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Five Quantum Register Error Correction Code For Higher Spin Systems

Research paper by H. F. Chau

Indexed on: 19 May '97Published on: 19 May '97Published in: Quantum Physics



Abstract

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.