Quantum Error Correction on Error-mitigated Physical Qubits

TL;DR

This paper introduces a framework for applying quantum error mitigation techniques directly to physical qubits, improving logical error rates without modifying quantum error correction decoders, and demonstrating resource-efficient enhancements in fault-tolerant quantum computing.

Contribution

The authors develop a general framework for integrating linear quantum error mitigation methods at the physical qubit level within logical qubits, enhancing error suppression without decoder modifications.

Findings

Logical error can be reduced by removing leading-order contributions.

Physical-level PEC achieves logical error rates comparable to higher-distance codes.

Resource savings of 40-64% in qubits for effective error mitigation.

Abstract

We present a general framework for applying linear quantum error mitigation (QEM) techniques directly to physical qubits within a logical qubit to suppress logical errors. By exploiting the linearity of quantum error correction (QEC), we demonstrate that any linear QEM method$\unicode{x2014}$including probabilistic error cancellation (PEC), zero-noise extrapolation (ZNE), and symmetry verification$\unicode{x2014}$can be integrated into the physical layer without requiring modifications to the subsequent QEC decoder. Applying this framework to memory experiments using PEC, we analytically prove and numerically verify that the leading-order contribution to the logical error can be removed, increasing the effective code distance by 2. Our simulations on repetition and rotated surface codes show that a distance-3 code with physical-level PEC achieves logical error rates lower than or similar to a distance-5 unmitigated code while using 40% and 64% fewer qubits, respectively. These results establish physical-level QEM as a widely compatible and resource-efficient strategy for enhancing logical performance in early fault-tolerant architectures.