Optimal correction of independent and correlated errors

TL;DR

This paper develops optimal quantum error correction codes for imperfect correction scenarios, especially with correlated errors, leading to improved fidelity and entanglement decay performance.

Contribution

It provides analytic solutions for n-qubit codes addressing correlated errors, enhancing quantum error correction strategies beyond perfect correction assumptions.

Findings

Improved fidelity bounds for quantum error correction.

Analytic n-qubit solutions for correlated errors.

Enhanced entanglement decay profiles.

Abstract

We identify optimal quantum error correction codes for situations that do not admit perfect correction. We provide analytic n-qubit results for standard cases with correlated errors on multiple qubits and demonstrate significant improvements to the fidelity bounds and optimal entanglement decay profiles.