Quantum Error Correction (QEC) is essential for protecting fragile quantum states against physical noise, a prerequisite for reliable quantum computation. A key component of QEC is syndrome decoding—determining which recovery operation to apply using measured error syndromes. While decoding linear classical codes is NP-complete, the quantum version is #P-complete, presenting an even greater challenge. Achieving practical solutions is therefore critical to unlock the exponential advantages promised by quantum computing.

In this talk, we introduce a new formulation of syndrome decoding for quantum stabilizer codes as a Quadratic Unconstrained Binary Optimization (QUBO) problem. By leveraging well-established QUBO algorithms, this approach allows tuning the trade-off between solution accuracy and algorithm runtime. Preliminary numerical results for various quantum low-density parity-check (qLDPC) codes show robust decoding performance and the emergence of a code-capacity threshold with polynomial runtime.

Zoom Link: https://uky.zoom.us/j/82369158320?pwd=N9RVyw0Gn2g85GKc6ZmSjnSxnz2pjc.1