Practical Code Surgery with Hypergraph Product Codes

Performing large quantum circuits using noisy qubits and gates will require using quantum error correcting codes and fault-tolerant gadgets, which incur a daunting overhead in practice. Recent works have reduced this overhead via quantum low-density parity check (QLDPC) codes and gadgets such as code surgery. Evaluating the performance of such techniques at a practical scale has significant implications for the future construction of quantum computers.

In this work, we present a collection of code surgery gadgets for hypergraph product (HGP) codes, a class of QLDPC codes. We explicitly construct and analyze a set of logical measurement gadgets for a [[900, 36, 10]] HGP code, and show that the logical error rates of these gadgets is comparable to the memory error rates for this code. We further showcase the design of more complicated Pauli product measurement gadgets from simple gadgets, and demonstrate parallel and low-time overhead surgery methods. These results suggest that HGP codes together with code surgery present a promising path for practical quantum error correction.