Constant-Time Surgery on 2D Hypergraph Product Codes with Near-Constant Space Overhead
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910038177611776 |
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| author | Chang, Kathleen He, Zhiyang Yoder, Theodore J. Zhu, Guanyu Jochym-O'Connor, Tomas |
| author_facet | Chang, Kathleen He, Zhiyang Yoder, Theodore J. Zhu, Guanyu Jochym-O'Connor, Tomas |
| contents | Generalized code surgery is a versatile and low-overhead technique for performing fault-tolerant computation on quantum low-density parity-check (qLDPC) codes. In many settings, surgery exhibits practical space overheads, while its time overhead remains a bottleneck at $O(d)$ syndrome rounds per operation. In this work, we construct surgery gadgets that perform parallel logical measurements on 2D hypergraph product codes in constant time overhead ($O(1)$) and near-constant space overhead ($\tilde{O}(1)$). The reduced time overhead is a result of amortization, as we show, following the formulation by Cowtan et al. (arXiv:2510.14895), that performing $d$ surgery operations in $O(d)$ time is fault tolerant. Our gadgets combine the strengths of different approaches to fault-tolerant logical operations: they partially retain the flexibility of surgery while achieving overheads comparable to transversal gates. Consequently, they are well-suited for near-term experimental realization and demonstrate new possibilities in the design of gadgets for fast logical computation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02157 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Constant-Time Surgery on 2D Hypergraph Product Codes with Near-Constant Space Overhead Chang, Kathleen He, Zhiyang Yoder, Theodore J. Zhu, Guanyu Jochym-O'Connor, Tomas Quantum Physics Generalized code surgery is a versatile and low-overhead technique for performing fault-tolerant computation on quantum low-density parity-check (qLDPC) codes. In many settings, surgery exhibits practical space overheads, while its time overhead remains a bottleneck at $O(d)$ syndrome rounds per operation. In this work, we construct surgery gadgets that perform parallel logical measurements on 2D hypergraph product codes in constant time overhead ($O(1)$) and near-constant space overhead ($\tilde{O}(1)$). The reduced time overhead is a result of amortization, as we show, following the formulation by Cowtan et al. (arXiv:2510.14895), that performing $d$ surgery operations in $O(d)$ time is fault tolerant. Our gadgets combine the strengths of different approaches to fault-tolerant logical operations: they partially retain the flexibility of surgery while achieving overheads comparable to transversal gates. Consequently, they are well-suited for near-term experimental realization and demonstrate new possibilities in the design of gadgets for fast logical computation. |
| title | Constant-Time Surgery on 2D Hypergraph Product Codes with Near-Constant Space Overhead |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.02157 |