Madelyn Cain

High-rate quantum LDPC (qLDPC) codes reduce space overhead by densely packing many logical qubits into a single block of physical qubits. Here we extend such savings to computation by constructing batched fault-tolerant operations that apply the same logical gate across many code blocks in parallel. By leveraging shared physical resources to execute many logical operations in parallel, these operations realize high rates in space-time and significantly reduce computational costs. For arbitrary CSS qLDPC codes, we build batched gadgets with constant space-time overhead for (i) single-shot error correction and state preparation, (ii) code switching, and (iii) addressable Clifford gates. Using these batched gadgets we also construct parallel non-Clifford gates with low space-time cost. We outline principles for designing parallel quantum algorithms optimized for a batched architecture, and show in particular how lattice Hamiltonian dynamical simulations can be compiled efficiently. We also propose a near-term–friendly implementation using new self-dual Bivariate-Bicycle codes with high encoding rates (∼ 1/10), transversal Clifford gates, and global T gates, enabling Hamiltonian simulations with a lower space-time cost than analogous surface-code protocols and low-rate qLDPC protocols. These results open new paths toward scalable quantum computation via co-design of parallel quantum algorithms and high-rate fault-tolerant protocols.