One aspect of this disclosure relates to a method for operating a quantum computing device. A request to execute a first n-qubit gate on a set of n target qubits is received. The first n-qubit gate is representable as an m-qubit diagonal gate conjugated by a Clifford gate, where m≤n. A set of m interface qubits on which to perform the m-qubit diagonal gate are identified. A Clifford operation is executed on each interface qubit and its corresponding target qubits. The m-qubit diagonal gate is executed on the set of m interface qubits.
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