Low-Weight High-Distance Error Correcting Fermionic Encodings
Abstract
We perform an extended numerical search for practical fermion-to-qubit encodings with error correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high minimum distance, low-weight fermionic logical operators, a small qubit to fermionic mode ratio and a simple qubit connectivity graph including ancilla qubits for the measurement of stabilizers. Our strategy consists of a three-step procedure in which we: first generate encodings with code distances up to by a brute-force enumeration technique; subsequently, we use these encodings as starting points and apply Clifford deformations to them which allows us to identify higher-distance codes with ; finally, we optimize the hardware connectivity graphs of resulting encodings in terms of the graph thickness and the number of connections per qubit. We report multiple promising high-distance encodings which significantly improve the weights of stabilizers and logical operators compared to previously reported alternatives.
Cite
@article{arxiv.2402.15386,
title = {Low-Weight High-Distance Error Correcting Fermionic Encodings},
author = {Fedor Simkovic and Martin Leib and Francisco Revson F. Pereira},
journal= {arXiv preprint arXiv:2402.15386},
year = {2024}
}