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arXiv:2001.10002 · International Symposium on Lattice Field Theory (LATTICE)

$(1+1)$-d $U(1)$ Quantum Link Models from Effective Hamiltonians of Dipolar Molecules

Jiayu Shen, Di Luo, Michael Highman, Bryan K. Clark, Brian DeMarco, Aida X El-Khadra, Bryce Gadway

Published Jan 26, 2020• 2 citations
arXivHTMLPDF

Abstract

We study the promising idea of using dipolar molecular systems as analog quantum simulators for quantum link models, which are discrete versions of lattice gauge theories. In a quantum link model the link variables have a finite number of degrees of freedom and discrete values. We construct the effective Hamiltonian of a system of dipolar molecules with electric dipole-dipole interactions, where we use the tunable parameters of the system to match it to the target Hamiltonian describing a $U(1)$ quantum link model in $1+1$ dimensions.

DOI
10.22323/1.363.0125

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(1+1)(1+1)(1+1)-d U(1)U(1)U(1) Quantum Link Models from Effective Hamiltonians of Dipolar Molecules
We study the promising idea of using dipolar molecular systems as analog quantum simulators for quantum link models, which are discrete versions of lattice gauge theories. In a quantum link model the link variables have a finite number of degrees of freedom and discrete values. We construct the effective Hamiltonian of a system of dipolar molecules with electric dipole-dipole interactions, where we use the tunable parameters of the system to match it to the target Hamiltonian describing a U(1)U(1)U(1) quantum link model in 1+11+11+1 dimensions.
Gauge theories appear broadly in physics, ranging from the standard model of particle physics to long-wavelength descriptions of topological systems in condensed matter. However, systems with sign problems are largely inaccessible to classical computations and also beyond the current limitations of digital quantum hardware. In this work, we develop an analog approach to simulating gauge theories with an experimental setup that employs dipolar spins (molecules or Rydberg atoms). We consider molecules fixed in space and interacting through dipole-dipole interactions, avoiding the need for itinerant degrees of freedom. Each molecule represents either a site or gauge degree of freedom, and Gauss's law is preserved by a direct and programmatic tuning of positions and internal state energies. This approach can be regarded as a form of analog systems programming and charts a path forward for near-term quantum simulation. As a first step, we numerically validate this scheme in a small-system study of U(1)\mathrm{U}(1)U(1) quantum link models in (1+11+11+1) dimensions with link spin S=1/2S=1/2S=1/2 and S=1S=1S=1 and illustrate how dynamical phenomena such as string inversion and string breaking could be observed in near-term experiments. Our work brings together methods from atomic and molecular physics, condensed matter physics, high-energy physics, and quantum information science for the study of nonperturbative processes in gauge theories.
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Photonic Analog Quantum Simulation of (1+1)-Dimensional U(1)U(1)U(1) Lattice Gauge Theory with Dynamical Matter
We propose a photonic scheme for analog quantum simulation of a U(1)U(1)U(1) Lattice Gauge Theory (LGT) with dynamical matter based on the Jaynes-Cummings-Hubbard (JCH) model. Here, an array of interacting cavities in the strong-coupling regime of cavity Quantum Electrodynamics is mapped onto the alternating matter and gauge-field sites of the spin-1/2 Quantum Link Model. In contrast to other analog LGT quantum simulation methods, our approach implements the desired gauge-invariant dynamics through the hopping of polaritonic excitations among the array sites. The hopping is mapped to the gauge theory via precise tuning of polaritonic resonances in individual cavities. Using exact diagonalization, we show that the real-time evolution of the JCH model accurately replicates that of a Quantum Link Model. Finally, we discuss feasible routes to the beyond-classical simulation capability with scalable implementations in photonic and superconducting systems. This provides a novel route towards understanding the real-time dynamics of lattice gauge theories with matter in higher dimensions.
State-of-the-art algorithms for simulating fermions coupled to gauge fields often rely on integrating fermion degrees of freedom. While successful in simulating QCD at zero chemical potential, at finite density these approaches are hindered by the sign problem. We discuss the simulation of lattice gauge theories in the Hamiltonian formalism and present a generalized meron-cluster algorithm for the simulation of the U(1)U\left(1\right)U(1) Quantum Link Model for spin 1/21/21/2. This enables the study of models directly relevant to current quantum simulators and is a promising first step toward constructing new efficient algorithms for more complicated gauge theories.
The (2+1)D U(1) pure gauge theory always exists in the confining phase, with strings of non-zero string tension giving a characteristic linear potential between static charges. This makes it a useful testing ground for quantum computing methods designed to study string dynamics of confining gauge theories. Here we implement a minimal U(1) quantum link model on a quantum computer with qubit degrees of freedom representing the dual height variables of the model. This facilitates an efficient realization of plaquette interactions and enables effective calculations of real-time dynamics that are inaccessible to traditional quantum Monte Carlo. A specifically tailored lattice geometry is chosen to match the heavy-hexagonal geometry of the IBM quantum hardware used here, minimizing non-adjacent qubit interactions. By performing quantum quenches from a simple initial string state, we probe the transverse quantum fluctuations of the string before it thermalizes. Our experimental results from digital quantum simulations, with up to 112 qubits, show good agreement with reference tensor-network calculations at short times and with thermal averages at long times. Near the phase transition, the quench dynamics exhibit large fluctuations of the initial string that extend across both spatial dimensions of the lattice. Nonetheless, our error-mitigated estimators from the quantum hardware also give accurate predictions in that regime, with noise-induced violations of local gauge symmetries comparable to finite-bond-dimension tensor-network results.
We use quantum link models to construct a quantum simulator for U(N) and SU(N) lattice gauge theories. These models replace Wilson's classical link variables by quantum link operators, reducing the link Hilbert space to a finite number of dimensions. We show how to embody these quantum link models with fermionic matter with ultracold alkaline-earth atoms using optical lattices. Unlike classical simulations, a quantum simulator does not suffer from sign problems and can thus address the corresponding dynamics in real time. Using exact diagonalization results we show that these systems share qualitative features with QCD, including chiral symmetry breaking and we study the expansion of a chirally restored region in space in real time.