# High-Distance Error-Correcting Codes for Fermion-to-Qubit Mappings in 2D and 3D

## TL;DR

This paper introduces high-distance fermion-to-qubit stabilizer codes for 2D and 3D systems that maintain locality and constant stabilizer weights, enabling scalable quantum simulation of fermionic systems.

## Contribution

It presents the first 3D construction achieving high distance, constant stabilizer weights, and locality preservation simultaneously.

## Key findings

- Achieves arbitrarily large code distances with constant stabilizer weights.
- Maintains locality by mapping local fermionic operators to local qubit operators.
- First 3D construction with high distance, constant weights, and locality preservation.

## Abstract

Quantum simulation of fermionic systems is a leading application of quantum computers. One promising approach is to represent fermions with qubits via fermion-to-qubit mappings. In this work, we present high-distance fermion-to-qubit stabilizer codes for simulating 2D and 3D fermionic systems. These codes achieve arbitrarily large code distances while keeping stabilizer weights constant. They also preserve locality by mapping local fermionic operators to local qubit operators at any fixed distance. Notably, our 3D construction is the first to simultaneously achieve high distance, constant stabilizer weights, and locality preservation. Our construction is based on concatenating a small-distance 2D or 3D fermion-to-qubit code with a high-distance fermionic color code. Together, these features provide a robust and scalable pathway to quantum simulation of fermionic systems.