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Volume 16
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10.3390/info16060466
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Article

Signal-Induced Heap Transform-Based QR-Decomposition and Quantum Circuit for Implementing 3-Qubit Operations

by
Artyom M. Grigoryan
1,*,
Alexis Gomez
1,
Isaac Espinoza
1 and
Sos S. Agaian
2
1
Department of Electrical and Computer Engineering, The University of Texas at San Antonio, San Antonio, TX 78249, USA
2
Department of Computer Science, School of Engineering, City University of New York (CUNY), New York, NY 10031, USA
*
Author to whom correspondence should be addressed.
Information 2025, 16(6), 466; https://doi.org/10.3390/info16060466
Submission received: 8 April 2025 / Revised: 17 May 2025 / Accepted: 28 May 2025 / Published: 30 May 2025
(This article belongs to the Section Information Theory and Methodology)
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Abstract

This article presents a novel approach to the decomposition of unitary operations for 3-qubit systems by 28 controlled rotations and no permutations. The QR decomposition is described, which is based on the concept of the discrete signal-induced heap transform (DsiHT) and its quantum analogue. This transform is generated by a given signal and may use different paths, or orders, of processing the data, and, among them, one can find paths that allow one to construct efficient quantum circuits for implementing multi-qubit unitary gates. The case of real unitary matrices is considered. The proposed approach is described in detail, and quantum circuits are presented for computing 3-qubit operations. This approach allowed us to write simple Qiskit codes to implement the decomposition of 3-qubit operations. Examples with quantum circuits for the quantum 3-qubit quantum cosine and Hartley transforms are described.
Keywords: quantum decomposition; QR decomposition; quantum signal-induced heap transform; quantum cosine transform quantum decomposition; QR decomposition; quantum signal-induced heap transform; quantum cosine transform

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MDPI and ACS Style

Grigoryan, A.M.; Gomez, A.; Espinoza, I.; Agaian, S.S. Signal-Induced Heap Transform-Based QR-Decomposition and Quantum Circuit for Implementing 3-Qubit Operations. Information 2025, 16, 466. https://doi.org/10.3390/info16060466

AMA Style

Grigoryan AM, Gomez A, Espinoza I, Agaian SS. Signal-Induced Heap Transform-Based QR-Decomposition and Quantum Circuit for Implementing 3-Qubit Operations. Information. 2025; 16(6):466. https://doi.org/10.3390/info16060466

Chicago/Turabian Style

Grigoryan, Artyom M., Alexis Gomez, Isaac Espinoza, and Sos S. Agaian. 2025. "Signal-Induced Heap Transform-Based QR-Decomposition and Quantum Circuit for Implementing 3-Qubit Operations" Information 16, no. 6: 466. https://doi.org/10.3390/info16060466

APA Style

Grigoryan, A. M., Gomez, A., Espinoza, I., & Agaian, S. S. (2025). Signal-Induced Heap Transform-Based QR-Decomposition and Quantum Circuit for Implementing 3-Qubit Operations. Information, 16(6), 466. https://doi.org/10.3390/info16060466

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