



01765nas a2200169   4500008004100000245008000041210006900121260001400190300001100204490000600215520126900221100001401490700001501504700001601519700002301535856003701558       2023                        eng d00aQubit-Oscillator Concatenated Codes: Decoding Formalism and Code Comparison0 aQubitOscillator Concatenated Codes Decoding Formalism and Code C  c6/14/2023  a0203420 v43 a<p>Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given that there are several bosonic codes and concatenation schemes to choose from, including the recently discovered Gottesman-Kitaev-Preskill (GKP)&thinsp;&ndash;&thinsp;stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020)] that allow protection of a logical bosonic mode from fluctuations of the conjugate variables of the mode. We develop efficient maximum-likelihood decoders for and analyze the performance of three different concatenations of codes taken from the following set: qubit stabilizer codes, analog or Gaussian stabilizer codes, GKP codes, and GKP-stabilizer codes. We benchmark decoder performance against additive Gaussian white noise, corroborating our numerics with analytical calculations. We observe that the concatenation involving GKP-stabilizer codes outperforms the more conventional concatenation of a qubit stabilizer code with a GKP code in some cases. We also propose a GKP-stabilizer code that suppresses fluctuations in both conjugate variables without extra quadrature squeezing and formulate qudit versions of GKP-stabilizer codes.</p>1 aXu, Yijia1 aWang, Yixu1 aKuo, En-Jui1 aAlbert, Victor, V.  uhttps://arxiv.org/abs/2209.0457301455nas a2200205   4500008004100000245006000041210005900101260001500160520078600175653002100961653002700982653003501009653003001044653003101074653005201105100001601157700002501173700001401198856003701212       2022                        eng d00aError-correcting codes for fermionic quantum simulation0 aErrorcorrecting codes for fermionic quantum simulation  c10/16/20223 a<p>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 &lfloor;d&minus;12&rfloor;-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.</p>10aFOS: Mathematics10aFOS: Physical sciences10aMathematical Physics (math-ph)10aQuantum Algebra (math.QA)10aQuantum Physics (quant-ph)10aStrongly Correlated Electrons (cond-mat.str-el)1 aChen, Yu-An1 aGorshkov, Alexey, V.1 aXu, Yijia  uhttps://arxiv.org/abs/2210.08411