Models of quantum computation and quantum programming languages The goal of the presented paper is to provide an introduction to the basic computational models used in quantum information theory. We review various models of quantum Turing machine, quantum circuits and quantum random access machine (QRAM) along with their classical counterparts. We also provide an introduction to quantum programming languages, which are developed using the QRAM model. We review the syntax of several existing quantum programming languages and discuss their features and limitations.
Models of quantum computation and quantum programming languages The goal of the presented paper is to provide an introduction to the basic computational models used in quantum information theory. We review various models of quantum Turing machine, quantum circuits and quantum random access machine (QRAM) along with their classical counterparts. We also provide an introduction to quantum programming languages, which are developed using the QRAM model. We review the syntax of several existing quantum programming languages and discuss their features and limitations.
Quantum computing is a promising approach of computation that is based on equations from Quantum Mechanics and nanotechnology. Understanding and simulating quantum operations on a classical computer has different approaches and is modeled in different ways. However, the most repute ways are Quantum Turing Machine, Network Model or circuit model of connected gates and Quantum Programming Language. Many simulators do exist that varies in many features such as implementation languages, target platforms, paradigms, visuality, and applied quantum algorithms. There was a developmental trade-off between the simplicity and the functionality of the simulator. The goals and research activities are outlined as follows: First, surveying the quantum computing world, its characteristics, issues, problems, and challenges. Second, surveying the existing quantum simulators, illustrating representative simulators of major approaches, their features, and functionalities. Third, introducing a framework to provide the power of quantum computing , while insisting the simplicity and high usability. Finally, providing a case study for a new quantum algorithm based on the introduced framework.
This manuscript is intended for readers who have a general interest in the subject of quantum computation and provides an overview of the most significant developments in the field. It begins by introducing foundational concepts from quantum mechanics—such as superposition, entanglement, and the no-cloning theorem—that underpin quantum computation. The primary computational models are discussed, including gate-based (circuit) quantum computing, adiabatic quantum computing, measurement-based quantum computing and the quantum Turing machine. A selection of significant quantum algorithms are reviewed, notably Grover’s search algorithm, Shor’s factoring algorithm, and Quantum Singular Value Transformation (QSVT), which enables efficient solutions to linear algebra problems on quantum devices. To assess practical performance, we compare quantum and classical implementations of support vector machines (SVMs) using several synthetic datasets. These experiments offer insight into the capabilities and limitations of near-term quantum classifiers relative to classical counterparts. Finally, we review leading quantum programming platforms—including Qiskit, PennyLane, and Cirq—and discuss their roles in bridging theoretical models with real-world quantum hardware. The paper aims to provide a concise yet comprehensive guide for those looking to understand both the theoretical foundations and applied aspects of quantum computing.
In the last 20 years, several approaches to quantum programming have been introduced. In this survey, we focus on the QRAM (Quantum Random Access Machine) architectural model. We explore the twofold perspective (theoretical and concrete) of the approach and we list the main problems one has to face in quantum language design. Moreover, we propose an overview of some interesting languages and open-source platforms for quantum programming currently available. We also provide the higher-order encoding in the functional languages qPCF and IQu of the well known Deutsch-Jozsa and Simon’s algorithms.
We propose the design of a programming language for quantum computing. Traditionally, quantum algorithms are frequently expressed at the hardware level, for instance in terms of the quantum circuit model or quantum Turing machines. These approaches do not encourage structured programming or abstractions such as data types. In this paper, we describe the syntax and semantics of a simple quantum programming language with high-level features such as loops, recursive procedures, and structured data types. The language is functional in nature, statically typed, free of run-time errors, and has an interesting denotational semantics in terms of complete partial orders of superoperators.
There is strong evidence that computers based upon the principles of quantum physics represent an inherently new and more powerful model of computation. Such computers violate the modern form of the Church-Turing thesis (which lies at the foundations of computer science). This thesis can be informally summarized as follows: all physical implementations of computing devices can be described by the same abstract model of computation-the probabilistic Turing Machine or the equivalent random access machine. In this paper, we will describe two formal models for quantum computers: quantum circuits and quantum Turing Machines, introduced by Deutsch [1985].
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically powerful computational tool. This review is about to tell the story of theoretical quantum computation. I left out the developing topic of experimental realizations of the model, and neglected other closely related topics which are quantum information and quantum communication. As a result of narrowing the scope of this paper, I hope it has gained the benefit of being an almost self contained introduction to the exciting field of quantum computation. The review begins with background on theoretical computer science, Turing machines and Boolean circuits. In light of these models, I define quantum computers, and discuss the issue of universal quantum gates. Quantum algorithms, including Shor's factorization algorithm and Grover's algorithm for searching databases, are explained. I will devote much attention to understanding what the origins of the quantum computational power are, and what the limits of this power are. Finally, I describe the recent theoretical results which show that quantum computers maintain their complexity power even in the presence of noise, inaccuracies and finite precision. I tried to put all results in their context, asking what the implications to other issues in computer science and physics are. In the end of this review I make these connections explicit, discussing the possible implications of quantum computation on fundamental physical questions, such as the transition from quantum to classical physics.