A Fully Gauge-Fixed SU(2) Hamiltonian for Quantum Simulations

• URL: http://arxiv.org/abs/2409.10610v1
• Date: Mon, 16 Sep 2024 18:00:03 GMT
• Title: A Fully Gauge-Fixed SU(2) Hamiltonian for Quantum Simulations
• Authors: Dorota M. Grabowska, Christopher F. Kane, Christian W. Bauer,
• Abstract summary: We show how to construct a fully gauge-fixed lattice Hamiltonian for a pure SU(2) gauge theory. Despite the global nature of the final gauge-fixing procedure, this Hamiltonian can be simulated using quantum resources scaling only to the lattice volume.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We demonstrate how to construct a fully gauge-fixed lattice Hamiltonian for a pure SU(2) gauge theory. Our work extends upon previous work, where a formulation of an SU(2) lattice gauge theory was developed that is efficient to simulate at all values of the gauge coupling. That formulation utilized maximal-tree gauge, where all local gauge symmetries are fixed and a residual global gauge symmetry remains. By using the geometric picture of an SU(2) lattice gauge theory as a system of rotating rods, we demonstrate how to fix the remaining global gauge symmetry. In particular, the quantum numbers associated with total charge can be isolated by rotating between the lab and body frames using the three Euler angles. The Hilbert space in this new `sequestered' basis partitions cleanly into sectors with differing total angular momentum, which makes gauge-fixing to a particular total charge sector trivial, particularly for the charge-zero sector. In addition to this sequestered basis inheriting the property of being efficient at all values of the coupling, we show that, despite the global nature of the final gauge-fixing procedure, this Hamiltonian can be simulated using quantum resources scaling only polynomially with the lattice volume.

Related papers

• Quantum computation of SU(2) lattice gauge theory with continuous variables [0.0]
  We present a quantum computational framework for SU(2) lattice gauge theory. We leverage continuous variables instead of discrete qubits to represent the infinite-dimensional Hilbert space of the gauge fields.
  arXiv  Detail & Related papers  (2024-10-18T16:29:39Z)
• 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)
• SU(d)-Symmetric Random Unitaries: Quantum Scrambling, Error Correction, and Machine Learning [11.861283136635837]
  We show that in the presence of SU(d) symmetry, the local conserved quantities would exhibit residual values even at $t rightarrow infty$. We also show that SU(d)-symmetric unitaries can be used to constructally optimal codes. We derive an overpartameterization threshold via the quantum neural kernel.
  arXiv  Detail & Related papers  (2023-09-28T16:12:31Z)
• A new basis for Hamiltonian SU(2) simulations [0.0]
  We develop a new basis suitable for the simulation of an SU(2) lattice gauge theory in the maximal tree gauge. We show how to perform a Hamiltonian truncation so that the eigenvalues of both the magnetic and electric gauge-fixed Hamiltonian are mostly preserved.
  arXiv  Detail & Related papers  (2023-07-21T18:03:26Z)
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders [37.69303106863453]
  We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
  arXiv  Detail & Related papers  (2023-05-11T15:57:27Z)
• A variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: a study of (2+1)-dimensional compact QED with dynamical fermions at finite density [0.7734726150561088]
  We present a variational, sign-problem-free Monte Carlo method for lattice gauge theories with continuous gauge groups. We apply it to (2+1)-dimensional compact QED with dynamical fermions at finite density.
  arXiv  Detail & Related papers  (2023-04-12T15:35:57Z)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory [44.99833362998488]
  We introduce quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple quantum numbers. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories.
  arXiv  Detail & Related papers  (2022-12-28T18:56:25Z)
• Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks [0.0]
  We present a loop-string-hadron (LSH) framework in 1+1 dimensions for describing the dynamics of SU(3) gauge fields coupled to staggered fermions. The LSH approach uses gauge invariant degrees of freedoms such as loop (segments), string (ends), and hadrons, is free of all nonabelian gauge redundancy, and is described by a Hamiltonian containing only local interactions.
  arXiv  Detail & Related papers  (2022-12-08T18:57:47Z)
• 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)
• Complete entropic inequalities for quantum Markov chains [17.21921346541951]
  We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional algebra satisfies a modified log-Sobolev inequality. We also establish the first general approximateization property of relative entropy.
  arXiv  Detail & Related papers  (2021-02-08T11:47:37Z)

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.