Symmetry defects and gauging for quantum states with matrix product unitary symmetries

• URL: http://arxiv.org/abs/2502.20257v1
• Date: Thu, 27 Feb 2025 16:45:33 GMT
• Title: Symmetry defects and gauging for quantum states with matrix product unitary symmetries
• Authors: Adrián Franco-Rubio, Arkadiusz Bochniak, J. Ignacio Cirac,
• Abstract summary: We study the consequences of the existence of a finite group of matrix product unitary (MPU) symmetries for matrix product states (MPS)<n>We introduce a condition, block independence, under which we can gauge the symmetries by promoting the symmetry defects to gauge degrees of freedom.
• Score: 0.3277163122167433
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, we examine the consequences of the existence of a finite group of matrix product unitary (MPU) symmetries for matrix product states (MPS). We generalize the well-understood picture of onsite unitary symmetries, which give rise to virtual symmetry defects given by insertions of operators in the bonds of the MPS. In the MPU case, we can define analogous defect tensors, this time sitting on lattice sites, that can be created, moved, and fused by local unitary operators. We leverage this formalism to study the gauging of MPU symmetries. We introduce a condition, block independence, under which we can gauge the symmetries by promoting the symmetry defects to gauge degrees of freedom, yielding an MPS of the same bond dimension that supports a local version of the symmetry given by commuting gauge constraints. Whenever block independence does not hold (which happens, in particular, whenever the symmetry representation is anomalous), a modification of our method which we call state-level gauging still gives rise to a locally symmetric MPS by promotion of the symmetry defects, at the expense of producing gauge constraints that do not commute on different sites.

Related papers

• Eigenmodes of latent-symmetric quantum photonic networks [37.69303106863453]
  We study the eigenmodes of a 9-site latent-symmetric photonic network. Latent symmetries introduce a powerful new set of tools to the design of systems with desired functionality on any nanophotonic platform.
  arXiv  Detail & Related papers  (2025-01-22T17:21:21Z)
• Entanglement asymmetry and symmetry defects in boundary conformal field theory [0.0]
  A state in a quantum system with a given global symmetry, $G$, can be sensitive to the presence of boundaries. We investigate how conformal invariant boundary conditions influence the symmetry breaking for both finite and compact Lie groups. We further explore the entanglement asymmetry following a global quantum quench, where a symmetry-broken state evolves under a symmetry-restoring Hamiltonian.
  arXiv  Detail & Related papers  (2024-11-14T20:05:25Z)
• Variational Inference Failures Under Model Symmetries: Permutation Invariant Posteriors for Bayesian Neural Networks [43.88179780450706]
  We investigate the impact of weight space permutation symmetries on variational inference. We devise a symmetric symmetrization mechanism for constructing permutation invariant variational posteriors. We show that the symmetrized distribution has a strictly better fit to the true posterior, and that it can be trained using the original ELBO objective.
  arXiv  Detail & Related papers  (2024-08-10T09:06:34Z)
• Symmetry-restricted quantum circuits are still well-behaved [45.89137831674385]
  We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2n)$. It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space.
  arXiv  Detail & Related papers  (2024-02-26T06:23:39Z)
• Latent Space Symmetry Discovery [31.28537696897416]
  We propose a novel generative model, Latent LieGAN, which can discover symmetries of nonlinear group actions. We show that our model can express nonlinear symmetries under some conditions about the group action. LaLiGAN also results in a well-structured latent space that is useful for downstream tasks including equation discovery and long-term forecasting.
  arXiv  Detail & Related papers  (2023-09-29T19:33:01Z)
• Identifying the Group-Theoretic Structure of Machine-Learned Symmetries [41.56233403862961]
  We propose methods for examining and identifying the group-theoretic structure of such machine-learned symmetries. As an application to particle physics, we demonstrate the identification of the residual symmetries after the spontaneous breaking of non-Abelian gauge symmetries.
  arXiv  Detail & Related papers  (2023-09-14T17:03:50Z)
• Gauging quantum states with non-anomalous matrix product operator symmetries [0.0]
  In quantum systems there can be obstructions to gauging a global symmetry. In this manuscript we study non-local symmetries that have an additional structure: they take the form of a matrix product operator (MPO) We show that our gauging procedure satisfies all the desired properties as the standard on-site case does.
  arXiv  Detail & Related papers  (2022-09-15T15:11:20Z)
• Entanglement-enabled symmetry-breaking orders [0.0]
  A spontaneous symmetry-breaking order is conventionally described by a tensor-product wave-function of some few-body clusters. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any tensor-product state.
  arXiv  Detail & Related papers  (2022-07-18T18:00:00Z)
• Noise-resilient Edge Modes on a Chain of Superconducting Qubits [103.93329374521808]
  Inherent symmetry of a quantum system may protect its otherwise fragile states. We implement the one-dimensional kicked Ising model which exhibits non-local Majorana edge modes (MEMs) with $mathbbZ$ parity symmetry. MEMs are found to be resilient against certain symmetry-breaking noise owing to a prethermalization mechanism.
  arXiv  Detail & Related papers  (2022-04-24T22:34:15Z)
• Classifying phases protected by matrix product operator symmetries using matrix product states [0.0]
  We classify the different ways in which matrix product states (MPSs) can stay invariant under the action of matrix product operator (MPO) symmetries. This is achieved through a local characterization of how the MPSs, that generate a ground space, remain invariant under a global MPO symmetry.
  arXiv  Detail & Related papers  (2022-03-23T17:25:30Z)
• Symmetry protected entanglement in random mixed states [0.0]
  We study the effect of symmetry on tripartite entanglement properties of typical states in symmetric sectors of Hilbert space. In particular, we consider Abelian symmetries and derive an explicit expression for the logarithmic entanglement negativity of systems with $mathbbZ_N$ and $U(1)$ symmetry groups.
  arXiv  Detail & Related papers  (2021-11-30T19:00:07Z)

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.