1997/02/28 by H. F. Chau · 47 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Arithmetic #Code (set theory) #Computer science #Mathematics #Multiplicative function #Physics #Programming language #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum computer #Quantum convolutional code #Quantum error correction #Quantum mechanics #Quantum-Dot Cellular Automata #Qubit #Spin (aerodynamics) #quant-ph
paper · pdf · doi:10.1103/physreva.56.r1
published in Physical Review A 56(1), R1-R4 (American Physical Society) · Revised version, to appear in Phys.Rev.A (Rapid Communications). 4 pages in Revtex 3.1, using amssymb.sty
arxiv created 1997/05/19 · openalex publication_date 1997/07/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.