Logical fermions for fault-tolerant quantum simulation

• URL: http://arxiv.org/abs/2110.10280v3
• Date: Fri, 7 Jul 2023 00:20:34 GMT
• Title: Logical fermions for fault-tolerant quantum simulation
• Authors: Andrew J. Landahl and Benjamin C. A. Morrison
• Abstract summary: 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. Our approach encodes Dirac fermions, a key data type for simulation applications, directly into logical Majorana fermions.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $N$-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 $\mathcal{O}(\sqrt{N})$ in a typical Jordan-Wigner encoding to $\mathcal{O}(1)$ in our encoding. Second, by exploiting optimizations manifest for logical fermions but less obvious for logical qubits, we reduce the $T$-count of the block-encoding \textsc{select} oracle by 20\% over standard implementations, even when realized by logical qubits and not logical fermions.

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