Lifted surgery: Fast processing with QLDPC codes

Quantum low-density parity-check (QLDPC) codes are highly efficient for fault-tolerant quantum computing, but performing logical operations on them remains computationally expensive. Standard code surgery, the primary technique for these measurements, requires repeated rounds of syndrome extraction proportional to the code distance, creating a significant time overhead. The authors seek to develop a faster, more parallelizable surgery method that maintains the low physical overhead of QLDPC codes.

The authors introduce "lifted surgery," a framework that exploits the algebraic symmetries inherent in Abelian group algebra codes. By decomposing the codespace into independent blocks using techniques from commutative algebra, the authors transform the complex problem of finding efficient surgery operations into a tractable computational task. They define lifted surgery as a chain map between the code and an auxiliary system, allowing them to classify and search for optimal surgery operations that preserve code distance while minimizing check weights.

Lifted surgery allows for fast, parallel, and addressable logical measurements. For specific quantum radial codes, such as the [[90, 8, 10]] and [[198, 8, 16]] instances, the authors demonstrate that arbitrary sets of independent logical operators can be measured in a single round of syndrome extraction. Numerical simulations under circuit-level depolarizing noise show that for the [[90, 8, 10]] code, lifted surgery performs comparably to standard code surgery but requires ten times fewer rounds of syndrome measurement. Furthermore, the authors generalize this to "bridged" lifted surgery, enabling joint measurements across separate code blocks.

This work provides a practical, scalable path toward low-overhead fault-tolerant quantum computing. By reducing the time cost of logical operations—a major bottleneck for QLDPC-based architectures—lifted surgery makes utility-scale quantum algorithms more feasible. The reliance on group algebra symmetries also makes this approach particularly well-suited for hardware platforms with reconfigurable connectivity, such as neutral atoms and trapped ions.