20 Jun 2024 | Thomas R. Scruby, Timo Hillmann, and Joschka Roffe
This paper introduces a new family of quantum low-density parity-check (LDPC) codes called radial codes, constructed using the lifted product of classical radial codes. These codes have parameters [2r²s, 2(r-1)², ≤2s] and are defined by a pair of integers (r, s). They exhibit single-shot decodability under circuit-level noise, requiring approximately five times fewer physical qubits than surface codes of similar distance. The codes have an intuitive visual representation, a canonical basis of logical operators, and optimal-length stabilizer measurement circuits. Numerical studies suggest that the average distance of these codes is linear in s. The codes are shown to have high error suppression capabilities, with single-shot decoding allowing for faster logical clock speeds and reduced decoding complexity. The paper also discusses the structure of these codes, their parameters, and their potential for implementation on near-term quantum devices. The results show that these codes can achieve competitive error suppression with fewer physical qubits compared to surface codes. The paper concludes that these codes are promising candidates for implementation on small-scale quantum devices due to their small size, flexibility, and powerful error-correction capabilities.This paper introduces a new family of quantum low-density parity-check (LDPC) codes called radial codes, constructed using the lifted product of classical radial codes. These codes have parameters [2r²s, 2(r-1)², ≤2s] and are defined by a pair of integers (r, s). They exhibit single-shot decodability under circuit-level noise, requiring approximately five times fewer physical qubits than surface codes of similar distance. The codes have an intuitive visual representation, a canonical basis of logical operators, and optimal-length stabilizer measurement circuits. Numerical studies suggest that the average distance of these codes is linear in s. The codes are shown to have high error suppression capabilities, with single-shot decoding allowing for faster logical clock speeds and reduced decoding complexity. The paper also discusses the structure of these codes, their parameters, and their potential for implementation on near-term quantum devices. The results show that these codes can achieve competitive error suppression with fewer physical qubits compared to surface codes. The paper concludes that these codes are promising candidates for implementation on small-scale quantum devices due to their small size, flexibility, and powerful error-correction capabilities.