Quantum Information: Qubits and Quantum Error Correction

Alexey A. Melnikov, Leonid Evgenevich Fedichkin

We considered the interaction of semiconductor quantum register with noisy environment leading to various types of qubit errors. We analysed both phase and amplitude decays during the process of electron-phonon interaction. The performance of quantum error correction codes (QECC) which will be inevitably used in full scale quantum information processors was studied in realistic conditions in semiconductor nanostructures. As a hardware basis for quantum bit we chose the quantum spatial states of single electron in semiconductor coupled double quantum dot system. The modified 5- and 9-qubit quantum error correction (QEC) algorithms by Shor and DiVincenzo without error syndrome extraction were applied to quantum register. 5-qubit error correction procedures were implemented for Si charge double dot qubits in the presence of acoustic phonon environment. ¬-matrix, Choi{Jamio lkowski state and measure of decoherence techniques were used to quantify qubit faulttolerance. Our results showed that the introduction of above quantum error correction techniques at small phonon noise levels provided quadratic improvement of output error rates. The effciency of 5-qubits quantum error correction algorithm in semiconductor quantum information processors was demonstrated.

Jincheng Zhang

This paper presents a novel approach to quantum error correction (QEC) utilizing redundancy coding, focusing on enhanced efficiency in quantum information transmission. The core claim revolves around designing multi-particle error-correcting codes to minimize the resource consumption associated with encoding and decoding. The proposed mechanism involves encoding information across multiple qubits, leveraging error detection and correction capabilities inherent in these codes. Crucially, the strategy optimizes the distribution of redundant qubits, significantly reducing unnecessary information redundancy. The research addresses the limitations of existing QEC schemes, which often rely on excessive redundancy, impacting transmission efficiency. This work demonstrates a pathway towards more practical and resource-conscious QEC, representing a key step toward reliable long-distance quantum communication. The primary goal is to reduce the overhead associated with error correction, making quantum information transfer more viable. This is achieved through a refined approach to redundancy, concentrating correction resources where they are most needed.

Ivan B. Djordjević

Jincheng Zhang

Quantum error correction (QEC) is a critical requirement for reliable quantum computation, as errors can quickly accumulate and compromise the integrity of quantum states. Current QEC approaches often rely on encoding information redundantly across multiple qubits, which introduces significant overhead and complexity. This paper proposes a novel dimension expansion quantum error correction protocol (DEQ) that leverages the concept of dimensional expansion to enhance quantum information storage and transmission capabilities, ultimately improving the efficiency of error correction. We introduce a new strategy by strategically manipulating the quantum state to expand the system's dimensionality, allowing for more robust error detection and correction. This work explores the potential of this approach in mitigating the limitations of existing QEC methods and provides a foundational framework for future advancements in quantum information security.