Logical fermions for fault-tolerant quantum simulation
arXiv:2110.10280
Abstract
We show how to absorb fermionic quantum simulation's expensive fermion-to-qubit mapping overhead into the overhead already incurred by surface-code-based fault-tolerant quantum computing. The key idea is to process information in surface-code twist defects, which behave like logical Majorana fermions. Our approach encodes Dirac fermions, a key data type for simulation applications, directly into logical Majorana fermions rather than atop a logical qubit layer in the architecture. Using quantum simulation of the -fermion 2D Fermi-Hubbard model as an exemplar, we demonstrate two immediate algorithmic improvements. First, by preserving the model's locality at the logical level, we reduce the asymptotic Trotter-Suzuki quantum circuit depth from in a typical Jordan-Wigner encoding to in our encoding. Second, by exploiting optimizations manifest for logical fermions but less obvious for logical qubits, we reduce the -count of the block-encoding \textsc{select} oracle by 20\% over standard implementations, even when realized by logical qubits and not logical fermions.
23 pages, 21 figures. v3 streamlines the title and makes minor corrections to the bibliography