Phase-space tableau simulation for quantum computation

We introduce a novel tableau-based classical simulation method for quantum computation, formulated within the phase-space framework of the extended stabilizer theory of closed noncontextual operators. This method enables the efficient classical simulation of a broader class of quantum circuits beyond the stabilizer formalism. We identify additional families of input states that are efficiently simulatable within this framework, going beyond stabilizer states, and implement the simulator and benchmark its performance on basic quantum algorithms, including the hidden shift and Deutsch–Jozsa algorithms.