# Tailored codes for small quantum memories

## TL;DR

This paper shows that customizing quantum error correction codes to specific noise models significantly improves small quantum memory performance, outperforming standard codes like Steane's in various realistic scenarios.

## Contribution

It introduces tailored quantum codes optimized for biased noise models, demonstrating substantial performance gains over standard codes in small quantum systems.

## Key findings

- Tailored codes outperform Steane code across various noise parameters.
- Customized codes nearly match optimal performance among many random codes.
- Realistic experimental noise conditions favor tailored codes without added complexity.

## Abstract

We demonstrate that small quantum memories, realized via quantum error correction in multi-qubit devices, can benefit substantially by choosing a quantum code that is tailored to the relevant error model of the system. For a biased noise model, with independent bit and phase flips occurring at different rates, we show that a single code greatly outperforms the well-studied Steane code across the full range of parameters of the noise model, including for unbiased noise. In fact, this tailored code performs almost optimally when compared with 10,000 randomly selected stabilizer codes of comparable experimental complexity. Tailored codes can even outperform the Steane code with realistic experimental noise, and without any increase in the experimental complexity, as we demonstrate by comparison in the observed error model in a recent 7-qubit trapped ion experiment.