Linear decomposition of approximate multi-controlled single qubit gates
Abstract
We provide a method for compiling approximate multi-controlled single qubit gates into quantum circuits without ancilla qubits. The total number of elementary gates to decompose an n-qubit multi-controlled gate is proportional to 32n, and the previous best approximate approach without auxiliary qubits requires 32nk elementary operations, where k is a function that depends on the error threshold. The proposed decomposition depends on an optimization technique that minimizes the CNOT gate count for multi-target and multi-controlled CNOT and SU(2) gates. Computational experiments show the reduction in the number of CNOT gates to apply multi-controlled U(2) gates. As multi-controlled single-qubit gates serve as fundamental components of quantum algorithms, the proposed decomposition offers a comprehensive solution that can significantly decrease the count of elementary operations employed in quantum computing applications.
Cite
@article{arxiv.2310.14974,
title = {Linear decomposition of approximate multi-controlled single qubit gates},
author = {Jefferson D. S. Silva and Thiago Melo D. Azevedo and Israel F. Araujo and Adenilton J. da Silva},
journal= {arXiv preprint arXiv:2310.14974},
year = {2025}
}