Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Conference on Electrical, Communication, and Computer Engineering (ICECCE)

Decomposition of Basic Controlled Gates in Quantum Circuits

Pedro Juan Roig, Salvador Alcaraz, Katja Gilly, Cristina Bernad, Blas Trigueros

Published Aug 27, 2025• 0 citations
Publisher

Abstract

Quantum gates typically represent either rotations of controlled gates. Rotation gates usually involve one qubit, although Ising coupling gates involve two qubits. On the other hand, controlled gates can have any number of control qubits with at least a target qubit. In this paper, the decomposition of controlled gates in terms of rotation gates around a given axis has been carried out. The focus herein has been set on the$\mathbf{X}$axis, such that AND-CmX gates and OR-CmX gates have been decomposed and proved for$\mathbf{m}=\{\mathbf{1, 2, 3, 4}\}$and different polarities.

DOI
10.1109/icecce67514.2025.11257886

Related papers

Decomposition of Diagonal Hermitian Quantum Gates Using Multiple-Controlled Pauli Z Gates

Mahboobeh Houshmand, Morteza Saheb Zamani, Mehdi Sedighi +1 more

Quantum logic decomposition refers to decomposing a given quantum gate to a set of physically implementable gates. An approach has been presented to decompose arbitrary diagonal quantum gates to a set of multiplexed-rotation gates around z axis. In this article, a special class of diagonal quantum gates, namely diagonal Hermitian quantum gates, is considered and a new perspective to the decomposition problem with respect to decomposing these gates is presented. It is first shown that these gates can be decomposed to a set that solely consists of multiple-controlled Z gates. Then a binary representation for the diagonal Hermitian gates is introduced. It is shown that the binary representations of multiple-controlled Z gates form a basis for the vector space that is produced by the binary representations of all diagonal Hermitian quantum gates. Moreover, the problem of decomposing a given diagonal Hermitian gate is mapped to the problem of writing its binary representation in the specific basis mentioned previously. Moreover, CZ gate is suggested to be the two-qubit gate in the decomposition library, instead of previously used CNOT gate. Experimental results show that the proposed approach can lead to circuits with lower costs in comparison with the previous ones.

arXiv:1405.6741•ACM Journal on Emerging Technologies in Computing Systems•Dec 30, 2014•13 citations

Matrix representation of basic quantum circuits

Pedro Juan Roig, Salvador Alcaraz, Katja Gilly +2 more

Quantum computing fundamentals are based on Hilbert spaces and linear algebra, which allows to describe quantum gates as matrix representations. In this paper, a matrix approach is taken in order to analyze basic quantum circuits, composed of basic quantum gates of 1, 2, and 3 qubits. The most common cases of all those gates are analyzed. One-qubit gates are expressed as 2x2 matrices, accounting for a rotation around a determined axis. Two-qubit gates are described as 4x4 matrices, standing for controlled gates. Three-quibit gates are defined as 8x8 matrices, extending the concept of controlled gates and rotations.

International Conference on Engineering and Emerging Technologies (ICEET)•Oct 22, 2025•0 citations

Analyzing and Implementing N-qubit Controlled Gates

Yang Liu, Yang Sun, Gui Lu Long

We present two recursive schemes which generally simulate N-qubit controlled gates with standard one-qubit rotation and CNOT gates respectively using exponential and polynomial complexity simulations. Explicit circuits and decomposition expressions are deduced. We compare exact numbers of basic operations required in these two approaches using a gate counting technique.

Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)•Aug 1, 2007•1 citation

Decomposition of Multi-controlled Special Unitary Single-Qubit Gates

Rafaella F. Vale, Thiago Melo D. Azevedo, Ismael C. S. Araújo +2 more

Multi-controlled unitary gates have been a subject of interest in quantum computing since its inception, and are widely used in quantum algorithms. The current state-of-the-art approach to implementing n-qubit multi-controlled gates involves the use of a quadratic number of single-qubit and CNOT gates. However, linear solutions are possible for the case where the controlled gate is a special unitary SU(2). The most widely-used decomposition of an n-qubit multi-controlled SU(2) gate requires a circuit with a number of CNOT gates proportional to 28n. In this work, we present a new decomposition of n-qubit multi-controlled SU(2) gates that requires a circuit with a number of CNOT gates proportional to 20n, and proportional to 16n if the SU(2) gate has at least one real-valued diagonal. This new approach significantly improves the existing algorithm by reducing the number of CNOT gates and the overall circuit depth. As an application, we show the use of this decomposition for sparse quantum state preparation. Our results are further validated by demonstrating a proof of principle on a quantum device accessed through quantum cloud services.

arXiv:2302.06377•Feb 13, 2023•4 citations

EQB: Synthesizing Permutative Quantum Gates and Circuits Using Rotation-Based Group Decomposition

Ishani Agarwal, Miroslav Saraivanov, Ali Al-Bayaty +1 more

The decomposition from the group theory-based methods of Sasao and Saraivanov is extended to design binary quantum cascades, using the quantum rotational gates by the X-axis (CNOT and RX), Y-axis (RY), and Z-axis (controlled-Z) of the Bloch sphere. A class of local transformations is also presented to simplify the final canonical cascade circuits. Our proposed methodology is well suited for quantum layouts, as each single-qubit gate has one target qubit and each double-qubit gate has one control qubit and one target qubit, thereby never creating a graph of triangular connectivity.

arXiv:2410.19229•Oct 25, 2024•0 citations

Circuit Decomposition of Multicontrolled Special Unitary Single-Qubit Gates

Rafaella F. Vale, Thiago Melo D. Azevedo, Ismael C. S. Araújo +2 more

Multicontrolled unitary gates have been a subject of interest in quantum computing since their conception and are widely used in quantum algorithms. The current state-of-the-art approach to implementing$n$-qubit multicontrolled gates with a single target without relying on auxiliary qubits or approximate results involves the use of a quadratic number of single-qubit and CNOT gates. However, linear solutions are possible for the case where the controlled gate is special unitary, SU(2). The decomposition of an$n$-qubit multicontrolled SU(2) gate requires a circuit with a number of CNOT gates proportional to$28n$. In this work, we present a new decomposition of$n$-qubit multicontrolled SU(2) gates that require a circuit with a number of CNOT gates proportional to$20n$and proportional to$16n$if the SU(2) gate has at least one real-valued diagonal. The proposed algorithms produce the most efficient known circuits and improve the existing algorithm by reducing the number of CNOT gates and the overall circuit depth. As an application, we show the use of this decomposition for sparse quantum state preparation. Our results are further validated by demonstrating a proof of principle on a quantum device accessed through quantum cloud services.

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems•Oct 24, 2023•23 citations
Quantum gates typically represent either rotations of controlled gates. Rotation gates usually involve one qubit, although Ising coupling gates involve two qubits. On the other hand, controlled gates can have any number of control qubits with at least a target qubit. In this paper, the decomposition of controlled gates in terms of rotation gates around a given axis has been carried out. The focus herein has been set on theX\mathbf{X}Xaxis, such that AND-CmX gates and OR-CmX gates have been decomposed and proved form={1,2,3,4}\mathbf{m}=\{\mathbf{1, 2, 3, 4}\}m={1,2,3,4}and different polarities.
Quantum logic decomposition refers to decomposing a given quantum gate to a set of physically implementable gates. An approach has been presented to decompose arbitrary diagonal quantum gates to a set of multiplexed-rotation gates around z axis. In this article, a special class of diagonal quantum gates, namely diagonal Hermitian quantum gates, is considered and a new perspective to the decomposition problem with respect to decomposing these gates is presented. It is first shown that these gates can be decomposed to a set that solely consists of multiple-controlled Z gates. Then a binary representation for the diagonal Hermitian gates is introduced. It is shown that the binary representations of multiple-controlled Z gates form a basis for the vector space that is produced by the binary representations of all diagonal Hermitian quantum gates. Moreover, the problem of decomposing a given diagonal Hermitian gate is mapped to the problem of writing its binary representation in the specific basis mentioned previously. Moreover, CZ gate is suggested to be the two-qubit gate in the decomposition library, instead of previously used CNOT gate. Experimental results show that the proposed approach can lead to circuits with lower costs in comparison with the previous ones.
Quantum computing fundamentals are based on Hilbert spaces and linear algebra, which allows to describe quantum gates as matrix representations. In this paper, a matrix approach is taken in order to analyze basic quantum circuits, composed of basic quantum gates of 1, 2, and 3 qubits. The most common cases of all those gates are analyzed. One-qubit gates are expressed as 2x2 matrices, accounting for a rotation around a determined axis. Two-qubit gates are described as 4x4 matrices, standing for controlled gates. Three-quibit gates are defined as 8x8 matrices, extending the concept of controlled gates and rotations.
Multi-controlled unitary gates have been a subject of interest in quantum computing since its inception, and are widely used in quantum algorithms. The current state-of-the-art approach to implementing n-qubit multi-controlled gates involves the use of a quadratic number of single-qubit and CNOT gates. However, linear solutions are possible for the case where the controlled gate is a special unitary SU(2). The most widely-used decomposition of an n-qubit multi-controlled SU(2) gate requires a circuit with a number of CNOT gates proportional to 28n. In this work, we present a new decomposition of n-qubit multi-controlled SU(2) gates that requires a circuit with a number of CNOT gates proportional to 20n, and proportional to 16n if the SU(2) gate has at least one real-valued diagonal. This new approach significantly improves the existing algorithm by reducing the number of CNOT gates and the overall circuit depth. As an application, we show the use of this decomposition for sparse quantum state preparation. Our results are further validated by demonstrating a proof of principle on a quantum device accessed through quantum cloud services.
The decomposition from the group theory-based methods of Sasao and Saraivanov is extended to design binary quantum cascades, using the quantum rotational gates by the X-axis (CNOT and RX), Y-axis (RY), and Z-axis (controlled-Z) of the Bloch sphere. A class of local transformations is also presented to simplify the final canonical cascade circuits. Our proposed methodology is well suited for quantum layouts, as each single-qubit gate has one target qubit and each double-qubit gate has one control qubit and one target qubit, thereby never creating a graph of triangular connectivity.
Multicontrolled unitary gates have been a subject of interest in quantum computing since their conception and are widely used in quantum algorithms. The current state-of-the-art approach to implementingnnn-qubit multicontrolled gates with a single target without relying on auxiliary qubits or approximate results involves the use of a quadratic number of single-qubit and CNOT gates. However, linear solutions are possible for the case where the controlled gate is special unitary, SU(2). The decomposition of annnn-qubit multicontrolled SU(2) gate requires a circuit with a number of CNOT gates proportional to28n28n28n. In this work, we present a new decomposition ofnnn-qubit multicontrolled SU(2) gates that require a circuit with a number of CNOT gates proportional to20n20n20nand proportional to16n16n16nif the SU(2) gate has at least one real-valued diagonal. The proposed algorithms produce the most efficient known circuits and improve the existing algorithm by reducing the number of CNOT gates and the overall circuit depth. As an application, we show the use of this decomposition for sparse quantum state preparation. Our results are further validated by demonstrating a proof of principle on a quantum device accessed through quantum cloud services.