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MANAGEMENT AND ECONOMICS SCIENTIFIC RESEARCH JOURNAL

ARCHITECTURE OF OPERATORS IN QUANTUM ALGORITHMS

Sh. A. Toirov

Published Apr 18, 2025• 0 citations
OpenAlex

Abstract

The article (paper) proposes the structure of operators of quantum algorithms,its mathematical and schematic representation. The general structure of the universal quantumalgorithm in the form of diagrams is realized in the article (paper). The diagram presents the mainelements, their properties, functions of the quantum algorithm. Each block of the schematicdiagrams are decomposed of successive processes and stages of quantum algorithms.

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The article (paper) proposes the structure of operators of quantum algorithms,its mathematical and schematic representation. The general structure of the universal quantumalgorithm in the form of diagrams is realized in the article (paper). The diagram presents the mainelements, their properties, functions of the quantum algorithm. Each block of the schematicdiagrams are decomposed of successive processes and stages of quantum algorithms.
This paper describes a detailed analysis of the fundamental components involved in the quantum algorithms design in accordance with the narrowly defined software and hardware for the implementation of quantum algorithms and the stages of their design. A modular development and subsequent simulation of the process of super dense quantum coding and quantum teleportation was realized. In accordance with the use of vector and matrix algebra, within the framework of quantum algorithms, the “quantum” software is defined. This software consists of quantum intermediate representation of information, quantum language of physical operations and quantum assembler. The software environment for quantum algorithms design and further implementation according to the defined stages is proposed and considered.
Fault-tolerant quantum computing requires system-level coordination of logical primitives. Here, we establish a logical compilation framework for the color code, grounded in its topological structure and supporting universal logical operations. Based on its anyon-condensation and domain-wall structure, we introduce a spacetime block-diagram representation capturing logical patches and operations and derive the rules governing block assembly. A correspondence with ZX diagrams further identifies the logical semantics of this representation and enables transformations that preserve the represented computation. Moreover, we develop a code-derived compilation strategy that converts ZX representations of logical computations into valid color-code spacetime layouts. In this strategy, edge-decorated ZX diagrams tailor the logical representation to the color code under the block-assembly constraints, and fusion-region-aware routing exploits semantic equivalence during geometric embedding. We automate the complete logical compilation process and demonstrate successful compilation across a broad range of algorithms. Our work advances color-code architecture from individual primitives to the automated synthesis of logical computations, marking a significant step toward its full-stack quantum computing.
Recently, generalized polar codes were introduced to provide more code lengths and rates without the need for shortening or puncturing. However, as the size of the kernel matrix increases, computing the Log-Likelihood Ratio (LLR) functions in successive cancellation decoder for these codes becomes mathematically more complicated. In this paper, a new simplified general method is proposed to calculate these LLR functions based on the schematic diagram of the selected kernel matrix for sizes higher than 2. Our proposed method fragments the main block into some basic components whose formulas have been previously proven by Arikan for 2×22 \times 22×2 kernel matrix. The validity of the resulting LLR functions is tested on different kernel matrices and proven to be similar to those in literature.
S imilarly to classical systems, quantum algorithms are a set of step-by-step instructions or rules designed to perform a specific task or solve a particular problem. They process information to solve a problem, by encoding information in the state of a single qubit, or the joint state of many qubits, and performing operations over them. Some algorithms are simple instructions and enable other algorithms, while others consist of many instructions to address more complex problems. To properly understand how algorithms work, it is important to take some factors into account, shown in Figure 4.1 , and which we review in this section.