Error-correcting codes for fermionic quantum simulation

TitleError-correcting codes for fermionic quantum simulation
Publication TypeJournal Article
Year of Publication2022
AuthorsChen, Y-A, Gorshkov, AV, Xu, Y
Date Published10/16/2022
KeywordsFOS: Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Algebra (math.QA), Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)

We provide ways to simulate fermions by qubits on 2d lattices using Z2 gauge theories (stabilizer codes). By studying the symplectic automorphisms of the Pauli module over the Laurent polynomial ring, we develop a systematic way to increase the code distances of stabilizer codes. We identify a family of stabilizer codes that can be used to simulate fermions with code distances of d=2,3,4,5,6,7 such that any ⌊d−12⌋-qubit error can be corrected. In particular, we demonstrate three stabilizer codes with code distances of d=3, d=4, and d=5, respectively, with all stabilizers and logical operators shown explicitly. The syndromes for all Pauli errors are provided. Finally, we introduce a syndrome-matching method to compute code distances numerically.