Tailored codes for small quantum memories

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.

6 pages, 2 figures, supplementary material; v2 published version

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Cited by in corpus (15)

• The XZZX Surface Code
• Ultrahigh Error Threshold for Surface Codes with Biased Noise
• Bias-preserving gates with stabilized cat qubits
• Fault-Tolerant Logical Gates in the IBM Quantum Experience
• Tailoring surface codes for highly biased noise
• Efficient estimation of Pauli channels
• 2-D Compass Codes
• Protecting quantum memories using coherent parity check codes
• Tailored XZZX codes for biased noise
• Pauli channels can be estimated from syndrome measurements in quantum error correction
• Efficient quantum error correction of dephasing induced by a common fluctuator
• Efficient diagnostics for quantum error correction
• Robustness-optimized quantum error correction
• Improving trapped-ion-qubit memories via code-mediated error-channel balancing
• Optimizing short stabilizer codes for asymmetric channels