Fold-Transversal Clifford Gates for Quantum Codes

Nikolas P. Breuckmann; Simon Burton

doi:10.22331/q-2024-06-13-1372

Fold-Transversal Clifford Gates for Quantum Codes

Nikolas P. Breuckmann¹ and Simon Burton²

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

Quantum error correcting codes (QECCs) encode quantum information into the non-local degrees of freedom of a many-body system. It is widely accepted that QECCs will play a crucial role in the development of scalable quantum computers.
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

@article{Breuckmann2024foldtransversal,
  doi = {10.22331/q-2024-06-13-1372},
  url = {https://doi.org/10.22331/q-2024-06-13-1372},
  title = {Fold-{T}ransversal {C}lifford {G}ates for {Q}uantum {C}odes},
  author = {Breuckmann, Nikolas P. and Burton, Simon},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1372},
  month = jun,
  year = {2024}
}

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