First fault-tolerant quantum memory demonstration for a generalized superfast encoding

Abstract: The Generalized Superfast Encoding (GSE) is a fermion-to-qubit mapping that has error-correcting/detecting properties. To this point, all demonstrations have been relegated to error-detection only, as no fault-tolerance under circuit-level noise has been observed. Here, we introduce an even-distance $d$ constant stabilizer-weight GSE where each of $N$ modes is assigned a $d$-qubit block arranged on a ring. The resulting stabilizer generators have constant weight 4 or 6 for any even distance $d$. Furthermore, the full stabilizer set of this construction can always be partitioned into four qubit-wise commuting groups, which enables compact syndrome-extraction scheduling. We simulate quantum memory experiments under circuit-level depolarizing noise for two instances of this code, $[[48,8,6]]$ and $[[64,8,8]]$ and the threshold is observed to be $\approx 4\times10<sup>{-3}$. This is, to our knowledge, the first fault-tolerant quantum-memory characterization of a fermion-mapping with threshold-like scaling.