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We demonstrate that small quantum memories, realized via quantum errorcorrection in multi-qubit devices, can benefit substantially by choosing aquantum code that is tailored to the relevant error model of the system. For abiased noise model, with independent bit and phase flips occurring at differentrates, we show that a single code greatly outperforms the well-studied Steanecode across the full range of parameters of the noise model, including forunbiased noise. In fact, this tailored code performs almost optimally whencompared with 10,000 randomly selected stabilizer codes of comparableexperimental complexity. Tailored codes can even outperform the Steane codewith realistic experimental noise, and without any increase in the experimentalcomplexity, as we demonstrate by comparison in the observed error model in arecent 7-qubit trapped ion experiment.

Tailored codes for small quantum memories