Error correction and quantum information spreading on sparse random graphs
Abstract
Quantum error-correcting codes on graph geometries beyond regular euclidean lattices have emerged as a promising route toward robust quantum information processing. A major challenge in quantum error correction is the trade-off between favorable properties of codes constructed in high dimensionality and the need for locality in practical implementations on near-term hardware. Sparse intermediate geometries may combine the advantages of both, but how their structure governs quantum information dynamics and code performance remains unclear. Here we show that the spectral dimension ds, defined from the low-energy spectrum of the graph Laplacian, is the universal parameter connecting these properties. Using Floquet random Clifford circuits on two distinct sparse graph architectures with tunable spectral dimension, we find that ds governs both quantum information spreading and the scaling of the resulting quantum error-correcting code distance. We identify a geometry-induced entanglement phase transition from localized area-law to ergodic volume-law, whose universality is determined by ds and exhibits long-range percolation criticality. In the ergodic phase, the circuit acts as a CSS code encoder whose code distance is set by the competition between two logical sectors --- the cost of severing the graph and the length of its shortest winding cycle --- which connectivity pushes in opposite directions. The spectral dimension organizes this trade-off, highlighting a maximum at intermediate ds retaining sparse connectivity and physical realizability.
Related
- Quantum information spreading via higher-order operator correlators
- Growth and spreading of quantum resources under random circuit dynamics
- Higher-order quantum information inequalities and error-correction of non-Markovian noise
- Operator spreading in random unitary circuits with orthogonal/symplectic-invariant gate distributions
- Partial projected ensembles reveal slow tilt-constrained information spreading
BibTeX
@misc{cemin2026error,
title = {{Error correction and quantum information spreading on sparse random graphs}},
author = {Giovanni Cemin and Marin Bukov and Andrea Solfanelli},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12597},
eprint = {2610.12597},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12597},
}
RIS
TY - UNPB
TI - Error correction and quantum information spreading on sparse random graphs
AU - Giovanni Cemin
AU - Marin Bukov
AU - Andrea Solfanelli
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12597
UR - https://arxiv.org/abs/2610.12597
AB - Quantum error-correcting codes on graph geometries beyond regular euclidean lattices have emerged as a promising route toward robust quantum information processing. A major challenge in quantum error correction is the trade-off between favorable properties of codes constructed in high dimensionality and the need for locality in practical implementations on near-term hardware. Sparse intermediate geometries may combine the advantages of both, but how their structure governs quantum information dynamics and code performance remains unclear. Here we show that the spectral dimension d_s, defined from the low-energy spectrum of the graph Laplacian, is the universal parameter connecting these properties. Using Floquet random Clifford circuits on two distinct sparse graph architectures with tunable spectral dimension, we find that d_s governs both quantum information spreading and the scaling of the resulting quantum error-correcting code distance. We identify a geometry-induced entanglement phase transition from localized area-law to ergodic volume-law, whose universality is determined by d_s and exhibits long-range percolation criticality. In the ergodic phase, the circuit acts as a CSS code encoder whose code distance is set by the competition between two logical sectors --- the cost of severing the graph and the length of its shortest winding cycle --- which connectivity pushes in opposite directions. The spectral dimension organizes this trade-off, highlighting a maximum at intermediate d_s retaining sparse connectivity and physical realizability.
ER -