Quantum Error Correction with Uniformly Mixed State Ancillae

TL;DR

This paper proposes and experimentally demonstrates a quantum error correction scheme that uses ancilla qubits in a uniformly mixed state, challenging the assumption that ancillae must be pure, and explores the quantum correlations involved.

Contribution

It introduces a novel QEC encoding scheme with mixed-state ancillae and experimentally verifies it using NMR quantum computing.

Findings

Successful implementation of QEC with mixed-state ancillae

The encoded state exhibits significant quantum discord

Experimental validation on a three-qubit NMR system

Abstract

It is often assumed that the ancilla qubits required for encoding a qubit in quantum error correction (QEC) have to be in pure states, $|00...0>$ for example. In this letter, we seek an encoding scheme, in which the ancillae may be in a uniformly mixed state. We demonstrate our scheme experimentally by making use of a three-qubit NMR quantum computer. Moreover, the encoded state has an interesting nature in terms of Quantum Discord, or purely quantum correlations between the data-qubit and ancillae.