Quantum Dual Extended Hamming Code Immune to Collective Coherent Errors

• URL: http://arxiv.org/abs/2503.05249v2
• Date: Fri, 14 Mar 2025 10:41:57 GMT
• Title: Quantum Dual Extended Hamming Code Immune to Collective Coherent Errors
• Authors: En-Jui Chang,
• Abstract summary: We propose a new family of excitation stabilizer codes with parameters $[[2r+1, 2r-(r+1), 4]]$.<n>Compared to the existing $[[20,1,4]]$ CE stabilizer code, our smallest instance, the $[[8,1,4]]$ CE stabilizer code, significantly reduces the number of physical qubits required.
• Score: 0.5439020425819
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Collective coherent (CC) errors are inevitable, as every physical qubit experiences evolution due to its kinetic Hamiltonian. Quantum error correction (QEC) codes are essential in protecting quantum information from both CC and stochastic Pauli errors. While stabilizer codes are designed to correct low-weight stochastic Pauli errors, they are less effective against high-weight errors. Constant excitation (CE) codes, however, are immune to CC errors by ensuring that codewords have constant excitation. However, this comes at the cost of increased qubit overhead, raising the expense of QEC hardware and logical qubit infrastructure. In this work, we propose a new family of CE stabilizer codes with parameters $[[2^{r+1}, 2^r-(r+1), 4]]$. Compared to the existing $[[20,1,4]]$ CE stabilizer code, our smallest instance, the $[[8,1,4]]$ CE stabilizer code, significantly reduces the number of physical qubits required. Furthermore, this new CE code family improves the asymptotics code rate from $\frac{1}{8}$ in our previous work~\cite{2412.16450} to $\frac{1}{2}$, offering a more efficient trade-off between error correction and qubit overhead.

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