Simplified Quantum Weight Reduction with Optimal Bounds
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914087014760448 |
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| author | Hsieh, Min-Hsiu Li, Xingjian Lin, Ting-Chun |
| author_facet | Hsieh, Min-Hsiu Li, Xingjian Lin, Ting-Chun |
| contents | Quantum weight reduction is the task of transforming a quantum code with large check weight into one with small check weight. Low-weight codes are essential for implementing quantum error correction on physical hardware, since high-weight measurements cannot be executed reliably. Weight reduction also serves as a critical theoretical tool, which may be relevant to the quantum PCP conjecture.
We introduce a new procedure for quantum weight reduction that combines geometric insights with coning techniques, which simplifies Hastings' previous approach while achieving better parameters. Given an arbitrary $[[n,k,d]]$ quantum code with weight $w$, our method produces a code with parameters $[[O(n w^2 \log w), k, Ω(d w)]]$ with check weight $5$ and qubit weight $6$.
When applied to random dense CSS codes, our procedure yields explicit quantum codes that surpass the square-root distance barrier, achieving parameters $[[n, \tilde O(n^{1/3}), \tilde Ω(n^{2/3})]]$. Furthermore, these codes admit a three-dimensional embedding that saturates the Bravyi-Poulin-Terhal (BPT) bound.
As a further application, our weight reduction technique improves fault-tolerant logical operator measurements by reducing the number of ancilla qubits. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_09601 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simplified Quantum Weight Reduction with Optimal Bounds Hsieh, Min-Hsiu Li, Xingjian Lin, Ting-Chun Quantum Physics Quantum weight reduction is the task of transforming a quantum code with large check weight into one with small check weight. Low-weight codes are essential for implementing quantum error correction on physical hardware, since high-weight measurements cannot be executed reliably. Weight reduction also serves as a critical theoretical tool, which may be relevant to the quantum PCP conjecture. We introduce a new procedure for quantum weight reduction that combines geometric insights with coning techniques, which simplifies Hastings' previous approach while achieving better parameters. Given an arbitrary $[[n,k,d]]$ quantum code with weight $w$, our method produces a code with parameters $[[O(n w^2 \log w), k, Ω(d w)]]$ with check weight $5$ and qubit weight $6$. When applied to random dense CSS codes, our procedure yields explicit quantum codes that surpass the square-root distance barrier, achieving parameters $[[n, \tilde O(n^{1/3}), \tilde Ω(n^{2/3})]]$. Furthermore, these codes admit a three-dimensional embedding that saturates the Bravyi-Poulin-Terhal (BPT) bound. As a further application, our weight reduction technique improves fault-tolerant logical operator measurements by reducing the number of ancilla qubits. |
| title | Simplified Quantum Weight Reduction with Optimal Bounds |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.09601 |