Qubitization strategies for bosonic field theories

• URL: http://arxiv.org/abs/2209.00098v1
• Date: Wed, 31 Aug 2022 20:30:42 GMT
• Title: Qubitization strategies for bosonic field theories
• Authors: Andrei Alexandru, Paulo F. Bedaque, Andrea Carosso, Michael J. Cervia, Andy Sheng
• Abstract summary: We show two different truncations that preserve the symmetries of the 1+1-dimensional $O(3)$ non-linear $sigma$-model. We provide evidence that the angular-momentum truncation fails to reproduce the $sigma$-model and that the anti-ferromagnetic fuzzy model agrees with the full theory.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum simulations of bosonic field theories require a truncation in field space to map the theory onto finite quantum registers. Ideally, the truncated theory preserves the symmetries of the original model and has a critical point in the same universality class. In this paper, we explore two different truncations that preserve the symmetries of the 1+1-dimensional $O(3)$ non-linear $\sigma$-model - one that truncates the Hilbert space for the unit sphere by setting an angular momentum cutoff and a fuzzy sphere truncation inspired by non-commutative geometry. We compare the spectrum of the truncated theories in a finite box with the full theory. We use open boundary conditions, a novel method that improves on the correlation lengths accessible in our calculations. We provide evidence that the angular-momentum truncation fails to reproduce the $\sigma$-model and that the anti-ferromagnetic fuzzy model agrees with the full theory.

Related papers

• Two-dimensional Asymptotic Generalized Brillouin Zone Theory [10.66748920431153]
  We show that for any given non-Hermitian Hamiltonian, the corresponding region should be independent of the open boundary geometry. A corollary of our theory is that most symmetry-protected exceptional semimetals should be robust to variations in OBC geometry.
  arXiv  Detail & Related papers  (2023-11-28T15:13:37Z)
• Broken Symmetry and Fractionalized Flux Strings in a Staggered U(1) Pure Gauge Theory [0.0]
  We study the case of $3D$ $mathrmU(1)$ pure gauge theory, simulating the staggered case numerically in its dual formulation. We find evidence of a continuum limit with a spontaneously broken $bbZ$ single-site symmetry, in contrast to the ordinary theory. Moreover, the confining string fractionalizes into multiple strands which separate spatial regions in distinct ground states of the broken symmetry.
  arXiv  Detail & Related papers  (2023-09-29T10:08:21Z)
• 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)
• Quantum quenches in fractonic field theories [0.0]
  We study out-of-equilibrium dynamics caused by global quantum quenches in fractonic scalar field theories. We discuss a generalization to $mathbbZ_n$-symmetric field theories, and introduce a proper regularization.
  arXiv  Detail & Related papers  (2023-06-26T18:00:02Z)
• 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)
• Universality of a truncated sigma-model [0.0]
  Even when regularized using a finite lattice, Bosonic quantum field theories possess an infinite dimensional Hilbert space. A qubitization of the $1+1$ dimensionalally free $sigma$-model based on ideas of non-commutative geometry was previously proposed. We provide evidence that it reproduces the physics of the $sigma$-model both in the infrared and the ultraviolet regimes.
  arXiv  Detail & Related papers  (2021-09-15T18:06:07Z)
• $\PT$ Symmetry and Renormalisation in Quantum Field Theory [62.997667081978825]
  Quantum systems governed by non-Hermitian Hamiltonians with $PT$ symmetry are special in having real energy eigenvalues bounded below and unitary time evolution. We show how $PT$ symmetry may allow interpretations that evade ghosts and instabilities present in an interpretation of the theory within a Hermitian framework.
  arXiv  Detail & Related papers  (2021-03-27T09:46:36Z)
• Quantum simulation of gauge theory via orbifold lattice [47.28069960496992]
  We propose a new framework for simulating $textU(k)$ Yang-Mills theory on a universal quantum computer. We discuss the application of our constructions to computing static properties and real-time dynamics of Yang-Mills theories.
  arXiv  Detail & Related papers  (2020-11-12T18:49:11Z)
• Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We present a family of topological quantum gravity theories associated with the geometric theory of the Ricci flow. First, we use BRST quantization to construct a "primitive" topological Lifshitz-type theory for only the spatial metric. We extend the primitive theory by gauging foliation-preserving spacetime symmetries.
  arXiv  Detail & Related papers  (2020-10-29T06:15:30Z)
• Quantum anomalous Hall phase in synthetic bilayers via twistless twistronics [58.720142291102135]
  We propose quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions. We show that our system exhibits topologicalband structures under appropriate conditions.
  arXiv  Detail & Related papers  (2020-08-06T19:58:05Z)

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.