Implementing clifford gates on quantum hardware systems

Abstract

In a method for implementing a Clifford gate on a quantum hardware system, a symplectic matrix representation of the Clifford gate is determined that factorizes as a product of at least a first matrix, a second matrix, a third matrix, and a fourth matrix. The first matrix corresponds to a CNOT circuit, the second matrix corresponds to an X-diagonal Clifford operator or a Z-diagonal Clifford operator, the third matrix corresponds to a Z-diagonal Clifford operator, and the fourth matrix corresponds to an X-diagonal Clifford operator. The Clifford gate is synthesized into a sequence of quantum gates, based on the symplectic matrix representation of the Clifford gate. The sequence of quantum gates is implemented on the quantum hardware system.

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