High-Rate Extended Binomial Codes for Multi-Qubit Encoding

• URL: http://arxiv.org/abs/2501.07093v3
• Date: Tue, 25 Mar 2025 06:49:40 GMT
• Title: High-Rate Extended Binomial Codes for Multi-Qubit Encoding
• Authors: En-Jui Chang,
• Abstract summary: We propose a mapping from qubit quantum error correction codes (QECCs) to bosonic QECCs.<n>Our work can be seen as the bosonic analogue of converting (K) uses of ([N_K,K,D]]) qubit codes into a single use of ([N_K,K,D]]) qubit codes.
• Score: 0.5439020425819
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a mapping from qubit quantum error correction codes (QECCs) to bosonic QECCs, yielding new families of bosonic codes that encode more information per excitation than multiple uses of the well-known binomial codes or permutation-invariant codes. In the asymptotic regime where many logical qubits are encoded, our construction improves the code rate by a factor of \(w+1\), enabling the correction of up to weight-\((w+1)\) amplitude-damping (AD) errors. Moreover, this mapping gives rise to a code family that mitigates undesired dephasing arising from collective coherent (CC) errors. By extending the original binomial codes to allow the simultaneous encoding of multiple logical qubits, our work can be seen as the bosonic analogue of converting \(K\) uses of \([[N_1,1,D]]\) qubit codes into a single use of \([[N_K,K,D]]\) qubit codes, with \(N_K \ll K\cdot N_1\).

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