Every Action in Every Code is Fault Tolerant: Fault Tolerance Quantum Computation in Quotient Algebra Partition

TL;DR

This paper introduces a general methodology within quotient algebra partition to construct fault-tolerant encodes for any action in error-correcting codes, advancing quantum fault tolerance techniques.

Contribution

It presents a novel, general approach for fault-tolerant encoding in quantum error correction using quotient algebra partition, applicable to any action.

Findings

Provides a new framework for fault-tolerant quantum encoding

Enables fault tolerance for arbitrary actions in error-correcting codes

Advances quantum fault tolerance methodology

Abstract

In the framework quotient algebra partition, a general methodology is introduced to construct fault tolerant encodes for an arbitrary action in an error-correcting code.