Competing automorphisms and disordered Floquet codes

• URL: http://arxiv.org/abs/2410.02398v2
• Date: Fri, 06 Jun 2025 10:03:18 GMT
• Title: Competing automorphisms and disordered Floquet codes
• Authors: Cory T. Aitchison, Benjamin Béri,
• Abstract summary: We study Floquet codes where automorphisms have atemporally heterogeneous distribution -- automorphisms "compete"<n>This perspective can explain the protection or measurement of logical information in a dynamic automorphism (DA) code when subjected to a noise model of missing measurements.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Topological order is a promising basis for quantum error correction, a key milestone towards large-scale quantum computing. Floquet codes provide a dynamical scheme for this while also exhibiting Floquet-enriched topological order (FET) where anyons periodically undergo a measurement-induced automorphism that acts uniformly in space. We study disordered Floquet codes where automorphisms have a spatiotemporally heterogeneous distribution -- the automorphisms "compete". We characterize the effect of this competition, showing how key features of the purification dynamics of mixed codestates can be inferred from anyon and automorphism properties for any Abelian topological order. This perspective can explain the protection or measurement of logical information in a dynamic automorphism (DA) code when subjected to a noise model of missing measurements. We demonstrate this using a DA color code with perturbed measurement sequences. The framework of competing automorphisms captures essential features of Floquet codes and robustness to noise, and may elucidate key mechanisms involving topological order, automorphisms, and fault-tolerance.

Related papers

• Automorphism gadgets in homological product codes [0.0]
  We investigate structured homological product codes that admit logical operations arising from permutation symmetries in their input codes.<n>In general, these logical operations can be performed by a combination of physical qubit permutations and a subsystem circuit.<n>Our results further advance the search for practical fault tolerance beyond topological codes in platforms capable of long-range connectivity.
  arXiv  Detail & Related papers  (2025-08-06T18:10:37Z)
• Avoided-crossings, degeneracies and Berry phases in the spectrum of quantum noise through analytic Bloch-Messiah decomposition [49.1574468325115]
  "analytic Bloch-Messiah decomposition" provides approach for characterizing dynamics of quantum optical systems.<n>We show that avoided crossings arise naturally when a single parameter is varied, leading to hypersensitivity of the singular vectors.<n>We highlight the possibility of programming the spectral response of photonic systems through the deliberate design of avoided crossings.
  arXiv  Detail & Related papers  (2025-04-29T13:14:15Z)
• Phases of Floquet code under local decoherence [0.0]
  Floquet code is a dynamical quantum memory with a periodically evolving logical space.<n>We show that below the decoherence threshold, the code is in a robust phase characterized by the anyon automorphism.<n>We analytically show that this diagnostic distinguishes the Floquet code from the toric code under repeated syndrome measurements.
  arXiv  Detail & Related papers  (2025-04-26T22:28:20Z)
• Emergent Topology in Many-Body Dissipative Quantum Matter [0.0]
  We study the dissipative dynamics of pseudo-Hermitian many-body quantum systems. We find the same topological features for a wide range of parameters suggesting that they are universal. In the limit of weak coupling to the bath, topological modes govern the approach to equilibrium.
  arXiv  Detail & Related papers  (2023-11-24T18:15:22Z)
• Floquet codes and phases in twist-defect networks [2.793095554369282]
  We introduce a class of models, dubbed paired twist-defect networks, that generalize the structure of Kitaev's honeycomb model. We show that the Honeycomb Floquet code of Haah and Hastings is governed by an irrational value of the chiral Floquet index.
  arXiv  Detail & Related papers  (2023-03-30T19:05:20Z)
• DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusion [66.21290235237808]
  We introduce an energy constrained diffusion model which encodes a batch of instances from a dataset into evolutionary states. We provide rigorous theory that implies closed-form optimal estimates for the pairwise diffusion strength among arbitrary instance pairs. Experiments highlight the wide applicability of our model as a general-purpose encoder backbone with superior performance in various tasks.
  arXiv  Detail & Related papers  (2023-01-23T15:18:54Z)
• Quantum hypergraph homomorphisms and non-local games [1.0152838128195465]
  We show that notions of quantum hypergraph homomorphisms and quantum hypergraph isomorphisms constitute partial orders and equivalence relations, respectively. Specialising to the case where the underlying hypergraphs arise from non-local games, we define notions of quantum non-local game homomorphisms and quantum non-local game isomorphisms.
  arXiv  Detail & Related papers  (2022-11-09T12:44:24Z)
• Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codes [0.0]
  "Honeycomb code" is a fault-tolerant quantum memory defined by a sequence of checks. We argue that a general framework to understand this code is to consider continuous adiabatic paths of gapped Hamiltonians. We turn this path back into a sequence of checks, constructing an automorphism code closely related to the honeycomb code.
  arXiv  Detail & Related papers  (2022-03-21T17:12:31Z)
• Equivariant Graph Mechanics Networks with Constraints [83.38709956935095]
  We propose Graph Mechanics Network (GMN) which is efficient, equivariant and constraint-aware. GMN represents, by generalized coordinates, the forward kinematics information (positions and velocities) of a structural object. Extensive experiments support the advantages of GMN compared to the state-of-the-art GNNs in terms of prediction accuracy, constraint satisfaction and data efficiency.
  arXiv  Detail & Related papers  (2022-03-12T14:22:14Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Bridging the gap between topological non-Hermitian physics and open quantum systems [62.997667081978825]
  We show how to detect a transition between different topological phases by measuring the response to local perturbations. Our formalism is exemplified in a 1D Hatano-Nelson model, highlighting the difference between the bosonic and fermionic cases.
  arXiv  Detail & Related papers  (2021-09-22T18:00:17Z)
• Topographic VAEs learn Equivariant Capsules [84.33745072274942]
  We introduce the Topographic VAE: a novel method for efficiently training deep generative models with topographically organized latent variables. We show that such a model indeed learns to organize its activations according to salient characteristics such as digit class, width, and style on MNIST. We demonstrate approximate equivariance to complex transformations, expanding upon the capabilities of existing group equivariant neural networks.
  arXiv  Detail & Related papers  (2021-09-03T09:25:57Z)
• Characterizing Topological Excitations of a Long-Range Heisenberg Model with Trapped Ions [0.0]
  We propose a Floquet protocol to realize the antiferromagnetic Heisenberg model with power-law decaying interactions. We show that this model features a quantum phase transition from a liquid to a valence bond solid that spontaneously breaks lattice translational symmetry. We moreover introduce an interferometric protocol to characterize the topological excitations and the bulk topological invariants of the interacting many-body system.
  arXiv  Detail & Related papers  (2020-12-16T19:00:02Z)
• Theory of Anomalous Floquet Higher-Order Topology: Classification, Characterization, and Bulk-Boundary Correspondence [1.9087335681007476]
  We provide a framework to understand anomalous Floquet higher-order topological insulators (AFHOTIs) Such AFHOTIs are defined by their robust, symmetry-protected corner modes pinned at special quasienergies. The corner-mode physics of an AFHOTI is found to be generically indicated by 3D Dirac/Weyl-like topological singularities.
  arXiv  Detail & Related papers  (2020-10-15T18:00:01Z)
• Lorentz Group Equivariant Neural Network for Particle Physics [58.56031187968692]
  We present a neural network architecture that is fully equivariant with respect to transformations under the Lorentz group. For classification tasks in particle physics, we demonstrate that such an equivariant architecture leads to drastically simpler models that have relatively few learnable parameters.
  arXiv  Detail & Related papers  (2020-06-08T17:54:43Z)
• Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems [74.80320120264459]
  We present an approach to learn such motions from a limited number of human demonstrations. The complex motions are encoded as rollouts of a stable dynamical system. The efficacy of this approach is demonstrated through validation on an established benchmark as well demonstrations collected on a real-world robotic system.
  arXiv  Detail & Related papers  (2020-05-27T03:51:57Z)
• Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
  We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
  arXiv  Detail & Related papers  (2020-03-24T17:31:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.