# Efficient quantum error correction of dephasing induced by a common fluctuator

## TL;DR

This paper introduces a new family of quantum error-correcting codes specifically designed to efficiently correct dephasing caused by a common fluctuator, significantly reducing overhead and suitable for near-term quantum devices.

## Contribution

The authors develop special-purpose quantum error-correcting codes that exponentially reduce overhead for correcting dephasing from a common fluctuator, tailored for small-scale quantum systems.

## Key findings

- Codes correct to order t^{O(2^n)} for n qubits
- Smallest code encodes 1 logical qubit into 2 physical qubits
- Codes are robust to model imperfections and improve error suppression

## Abstract

Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new family of special-purpose quantum error-correcting codes that offer an exponential reduction in overhead compared to the usual repetition code. They are tailored for a common and important source of decoherence in current experiments, whereby a register of qubits is subject to phase noise through coupling to a common fluctuator, such as a resonator or a spin defect. The smallest instance encodes one logical qubit into two physical qubits, and corrects decoherence to leading-order using a constant number of one- and two-qubit operations. More generally, while the repetition code on $n$ qubits corrects errors to order $t^{O(n)}$, with $t$ the time between recoveries, our codes correct to order $t^{O(2^n)}$. Moreover, they are robust to model imperfections in small- and intermediate-scale devices, where they already provide substantial gains in error suppression. As a result, these hardware-efficient codes open a potential avenue for useful quantum error correction in near-term, pre-fault tolerant devices.