Unitary Quantum Error Correction without Error Detection

TL;DR

This paper introduces a novel quantum error correction method that uses only unitary operations for encoding, recovery, and decoding, eliminating the need for error detection and simplifying implementation.

Contribution

It presents a new approach to quantum error correction that avoids error detection and uses only unitary operations, streamlining the process.

Findings

Encoding and recovery are implemented with unitary operators only.

The method produces a tensor product state after error correction.

No higher rank projection operators are needed.

Abstract

We propose a quantum error correction without error detection. A quantum state $\rho_0$ combined with an ancilla state $\sigma$ is encoded unitarily and an error operator is applied on the encoded state. The recovery operation then produces a tensor product state $\rho_0 \otimes \sigma'$. The decoding operation is combined with the recovery operation and the state $\rho_0$ is directly reproduced without referring to the code word. A higher rank projection operator required for a conventional operator quantum error correction is not necessary to implement. Encoding and the recovery operations are implemented with unitary operators only, which makes quantum error correction much easier than any other proposals.