Exploring Surface Code Decoding via Cryo-CMOS for Fault-Tolerant Quantum Computers

Surface codes are crucial for fault-tolerant quantum computing (FTQC) and rely on syndrome analysis to identify quantum errors. Superconducting qubits are operating at extremely low temperatures, but the room-temperature syndrome analyzer limits scalability. This paper explores syndrome analysis at an intermediate temperature (around 4 K) and focuses on a hardware-friendly exhaustive search algorithm. Results show that using 4-bit weights enables error correction with a code distance of 5 and a physical error rate of 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−4</sup>. The energy consumption per logical qubit per error correction is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1.13\times 10^{-3}$</tex> nJ, supporting up to 8.86 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\times {10}^{5}$</tex> logical qubits in a cryogenic environment.