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Conventional approaches to quantum error correction for fault-tolerant quantum computation are based on encoding a single logical qubit into many physical qubits, resulting in asymptotically zero encoding rates and therefore huge resource overheads. To overcome this issue, high-rate quantum codes, such as quantum low-density parity-check codes, have been studied over the past decade. However, such codes have complex structure, making it difficult to perform logical gate operations in parallel without sacrificing their advantage. Observing the simple structure and high rates of quantum error-detecting codes, here we propose concatenated high-rate quantum error-detecting codes as a new family of high-rate quantum codes. Their simple structure allows for a geometrical interpretation using hypercubes, each of which corresponds to a logical qubit. We thus call them many-hypercube codes. The encoding rate is remarkably high, e.g., 30% (64 logical qubits are encoded into 216 physical qubits). Developing a dedicated high-performance decoder, we achieve high error thresholds even in a circuit-level noise model. Logical gate operations are also parallelizable. Thus, the many-hypercube codes will pave the way to high-performance fault-tolerant quantum computation.
Hayato Goto (Sun,) studied this question.