Stabilizer

The stabilizer engine simulates Clifford circuits in time and memory that grow polynomially with the number of qubits. It can handle hundreds of qubits where a dense state could never exist.

Capabilities

Output	Supported
Counts	Yes
Expectation value	Yes (exact -1, 0 or +1 for a Pauli term)
Statevector	No

It does not track global phase, so it cannot produce a statevector, and a statevector request makes it infeasible with the reason the stabilizer engine does not track global phase -- only the dense engine can produce a statevector.

Which circuits

Only circuits whose every operation is a named Clifford gate:

X  Y  Z  H  S  Sdg  SX  SXdg  CX  CZ  SWAP

A single non-Clifford gate (T, RX(0.3), CP, CCX, or any unitary) makes the engine infeasible, and the reason names the first offending operation:

operation 8 (t) is not a Clifford gate

How it works

The engine keeps a bit-packed table of n stabilizer generators, each a Pauli string with a sign. A Clifford gate maps each generator to another Pauli string, which is a handful of bit operations. To sample, it reduces the final table once by Gaussian elimination over GF(2) to a base outcome plus a basis for the affine space of possible outcomes; each shot is the base XOR a random subset of the basis.

Cost

work = n                          row initialization
     + gates · n                  each gate touches each row
     + 2 · n² · words + n · words   (counts) elimination plus one sampling pass
words = ceil(n / 64)

Memory is n · 2 · words · 8 + words · 8 bytes, about 13 KB for 200 qubits. Nothing in it is exponential.

It does not always win

Being Clifford-only makes the engine eligible, not chosen. The planner compares work units, and for some Clifford circuits another engine is cheaper:

Circuit	Planned onto
Bell pair, counts	direct_stabilizer (16 work units against 32 dense, 34 MPS)
60-qubit random Clifford, counts	direct_stabilizer (dense and MPS are infeasible)
200-qubit GHZ, counts	direct_mps (3,400 against 361,000)

See the stabilizer example.

Routing rule for expectation values

A fully Clifford region is never given to Pauli propagation, even if that would estimate cheaper: the stabilizer engine handles a Clifford region's expectation value. This is a hard routing rule, not a cost preference.

Related

Pauli Propagation · Supported Gates