Logarithmic Depth Decomposition of Approximate Multi-Controlled Single-Qubit Gates Without Ancilla Qubits

• URL: http://arxiv.org/abs/2507.00400v1
• Date: Tue, 01 Jul 2025 03:30:39 GMT
• Title: Logarithmic Depth Decomposition of Approximate Multi-Controlled Single-Qubit Gates Without Ancilla Qubits
• Authors: Jefferson D. S. Silva, Adenilton J. da Silva,
• Abstract summary: We present improved decompositions of multi-controlled NOT gates with logarithmic depth using a single ancilla qubit.<n>We also reduce the constant factors in the circuit depth compared to previous work.<n>Our method is particularly suitable for both NISQ and fault-tolerant quantum architectures.
• Score: 0.9576327614980397
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The synthesis of quantum operators involves decomposing general quantum gates into the gate set supported by a given quantum device. Multi-controlled gates are essential components in this process. In this work, we present improved decompositions of multi-controlled NOT gates with logarithmic depth using a single ancilla qubit, while also reducing the constant factors in the circuit depth compared to previous work. We optimize a previously proposed decomposition of multi-target, multi-controlled special unitary SU(2) gates by identifying the presence of a conditionally clean qubit. Additionally, we introduce the best-known decomposition of multi-controlled approximate unitary U(2) gates without using ancilla qubits. This approach significantly reduces the overall circuit depth and CNOT count while preserving an adjustable error parameter, yielding a more efficient and scalable solution for synthesizing large controlled-unitary gates. Our method is particularly suitable for both NISQ and fault-tolerant quantum architectures. All software developed in this project is freely available.

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