Beyond Quantum Shannon: Circuit Construction for General n-Qubit Gates Based on Block ZXZ-Decomposition

This paper proposes a new optimized quantum block-ZXZ decomposition method [7,8,10] that results in more optimal quantum circuits than the quantum Shannon decomposition (QSD)[27], which was introduced in 2006 by Shende et al. The decomposition is applied recursively to generic quantum gates, and can take advantage of existing and future small-circuit optimizations. Because our method uses only one-qubit gates and uniformly controlled rotation-Z gates, it can easily be adapted to use other types of multi-qubit gates. With the proposed decomposition, a general 3-qubit gate can be decomposed using 19 CNOT gates (rather than 20). For general n-qubit gates, the proposed decomposition generates circuits that have 22/484^n - 3/22^n +5/3 CNOT gates, which is less that the best known exact decomposition algorithm by (4^n-2 -1)/3 CNOT gates.