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"Dynamically generated logical qubits", Matthew Hastings, Jeongwan Haah, 2021

Reviewed December 29, 2023

Citation: Hastings, Matthew B., and Jeongwan Haah. "Dynamically generated logical qubits." Quantum 5 (2021): 564.

Web: https://arxiv.org/abs/2107.02194

Tags: Error-correcting-codes, Foundational, Universal-scheme, Floquet-theory

This paper introduced what is now known as the Hastings-Haah code. This is a foundational error correcting code, which has become very influential in the development of the subject. The key point, as observed in the title, is that the qubits are dynamically generated. The stabilizer operations are measured in rounds, and the stabilizers in different rounds do not commute. Hence, the encoding of the logical qubits changes through time. Logical operations can be performed by measuring stabilizers in the correct order.

This code is important in particular because running the code only requires nearest neighbor pairs to perform Pauli measurements - no other gates are needed. Nearest neighbor measurements are operations which are native to the Majorana qubit architecture, and hence this code is the code of choice of Majorana based architectures.