This review outlines the principles of operation of quantum computers and their elements. The theory of ideal computers that do not interact with the environment and are immune to quantum decohering processes is presented. Decohering processes in quantum computers are investigated. The review considers methods for correcting quantum computing errors arising from the decoherence of the state of the quantum computer, as well as possible methods for the suppression of the decohering processes. A brief enumeration of proposed quantum computer realizations concludes the review.
This review outlines the principles of operation of quantum computers and their elements. The theory of ideal computers that do not interact with the environment and are immune to quantum decohering processes is presented. Decohering processes in quantum computers are investigated. The review considers methods for correcting quantum computing errors arising from the decoherence of the state of the quantum computer, as well as possible methods for the suppression of the decohering processes. A brief enumeration of proposed quantum computer realizations concludes the review.
Over the past several decades, quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit unique quantum properties? Today it is understood that the answer is yes, and many research groups around the world are working towards the highly ambitious technological goal of building a quantum computer, which would dramatically improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for quantum computation. However, it remains unclear which technology, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain the major challenges for the future. This review outlines the principles of operation of quantum computers and their elements. The theory of ideal computers that do not interact with the environment and are immune to quantum decohering processes is presented. Decohering processes in quantum computers are investigated. The review considers methods for correcting quantum computing errors arising from the decoherence of the state of the quantum computer, as well as possible methods for the suppression of the decohering processes. A brief enumeration of proposed quantum computer realizations concludes the review.
Quantum computing represents a transformative paradigm that exploits the principles of quantum mechanics—superposition, entanglement, and quantum interference—to perform computations beyond the capabilities of classical computers. This review presents a comprehensive overview of the fundamental concepts underlying quantum computation, including qubits, quantum gates, quantum algorithms and measurement theory. It further examines major physical implementations of quantum computers, such as superconducting circuits, trapped ions, photonic systems, spin-based qubits, and topological approaches, highlighting their operational principles, advantages, and technological limitations. Key challenges hindering large-scale quantum computation—decoherence, error rates, qubit scalability, and fault tolerance—are critically discussed. Additionally, recent progress in quantum error correction, hybrid quantum–classical algorithms, and hardware optimization is summarized. The review concludes by outlining future research directions and potential applications of quantum computing in cryptography, materials science, optimization, and drug discovery. By integrating theoretical foundations with experimental advancements, this article aims to provide a clear and accessible reference for students, researchers, and scientists entering the rapidly evolving field of quantum computing.
A quantum computer is an information processing systems that utilizes invertible logic elements to perform reversible logic operations. It can also perform irreversible logic operations. Thus, in principle, it can compute the information transformation rule of any physical system for which the rules are known. A quantum computer can be designed to perform parallel computation on a massive scale, and therefore can have fast execution time. The basic structure of a quantum computer includes 1) a quantum register, or a configuration of quantum-mechanical energy states to store quantum bits (qubits) of information, 2) a quantum processor designed to induce quantum mechanical interactions between any arbitrary pair of qubits to perform a specified logic operations. 3) a quantum bus or network for transferring qubits from the registers to the processor and vice versa, and 4) a physical mechanisms for non-destructive measurements on the qubits. Quantum mechanical systems with the potential for realizing quantum computers include ion-trap quantum computers, cavity quantum electrodynamics quantum computers, photon-trap quantum computers, nuclear magnetic resonance quantum computers, and superconducting quantum computers. Decoherence [1 ,2] possesses the greatest challenge to the practical realization of quantum computers, because it causes the collapse of the quantum superposition states that contain the vital results of qubit manipulations. Decoherence processes are measurement-induced, noise-induced, and environment-induced [3] . Schemes to correct or circumvent the detrimental effects of decoherence in quantum processors fall into active error-correction schemes, and passive error-correction schemes [4]. Active error-correction schemes are designed to detect and correct for errors during computation. Algorithmic fault-tolerant computing [5, 6] is the most promising active-error correction scheme. In fault-tolerant computing, ancillary qubits are encoded into data blocks of the quantum registers. They are then used to detect errors. Once detected appropriate error-correction algorithms are then employed to rectify the errors. The implementation of fault-tolerant quantum computing has been hampered by the lack of practical universal set of quantum gates that can process an encoded data without propagating or introducing additional errors. Passive-error correction schemes [7] attempt to finding Hilbert subspaces that are intrinsically free of decoherence effects [8]. The key to quantum computing in such a decoherence-free subspace is the identification of mechanisms that can effect quantum mechanical interactions between the decoherence-free states without taking the system out of the decoherence-free environment. The challenge is to identify and employ physical processes that can achieve these goals.
Basic concepts of quantum theory of information, principles of quantum calculations and the possibility of creation on this basis unique on calculation power and functioning principle device, named quantum computer, are briefly reviewed. The main blocks of quantum logic, schemes of implementation of quantum calculations, as well as some known today effective quantum algorithms, called to realize advantages of quantum calculations upon classical, are concerned. Among them special place is taken by Shor's algorithm of number factorization, Grover's algorithm of unsorted database search and, finally, the most promising in application methods of quantum phenomena simulation, particularly quantum chaos. The most perspective methods of experimental realization of quantum computer, namely nuclear-magnetic resonance and trapped ions realizations, are discussed. Phenomena of decoherence, its influence on quantum computer stability and methods of quantum error correction are described.
In this tutorial we review basic ideas of quantum computing, from quantum bits and state entanglement to quantum gates and quantum networks [1]. In addition, we give an overview over possible physical implementations of quantum gates[2-6], with emphasis on quantum optical systems: this includes ion traps [2,3], and cavity QED in the optical and microwave domain [4-6], Fundamental problems of building quantum computers, in particular the decoherence problem, and error correction schemes for quantum memory elements [7] and quantum gates [8] will be discussed. We conclude with a critical evaluation what should be expected from quantum computing ideas in terms of applications in physics (quantum optics) and mathematics within the nest few years.
A review of the principles of operation of quantum computers and their elements is presented. The radical advantage of quantum algorithms for processing information over the classical ones is discussed, quantum entanglement is considered as the basic resource of quantum computations, and the most promising and interesting proposals on realization of quantum computers on the basis of trapped ions, nuclear spins, quantum dots, superconducting structures, and others are described. This review reflects the materials of the report presented at the scientific session of the Department of Nanotechnologies and Information Technologies of the Russian Academy of Sciences on February 25, 2010.