Anomaly inflow, dualities, and quantum simulation of abelian lattice gauge theories induced by measurements

• URL: http://arxiv.org/abs/2402.08720v1
• Date: Tue, 13 Feb 2024 19:00:04 GMT
• Title: Anomaly inflow, dualities, and quantum simulation of abelian lattice gauge theories induced by measurements
• Authors: Takuya Okuda, Aswin Parayil Mana, Hiroki Sukeno
• Abstract summary: We show the anomaly inflow mechanism between the deconfining phase of the simulated gauge theory on the boundary and the SPT state in the bulk. We construct the resource state and the measurement pattern for the measurement-based quantum simulation of a lattice gauge theory with a matter field. We derive precise dualities between partition functions with insertion of defects corresponding to gauging higher-form global symmetries.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A previous work demonstrated that quantum simulation of abelian lattice gauge theories (Wegner models including the toric code in a limit) in general dimensions can be achieved by local adaptive measurements on symmetry-protected topological (SPT) states with higher-form generalized global symmetries. The entanglement structure of the resource SPT state reflects the geometric structure of the gauge theory. In this work, we explicitly demonstrate the anomaly inflow mechanism between the deconfining phase of the simulated gauge theory on the boundary and the SPT state in the bulk, by showing that the anomalous gauge variation of the boundary state obtained by bulk measurement matches that of the bulk theory. Moreover, we construct the resource state and the measurement pattern for the measurement-based quantum simulation of a lattice gauge theory with a matter field (Fradkin-Shenker model), where a simple scheme to protect gauge invariance of the simulated state against errors is proposed. We further consider taking an overlap between the wave function of the resource state for lattice gauge theories and that of a parameterized product state, and we derive precise dualities between partition functions with insertion of defects corresponding to gauging higher-form global symmetries, as well as measurement-induced phases where states induced by a partial overlap possess different (symmetry-protected) topological orders. Measurement-assisted operators to dualize quantum Hamiltonians of lattice gauge theories and their non-invertibility are also presented.

Related papers

• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• Measuring Topological Field Theories: Lattice Models and Field-Theoretic Description [2.541410020898643]
  Recent years have witnessed a surge of interest in performing measurements within topological phases of matter. We present a field-theoretic framework for describing measurements within topological field theories.
  arXiv  Detail & Related papers  (2023-10-26T19:26:04Z)
• Quantum Computation of Thermal Averages for a Non-Abelian $D_4$ Lattice Gauge Theory via Quantum Metropolis Sampling [0.0]
  We show the application of the Quantum Metropolis Sampling (QMS) algorithm to a toy gauge theory with discrete non-Abelian gauge group $D_4$ in (2+1)-dimensions.
  arXiv  Detail & Related papers  (2023-09-13T17:05:03Z)
• Normalizing flows for lattice gauge theory in arbitrary space-time dimension [135.04925500053622]
  Applications of normalizing flows to the sampling of field configurations in lattice gauge theory have so far been explored almost exclusively in two space-time dimensions. We discuss masked autoregressive with tractable and unbiased Jacobian determinants, a key ingredient for scalable and exact flow-based sampling algorithms. For concreteness, results from a proof-of-principle application to SU(3) gauge theory in four space-time dimensions are reported.
  arXiv  Detail & Related papers  (2023-05-03T19:54:04Z)
• Exploring critical systems under measurements and decoherence via Keldysh field theory [0.0]
  We employ an $n$-replica Keldysh field theory to investigate the effects of measurements and decoherence on long distance behaviors of quantum critical states. Low energy effective theories for various scenarios are then derived using the symmetry and fundamental consistency conditions of the Keldysh formalism. Our results demonstrate that the Keldysh formalism is a useful tool for systematically studying the effects of measurements and decoherence on long-wavelength physics.
  arXiv  Detail & Related papers  (2023-04-17T13:48:09Z)
• Measurement-based quantum simulation of Abelian lattice gauge theories [0.0]
  We show that sequential single-qubit measurements with the bases adapted according to the former measurement outcomes induce a deterministic Hamiltonian quantum simulation of the gauge theory on the boundary. We demonstrate that the generalized cluster state has a symmetry-protected topological order with respect to generalized global symmetries.
  arXiv  Detail & Related papers  (2022-10-19T22:14:45Z)
• Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions [51.52945471576731]
  This work presents gauge-equivariant architectures for flow-based sampling in fermionic lattice field theories using pseudofermions as estimators for the fermionic determinant. This is the default approach in state-of-the-art lattice field theory calculations, making this development critical to the practical application of flow models to theories such as QCD.
  arXiv  Detail & Related papers  (2022-07-18T21:13:34Z)
• Boundary theories of critical matchgate tensor networks [59.433172590351234]
  Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model.
  arXiv  Detail & Related papers  (2021-10-06T18:00:03Z)
• Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations [77.34726150561087]
  The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations. Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
  arXiv  Detail & Related papers  (2020-07-20T18:00:02Z)
• Origin of staircase prethermalization in lattice gauge theories [0.0]
  Quantum many-body systems with exact local gauge symmetries exhibit rich out-of-equilibrium physics. We present evidence of textitstaircase prethermalization in a $mathrmZ$ lattice gauge theory.
  arXiv  Detail & Related papers  (2020-04-15T18:00:08Z)
• Tensor network models of AdS/qCFT [69.6561021616688]
  We introduce the notion of a quasiperiodic conformal field theory (qCFT) We show that qCFT can be best understood as belonging to a paradigm of discrete holography.
  arXiv  Detail & Related papers  (2020-04-08T18:00:05Z)

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.