
TL;DR
This paper presents a general method to convert any quantum stabilizer code into a local subsystem code with minimal overhead, suitable for hardware with limited connectivity, by leveraging graph embeddings.
Contribution
It introduces a universal recipe for transforming stabilizer codes into local subsystem codes on arbitrary graphs with low overhead and optimal parameters.
Findings
Wire codes enable local implementation of quantum codes on various graphs.
The method achieves linear overhead in check degree and weight for weight reduction.
Codes on hypercubic lattices and expanding graphs attain optimal scaling in fixed dimensions.
Abstract
Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial connectivity. This raises the question of how to realize these codes with minimal overhead under physical hardware connectivity constraints. Here, we introduce a general recipe to transform any quantum stabilizer code into a subsystem code that has local interactions, with weight and degree three, on a given graph. We call the subsystem codes produced by our recipe wire codes, and their code parameters depend on the input code and the given graph. Wire codes can be adapted to have a local implementation on any graph that supports a low-density embedding of the input Tanner graph, with an overhead that depends on the embedding. In particular, applying our results…
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