Ideal Circuit

GHZ circuit ($H_0,C{X}_{01},\dots ,C{X}_{n-2,n-1}$) in statevector mode across n = 2 … 15 qubits.

All frameworks use their default CPU statevector simulator. qudit (mps) offloads to Apple Silicon GPU via Metal.

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Notes:

• qudit (cpu) uses index-aware tensor contraction — constant overhead is higher than dense Kronecker at small $n$, but Hilbert-space scaling is better past $n\approx 8$.
• qudit (mps) transfers tensors to Metal GPU — overhead dominates at small $n$, wins when statevector exceeds L3 cache (~$n\ge 12$).
• numpy builds the full embedded unitary per gate (dense Kronecker); fast at small $n$, exponential blow-up after $n=8$.
• PennyLane lightning.qubit is JIT-compiled C++; typically fastest on CPU past 8 qubits among third-party frameworks.
• braket and qiskit include IR serialisation overhead in each run.