On the energy barrier of hypergraph product codes

• URL: http://arxiv.org/abs/2407.20526v1
• Date: Tue, 30 Jul 2024 03:59:37 GMT
• Title: On the energy barrier of hypergraph product codes
• Authors: Guangqi Zhao, Andrew C. Doherty, Isaac H. Kim,
• Abstract summary: We prove tight bounds on the energy barrier applicable to any quantum code obtained from the hypergraph product of two classical codes. If the underlying classical codes are low-density parity-check codes (LDPC), the energy barrier of the quantum code is shown to be the minimum energy barrier of the underlying classical codes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A macroscopic energy barrier is a necessary condition for self-correcting quantum memory. In this paper, we prove tight bounds on the energy barrier applicable to any quantum code obtained from the hypergraph product of two classical codes. If the underlying classical codes are low-density parity-check codes (LDPC), the energy barrier of the quantum code is shown to be the minimum energy barrier of the underlying classical codes (and their transposes) up to an additive $O(1)$ constant.

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