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 at the quantum computing device. The n-qubit gate includes one or both of a diagonal gate and a diagonal gate conjugated by a multi-qubit Clifford gate. A set of n interface qubits on which to perform the first n-qubit gate is identified. A joint Z-Z measurement is executed on each target qubit and its corresponding interface qubit. The first n-qubit gate is executed on the set of n interface qubits. Computations are performed on one or more of the n target qubits prior to completion of the execution of the first n-qubit gate on the set of n interface qubits.
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