Logical Majorana Fermions for Fault-Tolerant Quantum Simulation

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 the 2D Fermi-Hubbard model as an exemplar, we show two applications of our approach that yield improvements in algorithms. First, by preserving the locality of fundamental fermionic operations, we can reduce the asymptotic circuit depth of a Trotter-Suzuki expansion of the time evolution operator. Second, by working in the paradigm of the Majorana fermion data type, we were able to obtain a T-count reduction for the block-encoding SELECT oracle that can be applied even without the use of the twist-defect/logical Majorana architecture described here.