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

Information

A Novel Approach to State-to-State Transformation in Quantum Computing

Artyom M. Grigoryan, Alexis A. Gomez, Sos С. Agaian

Published Aug 13, 2025• 5 citations
Publisher

Abstract

The article presents a new approach to the problem of transforming one quantum state into another. It is shown that a r-qubit superposition |x can be obtained from another r-qubit superposition |y, by using only (2r-1) rotations, each presented by one controlled rotation gate. The quantum superpositions with real amplitudes are considered. The traditional two-stage approach Uy-1Ux:|x→|0⊕r→|y requires twice as many rotations. Here, both transformations to the conventual basis state, Ux: |x→ |0⊕r and Uy: |y→ |0⊕r, use (2r-1) rotations each on two binary planes and many of these rotations require additional sets of CNOTs to be represented as 1- or 2-qubit controlled gates. The proposed method is based on the concept of the discrete signal-induced heap transform (DsiHT) which is unitary and generated by a vector and a set of angular equations with given parameters. The quantum analogue of this transform is described. The main characteristic of the DsiHT is the path of processing the data. It is shown that exist such fast paths that allow for effective computing of the DsiHT, which leads to the simple quantum circuits for state preparation and transformation. Examples of such paths are given and quantum circuits for preparation and transformation of 2-, 3-, and 4-qubits are described in detail. CNOT gates are not used, but only controlled gates of elementary rotations around the y-axis. It is shown that the transformation and, in particular, only rotation gates with control qubits are required for initialization of 4-qubits. The quantum circuits are simple and have a recursive form, which makes them easy to implement for arbitrary r-qubit superposition, with r≥2. This approach significantly reduces the complexity of quantum state transformations, paving the way for more efficient quantum algorithms and practical implementations on near-term quantum devices.

DOI
10.3390/info16080689

Related papers

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

Artyom M. Grigoryan, Alexis A. Gomez, Isaac Espinoza +1 more

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.

Information•May 30, 2025•1 citation

New Circuits for Simultaneously Initiating Two Different Quantum Superpositions

Artyom M. Grigoryan, Alexis A. Gomez

This article presents, for the first time, a new approach to building quantum circuits for the initialization of two multi-qubit superpositions, namely, two different superpositions in one circuit, not in two separate circuits. For this, we introduce the concept of the discrete two signal-induced heap transformation (D2siHT). This transformation is generated by two signals, or vectors, which we call generators. The quantum analogue of the D2siHT is described. It allows us to build a quantum circuit to transform two superpositions |x and |y into the first conventual basis states |000…0 and |010…0, respectively. Therefore, we can build a single quantum circuit to initiate two multi-qubit superpositions |x and |y from the basis states |000…0 and |010…0, respectively. Examples with quantum circuits for the preparation and transformation of two 2- and 3-qubit superpositions are described in detail. The results of circuit simulation using Qiskit are also presented. The main characteristic of the D2siHT is its path of processing the data of two generators and input qubits. We consider different paths to effectively compute the D2siHT. Such paths can reduce, for instance, the depth of the resulting quantum circuits, which can lead to a reduction in execution times and susceptibility to decoherence and noise. Multi-qubit superpositions are considered with real amplitudes, but the presented approach can be extended to initiate two such superpositions with complex amplitudes, as well.

Information•Nov 30, 2025•1 citation

Quantum Signal-Induced Heap Transform Based Realization of Multi-Qubit Operations

Artyom M. Grigoryan, Alex Gomez, Isaac Espinoza +1 more

The article presents a new approach to the decomposition of unitary operations by controlled rotations.A new method of quantum signal-induced heap transform based QR decomposition is described.This transform is an analogue of the discrete transform which is generated by a given signal and uses different paths of processing the data.It is shown that among such paths we can find paths that allow constructing efficient quantum circuits for implementing multiqubit unitary gates.The case of real unitary matrices is considered.The proposed approach is described in detail in examples and quantum circuits are presented for 2-qubit operations.The general case of 𝑟-qubit unitary operations, when 𝑟 ≥ 2, is considered similarly.

Computer Science Research Notes•Jan 1, 2025•0 citations

Unitary Operations with Five and More Qubits: Roadmaps and Effective Quantum Circuits

Artyom M. Grigoryan

This article presents the general method of QR decomposition of r-qubit operations, r≥ 3, by means of quantum signal-induced heap transformations (QsiHT). These are quantum analogues of discrete signal-induced heap transformations, which are generated by given signals and paths, or orders, of processing the data. The case of the 5-qubit operations is described in detail, and a recurrent form of calculation of all 5-qubit QsiHTs from the 4-qubit QsiHTs is given. For that, roadmaps and quantum circuits are presented for all 31 5-point QsiHTs that are used in the QR decomposition. New roadmaps, namely the schemes with paths for performing basic operations on qubits, and corresponding quantum circuits, are also described for the 4- and 3-qubit transformations. All QsiHTs use fast paths, which allow us to calculate the QR decomposition only on disjoint bit planes. As a result, we build the quantum circuits for 5- and more-qubit operations without permutations, only elementary rotations. Unitary operations with real numbers are considered. In the general case, the method of compositing all the roadmaps and quantum schemes for the calculation of any r-qubit operation by only (2r−1)2r−1 elementary rotations is described.

Information•Feb 6, 2026•0 citations

New effective methods of preparation of states of quantum image representation

Artyom M. Grigoryan, Alexis A. Gomez, Sos С. Agaian

The multi-qubit transformation is the important step in quantum computation in many applications. In recent works, this problem is addressed by solving by using the QR decomposition with elementary rotations with one- and two-qubit CNOT gates. Reducing the number of these gates is critical since operations on three or more qubits are difficult to implement on the current quantum computers. The quantum signal induced heap transform (QsiHT) provides an efficient method for state preparation in the realm of quantum image representation by amplitudes. This paper presents a detailed analysis of how the QsiHT, particularly through the strong path, is utilized to construct quantum states to represent images. The algorithm behind this method and the realization of the corresponding quantum circuits is outlined. Practical examples of the QsiHT on 2 and 3-qubit systems are given using the Qiskit Framework for quantum circuit simulation.

Multimodal Image Exploitation and Learning•May 28, 2025•0 citations

New Permutation-Free Quantum Circuits for Implementing 3- and 4-Qubit Unitary Operations

Artyom M. Grigoryan

The article presents the quantum signal-induced heap transform (QsiHT) method of the QR-decomposition of multi-qubit operations. This transform can be generated by a given signal, by using different paths, or orders, of processing the data. We propose using the concept of the fast path of calculation of the QsiHT and applying such transforms on each stage of the matrix decomposition. This allows us to build quantum circuits for multi-qubit unitary operation without permutations. Unitary operations with real and complex matrices are considered. The cases of 3- and 4-qubit operations are described in detail with quantum circuits. These circuits use a maximum of 28 and 120 Givens rotation gates for 3- and 4-qubit real operations, respectively. All rotations are performing only on adjacent bit planes. For complex unitary operation, each of the Givens gates is used in pairs with two Z-rotation gates. These two types of rotations and the global phase gate are the universal gate set for multi-qubit operations. The presented approach can be used for implementing quantum circuits for n-qubits when n≥2, with a maximum of (4n/2−2n−1) Givens rotations and no permutations.

Information•Jul 21, 2025•4 citations
The article presents a new approach to the problem of transforming one quantum state into another. It is shown that a r-qubit superposition |x can be obtained from another r-qubit superposition |y, by using only (2r-1) rotations, each presented by one controlled rotation gate. The quantum superpositions with real amplitudes are considered. The traditional two-stage approach Uy-1Ux:|x→|0⊕r→|y requires twice as many rotations. Here, both transformations to the conventual basis state, Ux: |x→ |0⊕r and Uy: |y→ |0⊕r, use (2r-1) rotations each on two binary planes and many of these rotations require additional sets of CNOTs to be represented as 1- or 2-qubit controlled gates. The proposed method is based on the concept of the discrete signal-induced heap transform (DsiHT) which is unitary and generated by a vector and a set of angular equations with given parameters. The quantum analogue of this transform is described. The main characteristic of the DsiHT is the path of processing the data. It is shown that exist such fast paths that allow for effective computing of the DsiHT, which leads to the simple quantum circuits for state preparation and transformation. Examples of such paths are given and quantum circuits for preparation and transformation of 2-, 3-, and 4-qubits are described in detail. CNOT gates are not used, but only controlled gates of elementary rotations around the y-axis. It is shown that the transformation and, in particular, only rotation gates with control qubits are required for initialization of 4-qubits. The quantum circuits are simple and have a recursive form, which makes them easy to implement for arbitrary r-qubit superposition, with r≥2. This approach significantly reduces the complexity of quantum state transformations, paving the way for more efficient quantum algorithms and practical implementations on near-term quantum devices.
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.
This article presents, for the first time, a new approach to building quantum circuits for the initialization of two multi-qubit superpositions, namely, two different superpositions in one circuit, not in two separate circuits. For this, we introduce the concept of the discrete two signal-induced heap transformation (D2siHT). This transformation is generated by two signals, or vectors, which we call generators. The quantum analogue of the D2siHT is described. It allows us to build a quantum circuit to transform two superpositions |x and |y into the first conventual basis states |000…0 and |010…0, respectively. Therefore, we can build a single quantum circuit to initiate two multi-qubit superpositions |x and |y from the basis states |000…0 and |010…0, respectively. Examples with quantum circuits for the preparation and transformation of two 2- and 3-qubit superpositions are described in detail. The results of circuit simulation using Qiskit are also presented. The main characteristic of the D2siHT is its path of processing the data of two generators and input qubits. We consider different paths to effectively compute the D2siHT. Such paths can reduce, for instance, the depth of the resulting quantum circuits, which can lead to a reduction in execution times and susceptibility to decoherence and noise. Multi-qubit superpositions are considered with real amplitudes, but the presented approach can be extended to initiate two such superpositions with complex amplitudes, as well.
The article presents a new approach to the decomposition of unitary operations by controlled rotations.A new method of quantum signal-induced heap transform based QR decomposition is described.This transform is an analogue of the discrete transform which is generated by a given signal and uses different paths of processing the data.It is shown that among such paths we can find paths that allow constructing efficient quantum circuits for implementing multiqubit unitary gates.The case of real unitary matrices is considered.The proposed approach is described in detail in examples and quantum circuits are presented for 2-qubit operations.The general case of 𝑟-qubit unitary operations, when 𝑟 ≥ 2, is considered similarly.
This article presents the general method of QR decomposition of r-qubit operations, r≥ 3, by means of quantum signal-induced heap transformations (QsiHT). These are quantum analogues of discrete signal-induced heap transformations, which are generated by given signals and paths, or orders, of processing the data. The case of the 5-qubit operations is described in detail, and a recurrent form of calculation of all 5-qubit QsiHTs from the 4-qubit QsiHTs is given. For that, roadmaps and quantum circuits are presented for all 31 5-point QsiHTs that are used in the QR decomposition. New roadmaps, namely the schemes with paths for performing basic operations on qubits, and corresponding quantum circuits, are also described for the 4- and 3-qubit transformations. All QsiHTs use fast paths, which allow us to calculate the QR decomposition only on disjoint bit planes. As a result, we build the quantum circuits for 5- and more-qubit operations without permutations, only elementary rotations. Unitary operations with real numbers are considered. In the general case, the method of compositing all the roadmaps and quantum schemes for the calculation of any r-qubit operation by only (2r−1)2r−1 elementary rotations is described.
The multi-qubit transformation is the important step in quantum computation in many applications. In recent works, this problem is addressed by solving by using the QR decomposition with elementary rotations with one- and two-qubit CNOT gates. Reducing the number of these gates is critical since operations on three or more qubits are difficult to implement on the current quantum computers. The quantum signal induced heap transform (QsiHT) provides an efficient method for state preparation in the realm of quantum image representation by amplitudes. This paper presents a detailed analysis of how the QsiHT, particularly through the strong path, is utilized to construct quantum states to represent images. The algorithm behind this method and the realization of the corresponding quantum circuits is outlined. Practical examples of the QsiHT on 2 and 3-qubit systems are given using the Qiskit Framework for quantum circuit simulation.
The article presents the quantum signal-induced heap transform (QsiHT) method of the QR-decomposition of multi-qubit operations. This transform can be generated by a given signal, by using different paths, or orders, of processing the data. We propose using the concept of the fast path of calculation of the QsiHT and applying such transforms on each stage of the matrix decomposition. This allows us to build quantum circuits for multi-qubit unitary operation without permutations. Unitary operations with real and complex matrices are considered. The cases of 3- and 4-qubit operations are described in detail with quantum circuits. These circuits use a maximum of 28 and 120 Givens rotation gates for 3- and 4-qubit real operations, respectively. All rotations are performing only on adjacent bit planes. For complex unitary operation, each of the Givens gates is used in pairs with two Z-rotation gates. These two types of rotations and the global phase gate are the universal gate set for multi-qubit operations. The presented approach can be used for implementing quantum circuits for n-qubits when n≥2, with a maximum of (4n/2−2n−1) Givens rotations and no permutations.