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arXiv · 2402.15386

Low-Weight High-Distance Error Correcting Fermionic Encodings

Fedor Simkovic IV·Martin Leib·Francisco Revson F. Pereira
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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 $d\leq4$ 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 $d\leq7$; 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.

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Fedor Simkovic IV, Martin Leib, Francisco Revson F. Pereira. 2024-02-23. Low-Weight High-Distance Error Correcting Fermionic Encodings. https://arxiv.org/abs/2402.15386

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