Quantum Error-Correcting Codes with Preexisting Protected Qubits

TL;DR

This paper introduces a systematic method for constructing entanglement-assisted quantum error-correcting codes using graph states, demonstrating improved performance with preexisting protected qubits and generalized error models.

Contribution

It presents a new construction approach for quantum codes leveraging preexisting protected qubits and extends the model to less-than-perfect protection scenarios.

Findings

Preexisting entanglement can surpass the quantum Hamming bound.

Codes outperform traditional quantum error-correcting codes under generalized error models.

The approach enhances quantum error correction performance with protected qubits.

Abstract

We provide a systematic way of constructing entanglement-assisted quantum error-correcting codes via graph states in the scenario of preexisting perfectly protected qubits. It turns out that the preexisting entanglement can help beat the quantum Hamming bound and can enhance (not only behave as an assistance) the performance of the quantum error correction. Furthermore we generalize the error models to the case of not-so-perfectly-protected qubits and introduce the quantity infidelity as a figure of merit and show that our code outperforms also the ordinary quantum error-correcting codes.