arXiv subjects

Avi Vadali

Publications and source records attributed to Avi Vadali.

4 recordsLinked to original sources

arXiv2026

Statistical Mechanics and Symmetries of Non-Abelian Anyon Proliferation: From Deformation to Decoherence

Topological quantum computation relies on braiding non-Abelian anyons, but requires the underlying topological order to survive imperfect state preparation and environmental noise. We show that the instability of topological order to wavefunction deformations and to decoherence, with the latter probed by syndrome distributions, is generically captured by stat-mech models whose $G\times \textrm{Rep}(G)$ symmetry naturally exposes the corrupting anyonic excitations. As an example, we combine this framework with Monte-Carlo simulations to resolve the stability of $D_4$ topological order under deformations and quantum channels that proliferate multiple non-Abelian anyon species that are individually unable to condense. We show that beyond a finite threshold, proliferation of two non-Abelian anyon species parasitically condenses a shared Abelian-anyon fusion outcome---destroying the topological order. Our symmetry-based approach suggests the resulting trivial phase is distinct from that obtained by condensing all Abelian anyons; in other words, the trivial phase "remembers" which anyons condensed. This framework provides a first step into identifying the relevant symmetry for optimal decoders, conditioned on syndrome measurements, of non-Abelian topological order.

quant-ph↗

arXiv2026

Equality of cycle lengths in one- and two-dimensional $σ$ automata

When the game Lights Out is played according to an algorithm specifying the player's sequence of moves, it can be modeled using deterministic cellular automata. One such model reduces to the $σ$ automaton, which evolves according to the 2-dimensional analog of Rule 90. We consider how the cycle lengths of multi-dimensional $σ$ automata depend on their dimension. We find that the cycle lengths of 1-dimensional $σ$ automata and 2-dimensional $σ$ automata (of the same size) are equal, and we prove this by relating the eigenvalues and Jordan blocks of their respective adjacency matrices. We also discover that cycle lengths of higher-dimensional $σ$ automata are bounded (despite the number of lattice sites increasing with dimension) and eventually saturate the upper bound.

cs.FL↗

arXiv2024

Composite subsystem symmetries and decoration of sub-dimensional excitations

Flux binding is a mechanism that is well-understood for global symmetries. Given two systems, each with a global symmetry, gauging the composite symmetry instead of individual symmetries corresponds to the condensation of the composite of gauge charges belonging to individually gauged theories and the binding of the gauge fluxes. The condensed composite charge is created by a "short" string given by the new minimal coupling corresponding to the composite symmetry. This paper studies what happens when combined subsystem symmetries are gauged, especially when the component charges and fluxes have different sub-dimensional mobilities. We investigate $3+1$D systems with planar symmetries where, for example, the planar symmetry of a planon charge is combined with one of the planar symmetries of a fracton charge. We propose the principle of $\textit{Remote Detectability}$ to determine how the fluxes bind and potentially change their mobility. This understanding can then be used to design fracton models with sub-dimensional excitations that are decorated with excitations having nontrivial statistics or non-abelian fusion rules.

cond-mat.str-el↗

arXiv2023

Quantum circuit fidelity estimation using machine learning

The computational power of real-world quantum computers is limited by errors. When using quantum computers to perform algorithms which cannot be efficiently simulated classically, it is important to quantify the accuracy with which the computation has been performed. In this work we introduce a machine-learning-based technique to estimate the fidelity between the state produced by a noisy quantum circuit and the target state corresponding to ideal noise-free computation. Our machine learning model is trained in a supervised manner, using smaller or simpler circuits for which the fidelity can be estimated using other techniques like direct fidelity estimation and quantum state tomography. We demonstrate that, for simulated random quantum circuits with a realistic noise model, the trained model can predict the fidelities of more complicated circuits for which such methods are infeasible. In particular, we show the trained model may make predictions for circuits with higher degrees of entanglement than were available in the training set, and that the model may make predictions for non-Clifford circuits even when the training set included only Clifford-reducible circuits. This empirical demonstration suggests classical machine learning may be useful for making predictions about beyond-classical quantum circuits for some non-trivial problems.

quant-ph↗