Construction of Error-Correction Code Application by Applying Finite Field and Hadamard Matrix Theory

Dalam dunia elektronik dan digital, informasi dapat dengan mudahditransfer melalui saluran komunikasi. Pada data yang ditransfer galatdapat muncul dikarenakan oleh berbagai akibat. Untuk menghindarimasalah ini diperlukan kode perbaikan-galat bersama aplikasinya. Konsepdari kode perbaikan-galat adalah untuk menambahkan bit-tambahanpada data agar disaat pengiriman, data tersebut lebih kuat dalammenghadapi gangguan yang hadir di saluran komunikasi. Random ParityCode (RPC) yang dikemukakan oleh Hershey dan Tiemann (1996) adalahsalah satu dari kode yang dimaksud. Artikel ini menunjukan pembuatanaplikasi kode perbaikan-galat yang dibuat berdasarkan konsep RPCdengan bantuan teori Lapangan Terbatas dan Matriks Hadamard. Aplikasidibuat menggunakan Metode Rapid Application Development (RAD).Aplikasi dihasilkan dalam bentuk perangkat lunak komputer. Perangkatlunak tersebut menjadi lebih efisien dengan menerapkan konsepalgoritma “Divide and Conquer”

Experimental demonstration of a graph state quantum error-correction code

Scalable quantum computing and communication requires the protection of quantum information from the detrimental effects of decoherence and noise. Previous work tackling this problem has relied on the original circuit model for quantum computing. However, recently a family of entangled resources known as graph states has emerged as a versatile alternative for protecting quantum information. Depending on the graph's structure, errors can be detected and corrected in an efficient way using measurement-based techniques. In this article we report an experimental demonstration of error correction using a graph state code. We have used an all-optical setup to encode quantum information into photons representing a four-qubit graph state. We are able to reliably detect errors and correct against qubit loss. The graph we have realized is setup independent, thus it could be employed in other physical settings. Our results show that graph state codes are a promising approach for achieving scalable quantum information processing

Five Quantum Register Error Correction Code For Higher Spin Systems

I construct a quantum error correction code (QECC) in higher spin systems using the idea of multiplicative group character. Each $N$ state quantum particle is encoded as five $N$ state quantum registers. By doing so, this code can correct any quantum error arising from any one of the five quantum registers. This code generalizes the well-known five qubit perfect code in spin-1/2 systems and is shown to be optimal for higher spin systems. I also report a simple algorithm for encoding. The importance of multiplicative group character in constructing QECCs will be addressed.Comment: Revised version, to appear in Phys.Rev.A (Rapid Communications). 4 pages in Revtex 3.1, using amssymb.st