Related papers: Spontaneous symmetry breaking in a $SO(3)$ non-Abelian lattice gauge theory in $2+1$D with quantum algorithms

Spontaneous symmetry breaking in a $SO(3)$ non-Abelian lattice gauge theory in $2+1$D with quantum algorithms

URL: http://arxiv.org/abs/2409.07108v1
Date: Wed, 11 Sep 2024 08:55:59 GMT
Title: Spontaneous symmetry breaking in a $SO(3)$ non-Abelian lattice gauge theory in $2+1$D with quantum algorithms
Authors: Sandip Maiti, Debasish Banerjee, Bipasha Chakraborty, Emilie Huffman,
Abstract summary: We study the ability of quantum algorithms to prepare ground states in a matter-free non-Abelian $SO(3)$ lattice gauge theory in $2+1$D. To deal with the large Hilbert space of gauge fields, we demonstrate how the exact imposition of the non-Abelian Gauss Law in the rishon representation of the quantum link operator significantly reduces the degrees of freedom.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: The simulation of various properties of quantum field theories is rapidly becoming a testing ground for demonstrating the prowess of quantum algorithms. Some examples include the preparation of ground states, as well as the investigation of various simple wave packets relevant for scattering phenomena. In this work, we study the ability of quantum algorithms to prepare ground states in a matter-free non-Abelian $SO(3)$ lattice gauge theory in $2+1$D in a phase where the global charge conjugation symmetry is spontaneously broken. This is challenging for two reasons: the necessity of dealing with a large Hilbert space for gauge theories compared to that of quantum spin models, and the closing of the gap between the two ground states which becomes exponentially small as a function of the volume. To deal with the large Hilbert space of gauge fields, we demonstrate how the exact imposition of the non-Abelian Gauss Law in the rishon representation of the quantum link operator significantly reduces the degrees of freedom. Further, to resolve the gap, we introduce symmetry-guided ans\"{a}tze in the Gauss-Law-resolved basis for trial states as the starting point for the quantum algorithms to prepare the two lowest energy states. In addition to simulation results for a range of two-dimensional system sizes, we also provide experimental results from the trapped-ion-based quantum hardware, IonQ, when working on systems with four quantum links. The experimental/simulation results derived from our theoretical developments indicate the role of metrics--such as the energy and the infidelity--to assess the obtained results.

Related papers

Analog Quantum Simulator of a Quantum Field Theory with Fermion-Spin Systems in Silicon [34.80375275076655]
Mapping fermions to qubits is challenging in $2+1$ and higher spacetime dimensions. We propose a native fermion-(large-)spin analog quantum simulator by utilizing dopant arrays in silicon.
arXiv Detail & Related papers (2024-07-03T18:00:52Z)
A vertical gate-defined double quantum dot in a strained germanium double quantum well [48.7576911714538]
Gate-defined quantum dots in silicon-germanium heterostructures have become a compelling platform for quantum computation and simulation. We demonstrate the operation of a gate-defined vertical double quantum dot in a strained germanium double quantum well. We discuss challenges and opportunities and outline potential applications in quantum computing and quantum simulation.
arXiv Detail & Related papers (2023-05-23T13:42:36Z)
Quantum and classical spin network algorithms for $q$-deformed Kogut-Susskind gauge theories [0.0]
We introduce $q$-deformed Kogut-Susskind lattice gauge theories, obtained by deforming the defining symmetry algebra to a quantum group. Our proposal simultaneously provides a controlled regularization of the infinite-dimensional local Hilbert space while preserving essential symmetry-related properties. Our work gives a new perspective for the application of tensor network methods to high-energy physics.
arXiv Detail & Related papers (2023-04-05T15:49:20Z)
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)
Photon-mediated Stroboscopic Quantum Simulation of a $\mathbb{Z}_{2}$ Lattice Gauge Theory [58.720142291102135]
Quantum simulation of lattice gauge theories (LGTs) aims at tackling non-perturbative particle and condensed matter physics. One of the current challenges is to go beyond 1+1 dimensions, where four-body (plaquette) interactions, not contained naturally in quantum simulating devices, appear. We show how to prepare the ground state and measure Wilson loops using state-of-the-art techniques in atomic physics.
arXiv Detail & Related papers (2021-07-27T18:10:08Z)
Gauge equivariant neural networks for quantum lattice gauge theories [2.14192068078728]
Gauge symmetries play a key role in physics appearing in areas such as quantum field theories of the fundamental particles and emergent degrees of freedom in quantum materials. Motivated by the desire to efficiently simulate many-body quantum systems with exact local gauge invariance, gauge equivariant neural-network quantum states are introduced.
arXiv Detail & Related papers (2020-12-09T18:57:02Z)
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)
From the Jaynes-Cummings model to non-Abelian gauge theories: a guided tour for the quantum engineer [0.0]
Non-Abelian lattice gauge theories play a central role in high energy physics, condensed matter and quantum information. We introduce the necessary formalism in well-known Abelian gauge theories, such as the Jaynes-Cumming model. We show that certain minimal non-Abelian lattice gauge theories can be mapped to three or four level systems.
arXiv Detail & Related papers (2020-06-01T20:53:36Z)
Observation of gauge invariance in a 71-site Bose-Hubbard quantum simulator [5.5847872095969375]
Gauge theories implement fundamental laws of physics by local symmetry constraints. In quantum electrodynamics, Gauss's law introduces an intrinsic local relation between charged matter and electromagnetic fields. We simulate gauge-theory dynamics in microscopically engineered quantum devices.
arXiv Detail & Related papers (2020-03-19T18:00:01Z)
Quantum fluctuations of the compact phase space cosmology [0.0]
This article applies effective methods to extract semi-classical regime of quantum dynamics. We find a nontrivial behavior of the fluctuations around the recollapse of the universe. An unexpected relation between the quantum fluctuations of the cosmological sector and the holographic Bousso bound is shown.
arXiv Detail & Related papers (2020-03-18T10:08:11Z)
Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond [46.39654665163597]
We report on experimental tests of topological defect formation via the one-dimensional transverse-field Ising model. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system.
arXiv Detail & Related papers (2020-01-31T02:55:35Z)

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