Quantum Computing and Error Correction

TL;DR

This paper introduces quantum error correction concepts, demonstrating how noise can be modeled with Pauli operators, and proposes a hierarchical quantum computer design to enhance noise tolerance.

Contribution

It provides an overview of quantum error correction techniques and introduces a hierarchical construction for quantum computers to improve robustness against noise.

Findings

Quantum noise can be modeled as Pauli operators.

Quantum error correction codes can correct specific error subsets.

Hierarchical quantum computer design enhances noise tolerance.

Abstract

The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be understood as a combination of Pauli operators acting on the system. Each quantum error correcting code allows a subset of these errors to be corrected. In many situations the noise is such that the remaining uncorrectable errors are unlikely to arise, and hence quantum error correction has a high probability of success. In order to achieve the best noise tolerance in the presence of noise and imprecision throughout the computer, a hierarchical construction of a quantum computer is proposed.