Unified Quantum Convolutional Coding

TL;DR

This paper introduces a quantum convolutional coding framework that combines multiple quantum resources to protect classical and quantum data streams efficiently, approaching the theoretical channel capacity.

Contribution

It presents a novel quantum convolutional coding method utilizing ancilla, entanglement, and gauge qubits, with explicit encoding/decoding circuits for near-capacity data protection.

Findings

Codes approach the 'grandfather' capacity of quantum channels.

The method integrates active and passive error correction.

Explicit circuits demonstrate practical implementation.

Abstract

We outline a quantum convolutional coding technique for protecting a stream of classical bits and qubits. Our goal is to provide a framework for designing codes that approach the ``grandfather'' capacity of an entanglement-assisted quantum channel for sending classical and quantum information simultaneously. Our method incorporates several resources for quantum redundancy: fresh ancilla qubits, entangled bits, and gauge qubits. The use of these diverse resources gives our technique the benefits of both active and passive quantum error correction. We can encode a classical-quantum bit stream with periodic quantum gates because our codes possess a convolutional structure. We end with an example of a ``grandfather'' quantum convolutional code that protects one qubit and one classical bit per frame by encoding them with one fresh ancilla qubit, one entangled bit, and one gauge qubit per frame. We explicitly provide the encoding and decoding circuits for this example.