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A Coding and Automatic Error-Correction Circuit Based on the Five-Particle Entangled State

Xi, Chen, Pei Pei, Zhang, Xiaoqing, Zhou Zhou

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

In this paper, we discuss the concepts of quantum coding and error correction for a five-particle entangled state. Error correction can correct bit-reverse or phase-flip errors of one and two quantum states and is no longer limited to only one quantum state. We encode a single quantum state into a five-particle entangled state before being transferred to the sender. We designed an automatic error-correction circuit to correct errors caused by noise. We also simplify the design process for a multiple quantum error-correction circuit. We compare error-correction schemes for five and three entangled particles in terms of efficiency and capabilities. The results show that error-correction efficiency and fidelity are improved.

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In this paper, we discuss the concepts of quantum coding and error correction for a five-particle entangled state. Error correction can correct bit-reverse or phase-flip errors of one and two quantum states and is no longer limited to only one quantum state. We encode a single quantum state into a five-particle entangled state before being transferred to the sender. We designed an automatic error-correction circuit to correct errors caused by noise. We also simplify the design process for a multiple quantum error-correction circuit. We compare error-correction schemes for five and three entangled particles in terms of efficiency and capabilities. The results show that error-correction efficiency and fidelity are improved.
While the communication between two sites in the quantum network is carried out,the data frames should be resent once the bit-reversed errors appear.Although this method can guarantee the accuracy of data,the pressure of channel is increased and the communication efficiency is reduced.In order to relieve the pressure of channel,the present quantum bit-reversed error correction circuits were analyzed and improved based on the replication of entanglement and the teleportation to design the seven-particle entanglement of quantum bit-reversed error correction circuits.This improvement can not correct more than three bit-reversed quantum states or phase flip error.The efficiency of protocol and utilization of channels before and after the improvement were compared,and the results show that the latter has higher data transmission utilization and it can supply reference evidence for multi-particle error correction.
Quantum error correction protects the quantum state against noise and decoherence in quantum communication and quantum computation, which enables one to perform fault-torrent quantum information processing. We experimentally demonstrate a quantum error correction scheme with a five-wave-packet code against a single stochastic error, the original theoretical model of which was firstly proposed by S. L. Braunstein and T. A. Walker. Five submodes of a continuous variable cluster entangled state of light are used for five encoding channels. Especially, in our encoding scheme the information of the input state is only distributed on three of the five channels and thus any error appearing in the remained two channels never affects the output state, i.e. the output quantum state is immune from the error in the two channels. The stochastic error on a single channel is corrected for both vacuum and squeezed input states and the achieved fidelities of the output states are beyond the corresponding classical limit.
In this paper, the cyclic code of the classic circuit is transformed and transplanted; then, the quantum encoding scheme based on cyclic code and quantum error-correction circuit is constructed. The proposed circuit can correct one-bit error, and the use of redundant bits to encode more than one-bit quantum information breaks the previous limitations of many bits encoding a quantum bit. Compared with the existing coding circuits (Shor code, Steane code and five stable subcode), it shows obvious superiority in the quantum coding efficiency and transmission efficiency.
An efficient coding circuit is given for the perfect quantum-error correction of a single quantum bit (qubit) against arbitrary one-qubit errors within a five-qubit code. The circuit presented employs a double ``classical'' code, i.e., one for bit flips and one for phase shifts. An implementation of this coding circuit on an ion-trap quantum computer is described that requires 26 laser pulses. Another circuit is presented requiring only 24 laser pulses, making it an efficient protection scheme against arbitrary one-qubit errors. In addition, the performances of two error-correction schemes, one based on the quantum Zeno effect and the other using standard methods, are compared. The quantum Zeno error correction scheme is found to fail completely for a model of noise based on phase diffusion.
This paper presents a novel protocol for quantum error correction and decoding leveraging the unique properties of quantum entanglement. The core concept involves utilizing multi-particle entanglement to construct an iterative error-correcting code. This code operates through iterative correction cycles combined with quantum measurements, achieving high-fidelity information encoding and decoding despite the detrimental effects of quantum decoherence and noise. The primary innovation lies in the strategic exploitation of multi-body entanglement, a relatively underexplored area in existing quantum error correction schemes. The protocol's performance is evaluated theoretically, demonstrating its potential to significantly improve the reliability of quantum communication and computation. The design incorporates key elements such as parity-check matrices tailored to the entangled state and optimized measurement strategies to minimize information loss during the decoding process. The presented approach represents a significant step towards building practical and robust quantum systems capable of handling the inherent challenges of quantum information processing.