Fold-Transversal Clifford Gates for Quantum Codes
1Department of Computer Science, University College London, WC1E 6BT London, United Kingdom
2Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków, Poland
| Published: | 2024-06-13, volume 8, page 1372 |
| Eprint: | arXiv:2202.06647v3 |
| Doi: | https://doi.org/10.22331/q-2024-06-13-1372 |
| Citation: | Quantum 8, 1372 (2024). |
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Abstract
We generalize the concept of folding from surface codes to CSS codes by considering certain dualities within them. In particular, this gives a general method to implement logical operations in suitable LDPC quantum codes using transversal gates and qubit permutations only.
To demonstrate our approach, we specifically consider a [[30, 8, 3]] hyperbolic quantum code called Bring's code. Further, we show that by restricting the logical subspace of Bring's code to four qubits, we can obtain the $full$ Clifford group on that subspace.
Featured image: In so-called topological quantum codes the symmetries that our construction is based on can have a geometric meaning, such as reflections or folds. However, our approach works more generally for more abstract code constructions.
Popular summary
A key challenge to utilize QECCs is to manipulate the encoded information in a fault-tolerant way. In this work we develop an approach that utilizes symmetries of QECCs to find non-trivial sets of quantum operations that can be implemented very efficiently and fault-tolerantly.
► BibTeX data
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