Study of Multiple Rounds of Error Correction in Solid State NMR QIP

TL;DR

This paper investigates the feasibility of implementing multiple rounds of quantum error correction in solid state NMR, focusing on error correction and ancilla refresh techniques, and analyzes the effects of imperfections.

Contribution

It introduces two algorithms for error correction and ancilla refreshing in solid state NMR, advancing practical quantum error correction methods.

Findings

Feasibility demonstrated for multiple rounds of error correction in NMR.

Two algorithms for 4-qubit testing and 6-qubit implementation.

Analysis of imperfections' impact on error correction and ancilla refresh.

Abstract

Methods to control errors will be essential for quantum information processing. It is widely believed that fault-tolerant quantum error correction is the leading contender to achieve this goal. Although the theory of fault-tolerant quantum error correction is very well understood, experimental implementation has been lagging. We study the feasibility of implementing repeated rounds of quantum error correction with refreshed ancillas in solid state nuclear magnetic resonance (NMR). In particular we study the procedure proposed for extracting entropy that consists of two stages; an error correcting code optimized to function at finite temperature, and an implementation of heat-bath algorithmic cooling to refresh the ancilla qubits. Two algorithms are presented which implement this method, one for performing tests on 4 qubits, the other for practical implementation on 6 qubits. The effects of imperfect implementation are examined in both the error correction and refreshing stages.