Tailoring Dynamical Codes for Biased Noise: The X$^3$Z$^3$ Floquet Code
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914050013659136 |
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| author | Setiawan, F. McLauchlan, Campbell |
| author_facet | Setiawan, F. McLauchlan, Campbell |
| contents | We propose the X$^3$Z$^3$ Floquet code, a dynamical code with improved performance under biased noise compared to other Floquet codes. The enhanced performance is attributed to a simplified decoding problem resulting from a persistent stabiliser-product symmetry, which surprisingly exists in a code without constant stabilisers. Even if such a symmetry is allowed, we prove that general dynamical codes with two-qubit parity measurements cannot admit one-dimensional decoding graphs, a key feature responsible for the high performance of bias-tailored stabiliser codes. Despite this, our comprehensive simulations show that the symmetry of the X$^3$Z$^3$ Floquet code renders its performance under biased noise far better than several leading Floquet codes. To maintain high-performance implementation in hardware without native two-qubit parity measurements, we introduce ancilla-assisted bias-preserving parity measurement circuits. Our work establishes the X$^3$Z$^3$ code as a prime quantum error-correcting code, particularly for devices with reduced connectivity, such as the honeycomb and heavy-hexagonal architectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04974 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tailoring Dynamical Codes for Biased Noise: The X$^3$Z$^3$ Floquet Code Setiawan, F. McLauchlan, Campbell Quantum Physics We propose the X$^3$Z$^3$ Floquet code, a dynamical code with improved performance under biased noise compared to other Floquet codes. The enhanced performance is attributed to a simplified decoding problem resulting from a persistent stabiliser-product symmetry, which surprisingly exists in a code without constant stabilisers. Even if such a symmetry is allowed, we prove that general dynamical codes with two-qubit parity measurements cannot admit one-dimensional decoding graphs, a key feature responsible for the high performance of bias-tailored stabiliser codes. Despite this, our comprehensive simulations show that the symmetry of the X$^3$Z$^3$ Floquet code renders its performance under biased noise far better than several leading Floquet codes. To maintain high-performance implementation in hardware without native two-qubit parity measurements, we introduce ancilla-assisted bias-preserving parity measurement circuits. Our work establishes the X$^3$Z$^3$ code as a prime quantum error-correcting code, particularly for devices with reduced connectivity, such as the honeycomb and heavy-hexagonal architectures. |
| title | Tailoring Dynamical Codes for Biased Noise: The X$^3$Z$^3$ Floquet Code |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2411.04974 |