Constructing quantum codes from any classical code and their embedding in ground space of local Hamiltonians

• URL: http://arxiv.org/abs/2012.01453v3
• Date: Fri, 22 Nov 2024 10:19:50 GMT
• Title: Constructing quantum codes from any classical code and their embedding in ground space of local Hamiltonians
• Authors: Ramis Movassagh, Yingkai Ouyang,
• Abstract summary: We introduce a framework that takes it any classical code and explicitly constructs the corresponding QEC code. A concrete advantage is that the desirable properties of a classical code are automatically incorporated in the design of the resulting quantum code.
• Score: 7.092674229752723
• License:
• Abstract: Implementing robust quantum error correction (QEC) is imperative for harnessing the promise of quantum technologies. We introduce a framework that takes {\it 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.

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