1IBM Research, MIT-IBM Watson AI lab, Cambridge MA, 02142, USA
2Google Quantum AI, Los Angeles, CA, 90291, USA
3School of Mathematical and Physical Sciences, University of Sheffield, Sheffield, UK
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Abstract
Implementing robust quantum error correction (QEC) is imperative for harnessing the promise of quantum technologies. We introduce a framework that takes $any$ classical code and explicitly constructs the corresponding QEC code. Our framework can be seen to generalize the CSS codes, and goes beyond the stabilizer formalism (Fig. 1). A concrete advantage is that the desirable properties of a classical code are automatically incorporated in the design of the resulting quantum code. We reify the theory by various illustrations some of which outperform the best previous constructions. We then introduce a local quantum spin-chain Hamiltonian whose ground space we analytically completely characterize. We utilize our framework to demonstrate that the ground space contains explicit quantum codes with linear distance. This side-steps the Bravyi-Terhal no-go theorem.
Blogpost “Bridging Classical to Quantum Error Correction” by Ramis Movassagh
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Cited by
[1] Nikolas P. Breuckmann and Jens Niklas Eberhardt, “Quantum Low-Density Parity-Check Codes”, PRX Quantum 2 4, 040101 (2021).
[2] Yingkai Ouyang, Yumang Jing, and Gavin K. Brennen, “Measurement-free code-switching for low overhead quantum computation using permutation invariant codes”, arXiv:2411.13142, (2024).
[3] Yingkai Ouyang and Gavin K. Brennen, “Finite-round quantum error correction on symmetric quantum sensors”, arXiv:2212.06285, (2022).
[4] Sergey Bravyi, Dongjin Lee, Zhi Li, and Beni Yoshida, “How much entanglement is needed for quantum error correction?”, arXiv:2405.01332, (2024).
[5] Radu Andrei, Marius Lemm, and Ramis Movassagh, “The spin-one Motzkin chain is gapped for any area weight $t<1$”, arXiv:2204.04517, (2022).
[6] Yingkai Ouyang, “Robust projective measurements through measuring code-inspired observables”, npj Quantum Information 10 1, 104 (2024).
[7] Weishun Zhong, Oles Shtanko, and Ramis Movassagh, “Advantage of Quantum Neural Networks as Quantum Information Decoders”, arXiv:2401.06300, (2024).
[8] Yingkai Ouyang and Peter P. Rohde, “A general framework for the composition of quantum homomorphic encryption & quantum error correction”, arXiv:2204.10471, (2022).
The above citations are from SAO/NASA ADS (last updated successfully 2024-11-27 11:46:19). The list may be incomplete as not all publishers provide suitable and complete citation data.
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This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
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