Error Correcting Codes In Quantum Theory, Scheme For Reducing Decoherence In Quantum Computer Memory, Correcting Quantum Computer Errors, Qubits Based On Quantum Spins, And Other Topics: A fomentation-Dissipation Model
We study attendant properties of the following system: Error Correcting Codes In Quantum Theory, Scheme For Reducing Decoherence In Quantum Computer Memory, Correcting Quantum Computer Errors, Qubits Based On Quantum Spins, Nine-Qubit State Is A Set Of Three Groups, Repeated Quantum Error Correction On A Continuously Encoded Qubit, Active Error Correction On A Continuously Protected Logical Qubit, Correction Of Errors In Encoded Quantum States, Connection Between The Observers Will Typically Be Subject To Disturbances That Can Disrupt The Entanglement, Reconstruct The Original Qubit From The Unchanged Pair, Quantum Error Correction That Extends The Lifetime Of Quantum Information, Error Correction Under Different Types Of Noise Key words: Quantum error correction, Qubit, Noise The full paper: http://www.iiste.org/PDFshare/APTA-PAGENO-548811-555137.pdf
We study attendant properties of the following system: Error Correcting Codes In Quantum Theory, Scheme For Reducing Decoherence In Quantum Computer Memory, Correcting Quantum Computer Errors, Qubits Based On Quantum Spins, Nine-Qubit State Is A Set Of Three Groups, Repeated Quantum Error Correction On A Continuously Encoded Qubit, Active Error Correction On A Continuously Protected Logical Qubit, Correction Of Errors In Encoded Quantum States, Connection Between The Observers Will Typically Be Subject To Disturbances That Can Disrupt The Entanglement, Reconstruct The Original Qubit From The Unchanged Pair, Quantum Error Correction That Extends The Lifetime Of Quantum Information, Error Correction Under Different Types Of Noise Key words: Quantum error correction, Qubit, Noise The full paper: http://www.iiste.org/PDFshare/APTA-PAGENO-548811-555137.pdf
Feedback Based On Multi-Qubit Measurements, Multiple-Particle Interference And Quantum Error Correction, Theory Of Quantum Error-Correcting Codes, Theory Of Quantum Error-Correcting Codes-2, Theory Of Quantum Error-Correcting Codes-3, New Class Of Quantum Error-Correcting Codes For A Bosonic Mode, New Class Of Quantum Error-Correcting Codes For A Bosonic Mode, Bosonic Quantum Memories, Photonic Quantum Communication, And Optical-To-Microwave Up- And Down-Conversion, Mixed State Entanglement And Quantum Error Correction, Mixed State Entanglement And Quantum Error Correction-2, Mixed State Entanglement And Quantum Error Correction-3, Universal Operator Theoretic Framework For Quantum Fault Tolerance, Efficiently Controllable Graphs. Foregoing system and its connected properties are studied in detail. The full paper: http://www.iiste.org/PDFshare/APTA-PAGENO-555138-561343.pdf
This work is a study of the influence of the medium on the quantum system of qubits. The article assumes a description of the fundamentals of the quantum information theory, as well as a place in it the concept of quantum entanglement. Quantum error correction is a set of methods for protecting quantum information and quantum state from unwanted interactions of the environment (decoherence) and other forms and types of noise. Today, there are modern quantum technologies that are capable of supporting fundamentally new computational algorithms based on the principles of quantum mechanics. The dependences of data distortion on noise and measures of decoherence on noise in one qubit are demonstrated. This article is devoted to solving the problem of research and development of corrective codes for correcting several types of quantum errors. These errors appear during computational processes in quantum algorithms and models of quantum computing devices. The aim of the work is to study existing methods for correcting various types of quantum errors and to create a corrective code for quantum error correction. The scientific novelty of this research is expressed in the one shortcoming exclusion of the quantum computing process. Currently, in many advanced countries of the world, intensive research is being carried out to develop and create quantum computers and their software, and there has been a rapid increase in interest in quantum computers. A large number of articles and monographs are published.
Quantum error correction is a set of methods to protect quantum information--that is, quantum states--from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting code, which is a subspace in a larger Hilbert space. This code is designed so that the most common errors move the state into an error space orthogonal to the original code space while preserving the information in the state. It is possible to determine whether an error has occurred by a suitable measurement and to apply a unitary correction that returns the state to the code space, without measuring (and hence disturbing) the protected state itself. In general, codewords of a quantum code are entangled states. No code that stores information can protect against all possible errors; instead, codes are designed to correct a specific error set, which should be chosen to match the most likely types of noise. An error set is represented by a set of operators that can multiply the codeword state. Quantum error correction is used to protect information in quantum communication (where quantum states pass through noisy channels) and quantum computation (where quantum states are transformed through a sequence of imperfect computational steps in the presence of environmental decoherence to solve a computational problem). In quantum computation, error correction is just one component of fault-tolerant design.
Quantum error correction is a set of methods to protect quantum information--that is, quantum states--from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting code, which is a subspace in a larger Hilbert space. This code is designed so that the most common errors move the state into an error space orthogonal to the original code space while preserving the information in the state. It is possible to determine whether an error has occurred by a suitable measurement and to apply a unitary correction that returns the state to the code space, without measuring (and hence disturbing) the protected state itself. In general, codewords of a quantum code are entangled states. No code that stores information can protect against all possible errors; instead, codes are designed to correct a specific error set, which should be chosen to match the most likely types of noise. An error set is represented by a set of operators that can multiply the codeword state. Quantum error correction is used to protect information in quantum communication (where quantum states pass through noisy channels) and quantum computation (where quantum states are transformed through a sequence of imperfect computational steps in the presence of environmental decoherence to solve a computational problem). In quantum computation, error correction is just one component of fault-tolerant design.
Quantum error correction is the art of protecting quantum states from the detrimental influence from the environment. To master this art, one must understand how the system interacts with the environment and gives rise to a full set of quantum phenomena, many of which have no correspondence in classical information theory. Such phenomena include decoherence, an effect that in general destroys superpositions of pure states as a consequence of entanglement with the environment. But decoherence can also be understood as “information leakage”, i.e., when knowledge of an encoded code block is transferred to the environment. In this event, the block’s information or entanglement content is typically lost.In a typical scenario, however, not all types of destructive events are likely to occur, but only those allowed by the information carrier, the type of interaction with the environment, and how the environment “picks up” information of the error events. These characteristics can be incorporated into a code, i.e., a channel-adapted quantum error-correcting code.Often, it is assumed that the environment’s ability to distinguish between error events is small, and I will denote such environments “memory-less”. But this assumption is not always valid, since the ability to distinguish error events is related to the temperature of the environment, and in the particular case of information coded onto photons, kBTR «ℏω typically holds, and one must then assume that the environment has a “memory”. In the thesis I describe a short quantum error-correction code adapted for photons interacting with a “cold” reservoir, i.e., a reservoir which continuously probes what error occurred in the coded state.I also study other types of environments, and show how to distill meaningful figures of merit from codes adapted for these channels, as it turns out that resource-based figures reflecting both information and entanglement can be calculated exactly for a well-studied class of channels: the Pauli channels. Starting from these resource-based figures, I establish the notion of efficiency and quality and show that there will be a trade-off between efficiency and quality for short codes. Finally I show how to incorporate, into these calculations, the choices one has to make when handling quantum states that have been detected as incorrect, but where no prospect of correcting them exists, i.e., so-called detection errors.
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum error-correcting codes allow the negation of these effects in order to successfully restore the original quantum information. We briefly describe the necessary quantum-mechanical background to be able to understand how quantum error correction works. We go on to construct quantum codes: firstly qubit stabilizer codes, then qubit non-stabilizer codes, and finally codes with a higher local dimension. We will delve into the geometry of these codes. This allows one to deduce the parameters of the code efficiently, deduce the inequivalence between codes that have the same parameters, and presents a useful tool in deducing the feasibility of certain parameters. We also include sections on quantum maximum distance separable codes and the quantum MacWilliams identities.