Generating Fault-Tolerant Cluster States from Crystal Structures

Michael Newman; Leonardo Andreta de Castro; Kenneth R. Brown

doi:10.22331/q-2020-07-13-295

Generating Fault-Tolerant Cluster States from Crystal Structures

Michael Newman¹, Leonardo Andreta de Castro^1,2, and Kenneth R. Brown¹

¹Departments of Electrical and Computer Engineering, Chemistry, and Physics, Duke University, Durham, NC, 27708, USA
²Q-CTRL Pty Ltd, Sydney, NSW, Australia

Published:	2020-07-13, volume 4, page 295
Eprint:	arXiv:1909.11817v2
Doi:	https://doi.org/10.22331/q-2020-07-13-295
Citation:	Quantum 4, 295 (2020).

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Abstract

Measurement-based quantum computing (MBQC) is a promising alternative to traditional circuit-based quantum computing predicated on the construction and measurement of cluster states. Recent work has demonstrated that MBQC provides a more general framework for fault-tolerance that extends beyond foliated quantum error-correcting codes. We systematically expand on that paradigm, and use combinatorial tiling theory to study and construct new examples of fault-tolerant cluster states derived from crystal structures. Included among these is a robust self-dual cluster state requiring only degree-$3$ connectivity. We benchmark several of these cluster states in the presence of circuit-level noise, and find a variety of promising candidates whose performance depends on the specifics of the noise model. By eschewing the distinction between data and ancilla, this malleable framework lays a foundation for the development of creative and competitive fault-tolerance schemes beyond conventional error-correcting codes.

Featured image: Decoder graphs for a cluster state built from the srs tiling in both phenomenological (left) and circuit-level (right) error models. Vertices represent local correlations used to correct errors, while edges represent linear-probability faults. In the phenomenological setting, the absence of correlated errors yields robust error-correction. In the circuit-level setting, construction of the cluster state itself yields a complicated network of correlated errors (red edges). Balancing the robustness of a cluster state with the complexity of its construction is key to tailoring measurement-based error-correction to different noise profiles.

► BibTeX data

@article{Newman2020generatingfault,
  doi = {10.22331/q-2020-07-13-295},
  url = {https://doi.org/10.22331/q-2020-07-13-295},
  title = {Generating {F}ault-{T}olerant {C}luster {S}tates from {C}rystal {S}tructures},
  author = {Newman, Michael and de Castro, Leonardo Andreta and Brown, Kenneth R.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {295},
  month = jul,
  year = {2020}
}

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[2] V. A. Bogatyrev, S. V. Bogatyrev, and A. V. Bogatyrev, Communications in Computer and Information Science 1748, 122 (2023) ISBN:978-3-031-30647-1.

[3] Kyungjoo Noh, Christopher Chamberland, and Fernando G.S.L. Brandão, "Low-Overhead Fault-Tolerant Quantum Error Correction with the Surface-GKP Code", PRX Quantum 3 1, 010315 (2022).

[4] Stefano Paesani and Benjamin J. Brown, "High-Threshold Quantum Computing by Fusing One-Dimensional Cluster States", Physical Review Letters 131 12, 120603 (2023).

[5] Matthias C. Löbl, Stefano Paesani, and Anders S. Sørensen, "Loss-tolerant architecture for quantum computing with quantum emitters", Quantum 8, 1302 (2024).

[6] Hassan Shapourian and Alireza Shabani, "Modular architectures to deterministically generate graph states", Quantum 7, 935 (2023).

[7] Héctor Bombín, Chris Dawson, Ryan V. Mishmash, Naomi Nickerson, Fernando Pastawski, and Sam Roberts, "Logical Blocks for Fault-Tolerant Topological Quantum Computation", PRX Quantum 4 2, 020303 (2023).

[8] Rui Chao, Michael E. Beverland, Nicolas Delfosse, and Jeongwan Haah, "Optimization of the surface code design for Majorana-based qubits", Quantum 4, 352 (2020).

[9] Zhaoyi Li, Issac Kim, and Patrick Hayden, 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) 773 (2022) ISBN:978-1-6654-9113-6.

[10] Jahan Claes, J. Eli Bourassa, and Shruti Puri, "Tailored cluster states with high threshold under biased noise", npj Quantum Information 9 1, 9 (2023).

[11] Zhaoyi Li, Isaac Kim, and Patrick Hayden, "Concatenation Schemes for Topological Fault-tolerant Quantum Error Correction", Quantum 7, 1089 (2023).

[12] N. Coste, D. A. Fioretto, N. Belabas, S. C. Wein, P. Hilaire, R. Frantzeskakis, M. Gundin, B. Goes, N. Somaschi, M. Morassi, A. Lemaître, I. Sagnes, A. Harouri, S. E. Economou, A. Auffeves, O. Krebs, L. Lanco, and P. Senellart, "High-rate entanglement between a semiconductor spin and indistinguishable photons", Nature Photonics 17 7, 582 (2023).

[13] Sam Roberts and Dominic J. Williamson, "3-Fermion Topological Quantum Computation", PRX Quantum 5 1, 010315 (2024).

[14] Benjamin J. Brown and Sam Roberts, "Universal fault-tolerant measurement-based quantum computation", Physical Review Research 2 3, 033305 (2020).

[15] Armanda O. Quintavalle, Michael Vasmer, Joschka Roffe, and Earl T. Campbell, "Single-Shot Error Correction of Three-Dimensional Homological Product Codes", PRX Quantum 2 2, 020340 (2021).

[16] Cupjin Huang, Xiaotong Ni, Fang Zhang, Michael Newman, Dawei Ding, Xun Gao, Tenghui Wang, Hui-Hai Zhao, Feng Wu, Gengyan Zhang, Chunqing Deng, Hsiang-Sheng Ku, Jianxin Chen, and Yaoyun Shi, "Alibaba Cloud Quantum Development Platform: Surface Code Simulations with Crosstalk", arXiv:2002.08918, (2020).

[17] Hayata Yamasaki, Kosuke Fukui, Yuki Takeuchi, Seiichiro Tani, and Masato Koashi, "Polylog-overhead highly fault-tolerant measurement-based quantum computation: all-Gaussian implementation with Gottesman-Kitaev-Preskill code", arXiv:2006.05416, (2020).

[18] Benjamin J. Brown and Sam Roberts, "Universal fault-tolerant measurement-based quantum computation", arXiv:1811.11780, (2018).

[19] Ye Wang, Mu Qiao, Zhengyang Cai, Kuan Zhang, Naijun Jin, Pengfei Wang, Wentao Chen, Chunyang Luan, Haiyan Wang, Yipu Song, Dahyun Yum, and Kihwan Kim, "Realization of two-dimensional crystal of ions in a monolithic Paul trap", arXiv:1912.04262, (2019).

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