Logical fermions for fault-tolerant quantum simulation

TL;DR

This paper introduces a novel method for fault-tolerant quantum simulation that encodes fermions directly into logical Majorana fermions, significantly reducing circuit depth and T-count in quantum algorithms.

Contribution

It presents a new encoding scheme using surface-code twist defects to process fermions directly as logical Majorana fermions, improving efficiency in quantum simulation.

Findings

Reduces quantum circuit depth from O(√N) to O(1) for the Fermi-Hubbard model.

Decreases T-count of the select oracle by 20% with logical fermion encoding.

Enhances locality preservation at the logical level for fermionic simulations.

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.