Topological subsystem bivariate bicycle codes with four-qubit check operators
arXiv:2605.04151
Abstract
High-rate bivariate bicycle (BB) codes are promising low-overhead quantum memories, but their stabilizer checks typically have weight or higher, making syndrome extraction challenging. We introduce subsystem bivariate bicycle (SBB) codes, a translation-invariant CSS subsystem construction that realizes BB-code logical structure using local weight- gauge measurements. Their stabilizer syndromes are inferred by multiplying the corresponding gauge outcomes. We further show that nonlocal stabilizers in translation-invariant CSS subsystem codes can be detected using a determinantal-ideal criterion based on the gauge-operator commutation matrix. When this criterion excludes nonlocal stabilizers, a finite-depth Clifford circuit decouples gauge qubits and identifies the protected subsystem with a corresponding BB stabilizer code. An SBB code is topological, meaning that it has no nontrivial local logical operators, if and only if the corresponding BB code is topological. A finite search yields low-overhead examples including , , and ; the latter encodes six times more logical qubits than a subsystem surface code at the same block length and distance. These results show how gauge degrees of freedom can make high-rate BB logical structure compatible with local weight- syndrome extraction.
7+29 pages, 3+2 figures