The memory cap is derived from system RAM (overridable with PRISM_MAX_SV_QUBITS). Above it, auto-dispatch falls back to Sparse or MPS.

Stabilizer

If your circuit uses only Clifford gates (H, S, Sdg, SX, SXdg, CX, CZ, SWAP, measurement), the stabilizer tableau simulates it in $O (n^{2})$ and scales to thousands of qubits. Auto-dispatch selects it whenever the circuit is Clifford-only.

Tip

Add even a single non-Clifford gate (T, Rz(θ) with arbitrary θ) and the stabilizer backend no longer applies. For a small number of such gates, see Clifford+T Simulation.

Sparse, MPS, Product, Tensor Network, Factored

Sparse wins when the state stays concentrated in a handful of computational-basis states (amplitude pruning keeps the map small).
MPS trades exactness for polynomial memory in the bond dimension. Ideal for low-entanglement circuits over many qubits.
Product is the degenerate, entanglement-free case: $O (n)$ memory, $O (1)$ per 1q gate.
Tensor Network defers contraction until measurement, useful for shallow or structured circuits.
Factored detects partial independence and simulates sub-registers separately, merging lazily via a Kronecker product computed on demand.

For the internal kernels behind each of these, read the architecture reference. For raw speed mechanics, see Performance and SIMD.

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PRISM-Q

Backends Deep Dive

Scaling at a glance

Statevector

Stabilizer

Sparse, MPS, Product, Tensor Network, Factored