A Topologically Fault-Tolerant Quantum Computer with Four Dimensional Geometric Codes
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arXiv
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| Autori principali: | , , , , , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916798920654848 |
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| author | Aasen, David Hastings, Matthew B. Kliuchnikov, Vadym Bello-Rivas, Juan M. Paetznick, Adam Chao, Rui Reichardt, Ben W. Zanner, Matt da Silva, Marcus P. Wang, Zhenghan Svore, Krysta M. |
| author_facet | Aasen, David Hastings, Matthew B. Kliuchnikov, Vadym Bello-Rivas, Juan M. Paetznick, Adam Chao, Rui Reichardt, Ben W. Zanner, Matt da Silva, Marcus P. Wang, Zhenghan Svore, Krysta M. |
| contents | Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional self-correcting quantum memory, and present codes targeted to both near-term and utility-scale quantum computers. We identify a full set of logical Clifford operations and with it design a universal fault-tolerant quantum architecture. Our design achieves single-shot error correction, significant reductions in required qubits, and low-depth logical operations. In turn, our proposed architecture relaxes the requirements for achieving fault tolerance and offers an efficient path for realization in several near-term quantum hardware implementations. Our [[96,6,8]] 4D Hadamard lattice code has low weight-6 stabilizers and depth-8 syndrome extraction circuits, a high pseudo-threshold of $\sim 0.01$, and a logical error rate of $\sim 10^{-6}$ per logical qubit per round of error correction at $10^{-3}$ physical error rate under a standard circuit-level noise model. A Clifford-complete logical gate set is presented, including a constructive and efficient method for Clifford gate synthesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15130 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Topologically Fault-Tolerant Quantum Computer with Four Dimensional Geometric Codes Aasen, David Hastings, Matthew B. Kliuchnikov, Vadym Bello-Rivas, Juan M. Paetznick, Adam Chao, Rui Reichardt, Ben W. Zanner, Matt da Silva, Marcus P. Wang, Zhenghan Svore, Krysta M. Quantum Physics Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional self-correcting quantum memory, and present codes targeted to both near-term and utility-scale quantum computers. We identify a full set of logical Clifford operations and with it design a universal fault-tolerant quantum architecture. Our design achieves single-shot error correction, significant reductions in required qubits, and low-depth logical operations. In turn, our proposed architecture relaxes the requirements for achieving fault tolerance and offers an efficient path for realization in several near-term quantum hardware implementations. Our [[96,6,8]] 4D Hadamard lattice code has low weight-6 stabilizers and depth-8 syndrome extraction circuits, a high pseudo-threshold of $\sim 0.01$, and a logical error rate of $\sim 10^{-6}$ per logical qubit per round of error correction at $10^{-3}$ physical error rate under a standard circuit-level noise model. A Clifford-complete logical gate set is presented, including a constructive and efficient method for Clifford gate synthesis. |
| title | A Topologically Fault-Tolerant Quantum Computer with Four Dimensional Geometric Codes |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2506.15130 |