High-threshold, low-overhead and single-shot decodable fault-tolerant quantum memory

High-threshold, low-overhead and single-shot decodable fault-tolerant quantum memory

20 Jun 2024 | Thomas R. Scruby, Timo Hillmann, Joschka Roffe
The paper introduces a new family of quantum low-density parity-check (LDPC) codes called radial codes, which are derived from the lifted product of classical quasi-cyclic codes. These codes are defined using a pair of integers $(r, s)$ and have parameters $\lceil 2r^2s, 2(r-1)^2, \leq 2s \rceil$. Numerical studies suggest that these codes have an average distance linear in $s$. Simulations under circuit-level noise show that radial codes achieve comparable error suppression to surface codes of similar distance but use approximately five times fewer physical qubits. The codes support single-shot decoding, which can enable faster logical clock speeds and reduced decoding complexity. The paper describes visual representations, a canonical basis of logical operators, and optimal-length stabilizer measurement circuits for these codes. The tunable parameters and small size of radial codes make them promising candidates for implementation on near-term quantum devices.The paper introduces a new family of quantum low-density parity-check (LDPC) codes called radial codes, which are derived from the lifted product of classical quasi-cyclic codes. These codes are defined using a pair of integers $(r, s)$ and have parameters $\lceil 2r^2s, 2(r-1)^2, \leq 2s \rceil$. Numerical studies suggest that these codes have an average distance linear in $s$. Simulations under circuit-level noise show that radial codes achieve comparable error suppression to surface codes of similar distance but use approximately five times fewer physical qubits. The codes support single-shot decoding, which can enable faster logical clock speeds and reduced decoding complexity. The paper describes visual representations, a canonical basis of logical operators, and optimal-length stabilizer measurement circuits for these codes. The tunable parameters and small size of radial codes make them promising candidates for implementation on near-term quantum devices.
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