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

Fuente: arXiv
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Main Authors: Silva, Jefferson D. S., da Silva, Adenilton J.
Format: Preprint
Published: 2025
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author Silva, Jefferson D. S.
da Silva, Adenilton J.
author_facet Silva, Jefferson D. S.
da Silva, Adenilton J.
contents 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 an improved decomposition of multi-controlled NOT gates with logarithmic depth using a single ancilla qubit while reducing the ancillary resource requirements compared to previous work. We further introduce a relative-phase multi-controlled NOT gate that eliminates the need for ancillas. Building on these results, 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, which do not require 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.
format Preprint
id arxiv_https___arxiv_org_abs_2507_00400
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Logarithmic Depth Decomposition of Approximate Multi-Controlled Single-Qubit Gates Without Ancilla Qubits
Silva, Jefferson D. S.
da Silva, Adenilton J.
Quantum Physics
Computational Complexity
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 an improved decomposition of multi-controlled NOT gates with logarithmic depth using a single ancilla qubit while reducing the ancillary resource requirements compared to previous work. We further introduce a relative-phase multi-controlled NOT gate that eliminates the need for ancillas. Building on these results, 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, which do not require 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.
title Logarithmic Depth Decomposition of Approximate Multi-Controlled Single-Qubit Gates Without Ancilla Qubits
topic Quantum Physics
Computational Complexity
url https://arxiv.org/abs/2507.00400