Feynman-path-type simulation using stabilizer projector decomposition of unitaries

We propose a classical simulation method for quantum circuits based on decomposing unitary gates into sum of stabilizer projectors. By only the non-Clifford gates, we take advantage Gottesman-Knill theorem and build bridge between stabilizer-based Feynman-path-type simulation. give two variants this method: path-integral recursion (SPIR) projector contraction (SPC). also analyze further advantages disadvantages our compared to Bravyi-Gosset algorithm recursive Feynman algorithms. construct parametrized circuit ensemble identify parameter regime in where offers superior performance. estimate time cost simulating supremacy experiments with motivate potential improvements method.