Clifford Backend

QuantumCircuitsMPS.jl also ships a stabilizer-tableau backend, built on QuantumClifford.jl, for circuits built entirely out of Clifford-group gates. Instead of an MPS or a dense state vector, the state is stored as a MixedDestabilizer tableau, a compact O(L)-generator representation that only Clifford operations can update. apply!, track!, record!, and simulate! all work exactly as on the other two backends; only the SimulationState(...) constructor call changes.

When to use it: MIPT/CIPT studies that only need Clifford gates (Pauli twirls, random Clifford circuits, stabilizer measurements) and want to reach system sizes L = 100-1000+, far beyond what MPS or the state-vector backend can practically reach.

When not to use it: any circuit that needs a non-Clifford gate, HaarRandom, Rx/Ry/Rz, MatrixGate, or a general Projection/SpinSectorProjection. Use backend=:mps (see MPS Backend) or backend=:statevector (see State Vector Backend) for those. The Clifford backend is also qubit-only — arbitrary spin-S sites (see Arbitrary Spin-S Support) are MPS/state-vector-only.

Quick Example

using QuantumCircuitsMPS

# Stabilizer-tableau simulation: scales to L=100-1000+ qubits for Clifford-only circuits
L = 100
state = SimulationState(L=L, bc=:open, backend=:clifford,
    rng=RNGRegistry(gates_spacetime=1, gates_realization=2, born_measurement=3))
initialize!(state, ProductState(binary_int=0))
track!(state, :entropy => EntanglementEntropy(cut=L÷2))

apply!(state, RandomClifford(2), Bricklayer(:odd))
apply!(state, RandomClifford(2), Bricklayer(:even))
apply!(state, Measure(:Z), SingleSite(1))
record!(state)
println("Entropy after one layer + measurement: $(state.observables[:entropy][end])")

Physics: RandomClifford(2) draws an independent random two-qubit Clifford operator for each bond (from the :gates_realization stream) and applies it natively to the tableau, no dense matrix is ever built, so the entangling layer costs the same whether L is 8 or 800.

Scalability

Unlike the state-vector backend's 2^L memory or the MPS backend's bond-dimension-dependent cost, the stabilizer-tableau representation scales polynomially: O(L²) memory (L stabilizer generators, each an L-bit string) and O(L²)-O(L³) per gate or measurement update. In practice, a full even+odd RandomClifford(2) bricklayer sweep over all L qubits completes in well under a second at L=500 or L=1000 on a single core, sizes that are simply unreachable for a dense state vector (2^500 amplitudes) and impractical for MPS once entanglement growth forces maxdim up.

Supported Gates

Observable coverage: EntanglementEntropy, Magnetization(:Z), BornProbability, PauliString, and MutualInformation all work on the Clifford backend (poly-time via the stabilizer formalism). StringOrder and DomainWall are MPS/state-vector only and raise an informative ArgumentError on Clifford states — see the Backend Interface Contract's observable support matrix.

Gate Validation

Any gate outside the supported set, HaarRandom, Rx/Ry/Rz, MatrixGate, Projection, SpinSectorProjection, has no stabilizer-tableau representation and raises an informative error rather than being silently approximated:

using QuantumCircuitsMPS

state = SimulationState(L=4, bc=:open, backend=:clifford,
    rng=RNGRegistry(gates_spacetime=1, gates_realization=2, born_measurement=3))
initialize!(state, ProductState(binary_int=0))
apply!(state, HaarRandom(), SingleSite(1))

ArgumentError: Clifford backend only supports Clifford gates (PauliX, PauliY, PauliZ, Hadamard, PhaseGate, CZ, CNOT, SWAP, RandomClifford, Measure, Reset). Received: HaarRandom. Please switch to backend=:mps or backend=:statevector for non-Clifford gates.

Entanglement Spectrum

Stabilizer states have an exactly flat entanglement spectrum: for any bipartition, every nonzero Schmidt coefficient has the same magnitude. As a direct consequence, every Rényi-n entropy, including the von Neumann limit, is identical for a stabilizer state, so the renyi_index keyword on EntanglementEntropy is automatically satisfied for any value:

using QuantumCircuitsMPS

state = SimulationState(L=4, bc=:open, backend=:clifford,
    rng=RNGRegistry(gates_spacetime=1, gates_realization=2, born_measurement=3))
initialize!(state, ProductState(binary_int=0))
apply!(state, Hadamard(), SingleSite(1))
apply!(state, CNOT(), Sites([1,2]))
apply!(state, CNOT(), Sites([2,3]))
apply!(state, CNOT(), Sites([3,4]))  # GHZ state
for r in (1, 2, 3, 5)
    println("renyi_index=$r -> S = $(EntanglementEntropy(cut=2, renyi_index=r)(state))")
end

renyi_index=1 -> S = 1.0
renyi_index=2 -> S = 1.0
renyi_index=3 -> S = 1.0
renyi_index=5 -> S = 1.0

Cross-Backend RNG Reproducibility (Redundant Draw)

Every measurement consumes exactly one :born_measurement draw per measured site — on the Clifford backend just like on MPS and state-vector. This is a deliberate redundant draw: for a stabilizer state the tableau often fixes the outcome in advance (probability exactly 0 or 1), and in that deterministic case the drawn value is simply discarded. The draw is made anyway so that the :born_measurement stream position advances identically on all three backends.

This redundancy is what buys absolute cross-backend reproducibility: with the same RNGRegistry seeds, the measurement record (sites, outcomes, and every downstream stochastic branch) is identical whether you run the circuit on the Clifford, MPS, or state-vector backend. You can prototype at small L on the exact state-vector backend, then rerun the same seeded trajectory at L = 1000 on Clifford.

See the Backend Interface Contract's _measure_single_site! section for the full contract wording.