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IEEE Annual Computing and Communication Workshop and Conference (CCWC)

Novel Encoding method for Quantum Error Correction

Swathi Mummadi, Bhawana Rudra

Published Jan 26, 2022• 22 citations
Publisher

Abstract

Quantum error correction plays a vital role in the Quantum information process. Nowadays, the research has been increased in quantum technology and is being applied in various applications like secure communications, finance, machine learning, drug analysis and etc. But the quantum information process is difficult compared to the classical due to the challenges in quantum technology like no-cloning theorem, decoherence, and the difficulty in quantum states measurement. Thus the error rate is high and it is not possible to build a quantum computer without an error detection and correction mechanism. In this paper, we are discussing various error correction methods and proposing a novel encoding method for quantum error correction.

DOI
10.1109/ccwc54503.2022.9720880

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Quantum error correction plays a vital role in the Quantum information process. Nowadays, the research has been increased in quantum technology and is being applied in various applications like secure communications, finance, machine learning, drug analysis and etc. But the quantum information process is difficult compared to the classical due to the challenges in quantum technology like no-cloning theorem, decoherence, and the difficulty in quantum states measurement. Thus the error rate is high and it is not possible to build a quantum computer without an error detection and correction mechanism. In this paper, we are discussing various error correction methods and proposing a novel encoding method for quantum error correction.
This paper presents a novel quantum error correction information encoder designed to mitigate the detrimental effects of decoherence on quantum information. The core of the proposed scheme relies on exploiting multi-particle entanglement to establish a robust coding strategy. The system utilizes a carefully crafted sequence of measurements to detect and correct errors effectively, while simultaneously minimizing the required redundancy. The fundamental difference from existing classical error correction methods lies in the leveraging of quantum mechanical phenomena, specifically entanglement, to ensure information integrity. This approach offers a potential pathway towards reliable quantum communication and computation, addressing a critical bottleneck in the field. The theoretical framework is presented, outlining the key components and operational principles of the encoder. The presented model is scalable and adaptable, providing a foundation for future research and development in quantum error correction technologies.
The quantum computing must be the initial mark of the second technological revolution caused by the deepening knowledge of the humankind about the peculiar features of the quantum mechanics. If we want to unlock all the potential of this new technology, a development of a fault-tolerant quantum computing will be needed. In order to reach this stage, it is necessary an implementation of quantum error correcting codes that guarantee an exponential suppression of the errors at each step of the execution of an algorithm. Besides that, we need to learn how to isolate our qubits aiming a suppression of the decoherence effects. Quantum mechanics imposes various constraints to the process of construction of the error correction codes, one of them is the impossibility of using copies as redundancy mechanism, once no-cloning theorem does not allow the creation of an universal copy machine of quantum states. Another issue to be noted within this context, is that the measurement process causes a collapse in the quantum state, thus leading to a corruption of the information encoded in the state. Fortunately, there are some ways to bypass the problems pointed out through the entanglement and the stabilizer formalism, the first one allows us to recover the redundancy through the delocalization of the information in the Hilbert spaces of the parts that share quantum correlations, while the second one provides a process of gathering information about the errors that can occur in the quantum state without measuring it. The surface codes are one of the quantum codes that use the features highlighted to correct the errors, this type of code is one of the main candidates to be experimentally implemented on a large scale and it presents promising results in the preliminary studies.
Quantum computer performs operations by adopting the principles of quantum physics and quantum mechanics. With these principles, it performs operations exponentially faster compared to classical computers. The major problem observed in quantum computation is noise and decoherence. The noise and decoherence generate errors while performing the operations on quantum states. As a solution to this Quantum error correction(QEC) methods are introduced. Encoding plays a key role in QEC. In the encoding process, the logical qubits are encoded into physical qubits by appending extra qubits to them. With this, the logical qubit will be strengthened and can be transferred safely. Initially, the experimental results of quantum computation are theoretical or mathematical. But with the existence of quantum computers, it is possible to develop and run new quantum architectures on publicly available quantum computers. Thus in this paper, we developed an efficient algorithm for encoding quantum information using various quantum gates. The developed algorithm is executed on various quantum systems and the performance is analyzed in terms of frequency, run time, error rate, number of qubits, and quantum volume. This analysis helps the researchers to opt an efficient quantum system to perform the experiments.
Abstract In this paper we present an effective error correction method to correct the errors that occur during quantum information processing. (There are various methods of quantum error correction such as error correcting code or decoherence free subspace which protect quantum information from noise, and they are useful for storage and communication; however, it would be difficult to adapt them to quantum information processing practically.) In this method the error detection is carried out through the asymmetry or the irreversibility of quantum computers, which ought to be inherently symmetric and reversible. The irreversibility is usually caused by decoherence and dissipation, and the processing's own adjoint operator can, therefore, be used to condense such errors and enable their detection. The effectiveness of this method is investigated with an NMR quantum computer. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007
Quantum technologies have shown immeasurable potential to effectively solve several information processing tasks such as prime number factorization, unstructured database search or complex macromolecule simulation. As a result of such capability to solve certain problems that are not classically tractable, quantum machines have the potential revolutionize the modern world via applications such as drug design, process optimization, unbreakable communications or machine learning. However, quantum information is prone to suffer from errors caused by the so-called decoherence, which describes the loss in coherence of quantum states associated to their interactions with the surrounding environment. This decoherence phenomenon is present in every quantum information task, be it transmission, processing or even storage of quantum information. Consequently, the protection of quantum information via quantum error correction codes (QECC) is of paramount importance to construct fully operational quantum computers. Understanding environmental decoherence processes and the way they are modeled is fundamental in order to construct effective error correction methods capable of protecting quantum information. In this thesis, the nature of decoherence is studied and mathematically modelled; and QECCs are designed and optimized so that they exhibit better error correction capabilities.
This paper introduces a novel Quantum Error Correction Embedding Algorithm designed to significantly enhance the success rate of quantum error correction. The core claim rests on leveraging the redundancy inherent in error-correcting codes to embed controllable quantum error correction (QEC) information directly into the encoding of quantum states. The fundamental mechanism involves a newly designed code that integrates error information within the superposition state of a quantum state, rather than solely focusing on error detection and correction. This approach exploits the inherent properties of superposition to perform error correction. The algorithm's potential impact lies in overcoming limitations of traditional QEC methods, particularly in scenarios where the error rate is high or the complexity of error correction is significant. This work presents a theoretical framework and outlines the key components of the algorithm, establishing a foundation for future research and development in robust quantum computation. The algorithm's success hinges on precisely controlling the superposition state to encode and decode error information effectively. Further investigation is needed to optimize the parameters and explore the algorithm's performance across various quantum systems and error models.