Circuits Built from Pairwise Difference Conserving Gates: From Loop Symmetries to Localization Transitions
Pavel Orlov
Nanocenter CENN, Slovenia
We introduce a class of dynamical models built from local “pairwise difference conserving” (PDC) gates, which can be defined on arbitrary graphs for both classical and quantum spins. These gates generate an extensive set of conserved loop charges associated with closed paths on the graph, leading to strong fragmentation of the state space into many disconnected dynamical sectors. As an example, we study a classical cellular automaton on a square lattice that exhibits a localization–delocalization transition in information spreading controlled by these charges. The transition is continuous and shows critical behavior similar to second-order phase transitions. Our results identify PDC circuits as a simple framework for studying constrained dynamics, emergent conservation laws, and fragmentation phenomena in both classical and quantum systems.
Related publications:
https://arxiv.org/abs/2509.22368
https://arxiv.org/abs/2510.18992
Constrained dynamics of false vacuum decay in one- and two-dimensional tilted Ising models
Gregor Humar
Complex Matter Department, Jozef Stefan Institute & Nanocenter CENN, Slovenia
False vacuum decay, describing the transition from a metastable state to a true vacuum configuration, is a fundamental non-perturbative phenomenon in quantum field theory and non-equilibrium statistical mechanics, yet remains difficult to study experimentally. Using programmable quantum annealers and numerical simulations we investigate false vacuum decay in tilted Ising models in one and two dimensions. In one-dimensional quantum annealer experiments we directly observe the quantized nucleation of true-vacuum bubbles and develop an effective description that captures their formation and interactions [1]. Extending to two dimensions, we identify a regime where true-vacuum bubbles spread resonantly as the energy gain from the true vacuum compensates the cost of domain-wall creation. This mechanism produces fractal-like growth with a ballistically propagating wavefront that remains robust against disorder and dissipation. Further analysis of the wavefront broadening reveals scaling behaviour consistent with KPZ-type dynamics. These results establish a framework for studying false vacuum decay in large quantum systems.
[1] Vodeb, J. et al. Stirring the false vacuum via interacting quantized bubbles on a 5,564-qubit quantum annealer. Nat. Phys. 21, 386–392 (2025). https://doi.org/10.1038/