Computational Power of Clifford and Ising Quantum Computers

arXiv:2611.13347v1 Announce Type: new Abstract: We extend the efficient classical simulation of Ising quantum computers from braidings to measurements. We investigate several different definitions of efficient Clifford quantum computation by varying the power of the circuit generator. In case the circuit generator can see the entire input, we give a detailed proof that efficient simulation of classical computation would imply the separation of complexity classes $\mathbf{P}$ and $\mathbf{PSPACE}$. If the circuit generator sees only the input length, we prove that Clifford quantum computers decide what we call affine languages.