In this talk, we introduce a new classical simulation method for qubit Clifford circuits using the framed Wigner function, an extension of the Wigner function with additional phase degree of freedom. Our approach prevents negativity from Clifford gates by switching to an appropriate frame, allowing some nonstabilizer states to be represented positively. The method enables efficient sampling of certain marginal outcomes of Clifford circuits with nonstabilizer inputs using polynomial time and memory. We also develop a graph-theoretical technique to identify the classically simulatable marginal qubits.

 

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