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System Analysis in Science and Education

Quantum software engineering. Pt. I: Quantum Circuit (Gate) Model based Computing – education Lectures and pedagogical workshop

Sergey Victorovich Ulyanov, Andrey G. Reshetnikov, Olga Tyatyushkina, V. Korenkov

Published Sep 30, 2020• 0 citations
Publisher

Abstract

All the quantum algorithms are based on a certain quantum computing model, varying from the quantum circuit, one-way quantum computation, adiabatic quantum computation and topological quantum computation. These four models are equivalent in computational power; among them, the quantum circuit model is most frequently used. In the circuit model, it has been proved that arbitrary single-qubit rotations plus twoqubit controlled-NOT gates are universal, i.e. they can provide a set of gates to implement any quantum algorithm. This article discusses the goal for this research: it is to given a lightning-fast (as-barebones-as-possible) definition of the quantum circuit model computing and leisurely development of quantum computation before actually getting around to sophisticated algorithms. In this article the main ideas of quantum software engineering is described.

DOI
10.37005/2071-9612-2020-3-129-201

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Principles and methodologies of quantum algorithmic gate-based design on small quantum computer described. The possibilities of quantum algorithmic gates simulation on classical computers discussed. A new approach to a circuit implementation design of quantum algorithm gates for fast quantum massive parallel computing presented. SW & HW support sophisticated smart toolkit of supercomputing accelerator of quantum algorithm simulation on small quantum programmable computer algorithm gate (that can program in SW to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates) described
Principles and methodologies of quantum algorithmic gates design for master course and PhD students in computer science, control engineering and intelligent robotics described. The possibilities of quantum algorithmic gates simulation on classical computers discussed. Applications of quantum gate of nanotechnology in intelligent quantum control introduced. Anew approach to a circuit implementation design of quantum algorithm gates for fast quantum massive parallel computing presented. The main attention focused on the development of design method of fast quantum algorithm operators as superposition, entanglement and interference, which are in general time-consuming operations due to the number of products that have performed. SW & HW support sophisticated smart toolkit of supercomputing accelerator of quantum algorithm simulation on small quantum programmable computer algorithm gate (that can program in SW to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates) described. As example, the method for performing Grover’s interference operator without product operations introduced. The background of developed information technology is the "Quantum / Soft Computing Optimizer" (QSCOptKBTM) SW based on soft and quantum computational intelligence toolkit.
The principles of quantum mechanics – superposition, entanglement, measurement, and decoherence – form the foundation of quantum computing. Qubits, which are abstract objects having a mathematical expression to implement the rules of quantum physics, are the fundamental building blocks of computation. Software is a key component of quantum computing, along with quantum hardware. Algorithms make up software, and they are implemented using logic gates and quantum circuits. These qualities make quantum computing a paradigm that non-physicists find difficult to comprehend. It is crucial to incorporate a conceptual framework of the principles upon which quantum computing is founded into this new method of creating software. In this paper, we present a kind of taxonomical view of the fundamental concepts of quantum computing and the derived concepts that integrate the emerging discipline of quantum software engineering. Because the systematic review's main goal is to identify the core ideas behind quantum computing and quantum software, we conducted a quasi-systematic mapping as part of the review process. The findings can serve as a starting point for computer science teachers and students to address the study of this field.
The simulation of quantum circuits is significantly important for the implementation of quantum information technologies. The main difficulty of such modeling is the exponential growth of dimensionality, thus the usage of modern high-performance parallel computations is relevant. As it is well known, arbitrary quantum computation in circuit model can be done by only single- and two-qubit gates, and we analyze the computational structure and properties of the simulation of such gates. We investigate the fact that the unique properties of quantum nature lead to the computational properties of the considered algorithms: the quantum parallelism make the simulation of quantum gates highly parallel, and on the other hand, quantum entanglement leads to the problem of computational locality during simulation. We use the methodology of the AlgoWiki project (algowiki-project.org) to analyze the algorithm. This methodology consists of theoretical (sequential and parallel complexity, macro structure, and visual informational graph) and experimental (locality and memory access, scalability and more specific dynamic characteristics) parts. Experimental part was made by using the petascale Lomonosov supercomputer (Moscow State University, Russia). We show that the simulation of quantum gates is a good base for the research and testing of the development methods for data intense parallel software, and considered methodology of the analysis can be successfully used for the improvement of the algorithms in quantum information science.
Abstract In this chapter, we shift our perspective from seeing the unitary evolution of a quantum state as a physical process that ‘just happens’ to instead seeing it as an executable operation in a programmable computer. To do this, we introduce the quantum circuit (or gate) model, which subsequently allows us to present and analyse quantum algorithms and quantum communication protocols. The universality of quantum computing – that every quantum mechanical system (composed of qubits) can be represented as such – is established, as is the closely related notion of universal gatesets. The chapter also briefly introduces some important topics in quantum compilation, in which some quantum circuit is rewritten as a functionally equivalent alternative that is more suitable (in some sense) for running on a particular quantum computer.
Abstract Quantum walk has been regarded as a primitive to universal quantum computation. By using the operations required to describe the single particle discrete-time quantum walk on a position space we demonstrate the realization of the universal set of gates on two-and three-qubit system. The idea is to reap the effective Hilbert space of the single qubit and the position space on which it evolves in superposition of position space in order to realize multi-qubit states and universal set of quantum gates on them. Realization of many non-trivial gates in the form of engineering arbitrary states is simpler in the proposed quantum walk model when compared to the circuit based model of computation. We will also discuss the scalability of the model and some propositions for using lesser number of qubits in realizing larger qubit systems.