Fundamental concepts of quantum computing

Marek Kuś

Weisi Tang, Xin Luo

Matrix theory play a fundamental role in classical and quantum computing. Among this paper, we study the fundamental concepts of some matrices including unitary matrix and Hermitian matrix, which may convert some initial qubits into various kinds of qubits. We also explore the fundamental concept of eigenvalues. Furthermore, we input the concept of product vectors. Finally we use above-mentioned concepts examing the entanglement witness for verifying the entanglement in quantum computing and circuits.

Hafiz Md. Hasan Babu

Reyes Juárez‐Ramírez, Christian X. Navarro, Samantha Jiménez +5 more

Abstract Quantum computing is based on the principles of quantum mechanics, such as superposition, entanglement, measurement, and decoherence. The basic units of computation are qubits, which are abstract objects with a mathematical expression to implement the quantum mechanics principles. Alongside quantum hardware, software is a principal element for conducting quantum computing. The software consists of logic gates and quantum circuits that implement algorithms for the execution of quantum programs. Due to those characteristics, quantum computing is a paradigm that non-physics experts cannot understand. Under this new scheme for developing software, it is important to integrate a conceptual framework of the fundamentals on which quantum computing is based. 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. We performed a quasi-systematic mapping for conducting the systematic review because the objective of the review only intends to detect the fundamental concepts of quantum computing and quantum software. The results can help computer science students and professors as a starting point to address the study of this discipline.

Venkateswaran Kasirajan

Kamaljit I. Lakhtaria, Vrunda Gadesha

When we aim to demonstrate that a programmable quantum device can solve complex problems which cannot be addressed by classic computers, this fundamental goal is known as quantum supremacy. This concept has changed every fundamental rule of computation. In this chapter, the detailed concept of quantum computing and quantum supremacy is explained along with various open source tools and real-time applications of this technology. The major base concepts, quantum computing, the difference between classical and quantum computer on physical level, programing quantum device, and the experiment-quantum supremacy are explained conceptually. This chapter also includes an introduction of the tools Cirq and OpenFermion plus the applications like quantum simulation, error mitigation technique, quantum machine learning, and quantum optimization, which are explained with illustrations.