This chapter begins with a short introduction to the topic of quantum information processing. We presume only a very limited familiarity with quantum mechanics; in fact, all the really essential ideas, terminology and formalism will be introduced as we go along. The introductionwill discuss classical and quantum information, the qubit, entanglement, and the basic operations of quantum computer. It will include a brief look at how accelerated searching can be performed, and finally a discussion of the problem of decoherence and how to fight it. We will then introduce endohedral fullerenes, the key molecular building blocks that have been identified as promising components of a quantum technology. We will describe the synthesis of these structures, togetherwith the key experimental demonstrations of quantum phenomena.
This chapter begins with a short introduction to the topic of quantum information processing. We presume only a very limited familiarity with quantum mechanics; in fact, all the really essential ideas, terminology and formalism will be introduced as we go along. The introductionwill discuss classical and quantum information, the qubit, entanglement, and the basic operations of quantum computer. It will include a brief look at how accelerated searching can be performed, and finally a discussion of the problem of decoherence and how to fight it. We will then introduce endohedral fullerenes, the key molecular building blocks that have been identified as promising components of a quantum technology. We will describe the synthesis of these structures, togetherwith the key experimental demonstrations of quantum phenomena.
Abstract Since the 1980s, quantum computing has progressed significantly, evolving from theoretical models to early working devices. Due to their unique molecular structure, endohedral fullerenes offer long decoherence times, stable operation under ambient conditions, and cost‐effective fabrication, making them promising candidates for qubit implementation in quantum computing. In this review, we examine research efforts on endohedral fullerene‐based quantum computing across various platforms and molecular types, with a particular focus on the synthetic challenges that remain a critical bottleneck for practical device integration. This review classifies the different types of endohedral fullerene‐based quantum devices, explores their current limitations, and discusses future prospects. Endohedral fullerene‐based quantum technology has the potential to transform endohedral fullerene‐based quantum computing, enabling solutions to complex industrial problems and advancing the development of fault‐tolerant quantum technologies. image
Quantum computing represents a fundamentally new paradigm in information processing, in which information is encoded and manipulated using two-level quantum systems known as qubits, whose evolution is governed by the principles of quantum mechanics. This chapter presents a structured introduction to the theoretical foundations of quantum computation, beginning with the limitations of classical computation and the physical constraints that motivate the need for a quantum model of computation. We develop the mathematical framework required to describe quantum information, introducing qubits as state vectors in Hilbert space and examining the roles of superposition, measurement, and unitary evolution. Single-qubit operations are presented through the Pauli and Hadamard gates, along with their geometric interpretation on the Bloch sphere. Building on this formalism, the discussion is extended to multi-qubit systems using tensor products, and quantum entanglement is introduced as a non-classical correlation fundamental to quantum information processing. The chapter then explores quantum algorithms, focusing on Grover’s unstructured search algorithm, to demonstrate how superposition, interference, and entanglement can be harnessed to achieve computational advantages over classical approaches. Finally, the chapter discusses applications of quantum computation, including quantum simulation, cryptography, search and optimization problems, and near-term hybrid quantum algorithms such as the Variational Quantum Eigensolver (VQE)and the Quantum Approximate Optimization (QAO) Algorithm, highlighting their relevance in the noisy intermediate-scale quantum (NISQ) era.
"Introduction to Quantum Mechanics And Quantum Computing" is a comprehensive book chapter that provides an in-depth exploration of the groundbreaking field of quantum computing. Beginning with an introduction to the fundamental principles of quantum mechanics, the chapter navigates through the evolution of quantum computing, from its conceptual origins to the challenges faced in its development. The core concepts of quantum bits (qubits) and their unique properties, such as entanglement and superposition, are explained, laying the foundation for understanding quantum information processing. The chapter further delves into the building blocks of quantum computing—qubits—detailing their diverse physical implementations. Quantum gates and circuits, analogous to classical computing, are explored, shedding light on the mechanisms enabling quantum algorithms to perform complex tasks efficiently. Highlighting renowned algorithms like Shor's and Grover's, the chapter emphasizes the potential computational supremacy of quantum computers over classical counterparts. Recognizing the sensitivity of quantum systems to noise and decoherence, the chapter introduces quantum error correction as a crucial aspect of ensuring reliable quantum computation. The exploration concludes with an examination of the current state of quantum computing, outlining progress in industry and academia while addressing the challenges in building large-scale, fault-tolerant quantum computers. The potential applications of quantum computing in cryptography, drug discovery, optimization problems, and beyond are discussed, offering a glimpse into the transformative impact this emerging technology may have on various industries. "Introduction to Quantum Mechanics And Quantum Computing" serves as a comprehensive guide for readers seeking a nuanced understanding of the theoretical foundations and practical applications of quantum computing.
This chapter introduces the basic building blocks of quantum computing and a variety of specific algorithms. It begins with a brief review of classical computing and discusses how its key elements – bits, gates, circuits – carry over to the quantum realm. It highlights crucial differences to the classical case, such as the impossibility of copying a qubit. The quantum circuit model is shown to be universal, and a peculiar variant of quantum computing, based on measurements only, is illustrated. That a quantum computer can perform some calculations more efficiently than a classical computer, at least in principle, is exemplified with the Deutsch-Jozsa algorithm. Other examples covered in this chapter are the variational quantum eigensolver, which can be applied to the study of molecules and classical optimization problems; quantum simulation; and entanglement-assisted metrology.
A potential quantum-information processor is proposed using an array of the endohedral fullerenes 15N@C60 or 31P@C60 contained in a single walled carbon nanotube (SWCNT). The qubits are encoded in the nuclear spins of the doped atoms, while the electronic spins are used for initialization and readout, as well as for two-qubit operations.
We present a scheme to perform universal quantum computation using global addressing techniques as applied to a physical system of endohedrally doped fullerenes. The system consists of an ABAB linear array of group-V endohedrally doped fullerenes. Each molecule spin site consists of a nuclear spin coupled via a hyperfine interaction to an electron spin. The electron spin of each molecule is in a quartet ground state S=3/2. Neighboring molecular electron spins are coupled via a magnetic dipole interaction. We find that an all-electron construction of a quantum cellular automaton is frustrated due to the degeneracy of the electronic transitions. However, we can construct a quantum-cellular-automata quantum computing architecture using these molecules by encoding the quantum information on the nuclear spins while using the electron spins as a local bus. We deduce the NMR and ESR pulses required to execute the basic cellular automaton operation and obtain a rough figure of merit for the number of gate operations per decoherence time. We find that this figure of merit compares well with other physical quantum computer proposals. We argue that the proposed architecture meets well the first four DiVincenzo criteria and we outline various routes toward meeting the fifth criterion: qubit readout.