Fault-Tolerant Error Correction with Efficient Quantum Codes

TL;DR

This work exhibits a simple, systematic procedure for detecting and correcting errors using any of the recently reported quantum error-correcting codes, derived using a recently introduced group-theoretic framework for unifying all known quantum codes.

Abstract

We exhibit a simple, systematic procedure for detecting and correcting errors using any of the recently reported quantum error-correcting codes. The procedure is shown explicitly for a code in which one qubit is mapped into five. The quantum networks obtained are fault tolerant, that is, they can function successfully even if errors occur during the error correction. Our construction is derived using a recently introduced group-theoretic framework for unifying all known quantum codes.

Figures (1)

• Figure 1: Quantum network to correct for one-bit errors in the 5-bit code in the $S$ presentation. Four different code presentations $L_{3,4,0,1}$ are used in the different stages of error detection. By a simple modification of the ancilla space $a$, and by appropriate repetitions of the syndrome computation, this error-correction network can be made fault tolerant.