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Register a new userQuantum algorithms for transport coefficients in gauge theories
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In the future, ab initio quantum simulations of heavy ion collisions may become possible with large-scale fault-tolerant quantum computers. We propose a quantum algorithm for studying these collisions by looking at a class of observables requiring dramatically smaller volumes: transport coefficients. These form nonperturbative inputs into theoretical models of heavy ions; thus, their calculation reduces theoretical uncertainties without the need for a full-scale simulation of the collision. We derive the necessary lattice operators in the Hamiltonian formulation and describe how to obtain them on quantum computers. Additionally, we discuss ways to efficiently prepare the relevant thermal state of a gauge theory.
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Quantum technologies offer the prospect to efficiently simulate sign-problem afflicted regimes in lattice field theory, such as the presence of topological terms, chemical potentials, and out-of-equilibrium dynamics. In this work, we derive the 3+1D topological $theta$-term for Abelian and non-Abelian lattice gauge theories in the Hamiltonian formulation, paving the way towards Hamiltonian-based simulations of such terms on quantum and classical computers. We further study numerically the zero-temperature phase structure of a 3+1D U(1) lattice gauge theory with the $theta$-term via exact diagonalization for a single periodic cube. In the strong coupling regime, our results suggest the occurrence of a phase transition at constant values of $theta$, as indicated by an avoided level-crossing and abrupt changes in the plaquette expectation value, the electric energy density, and the topological charge density. These results could in principle be cross-checked by the recently developed 3+1D tensor network methods and quantum simulations, once sufficient resources become available.
A conceptually simple model for strongly interacting compact U(1) lattice gauge theory is expressed as operators acting on qubits. The number of independent gauge links is reduced to its minimum through the use of Gausss law. The model can be implemented with any number of qubits per gauge link, and a choice as small as two is shown to be useful. Real-time propagation and real-time collisions are observed on lattices in two spatial dimensions. The extension to three spatial dimensions is also developed, and a first look at 3-dimensional real-time dynamics is presented.
The solution of gauge theories is one of the most promising applications of quantum technologies. Here, we discuss the approach to the continuum limit for $U(1)$ gauge theories regularized via finite-dimensional Hilbert spaces of quantum spin-$S$ operators, known as quantum link models. For quantum electrodynamics (QED) in one spatial dimension, we numerically demonstrate the continuum limit by extrapolating the ground state energy, the scalar, and the vector meson masses to large spin lengths $S$, large volume $N$, and vanishing lattice spacing $a$. By analytically solving Gauss law for arbitrary $S$, we obtain a generalized PXP spin model and count the physical Hilbert space dimension analytically. This allows us to quantify the required resources for reliable extrapolations to the continuum limit on quantum devices. We use a functional integral approach to relate the model with large values of half-integer spins to the physics at topological angle $Theta=pi$. Our findings indicate that quantum devices will in the foreseeable future be able to quantitatively probe the QED regime with quantum link models.
A thermal gradient and/or a chemical potential gradient in a conducting medium can lead to an electric field, an effect known as thermoelectric effect or Seebeck effect. In the context of heavy-ion collisions, we estimate the thermoelectric transport coefficients for quark matter within the ambit of the Nambu-Jona Lasinio (NJL) model. We estimate the thermal conductivity, electrical conductivity, and the Seebeck coefficient of hot and dense quark matter. These coefficients are calculated using the relativistic Boltzmann transport equation within relaxation time approximation. The relaxation times for the quarks are estimated from the quark-quark and quark-antiquark scattering through in-medium meson exchange within the NJL model.
QCD monopoles are magnetically charged quasiparticles whose Bose-Einstein condensation (BEC) at $T<T_c$ creates electric confinement and flux tubes. The magnetic scenario of QCD proposes that scattering on the non-condensed component of the monopole ensemble at $T>T_c$ plays an important role in explaining the properties of strongly coupled quark-gluon plasma (sQGP) near the deconfinement temperature. In this paper, we study the phenomenon of chiral symmetry breaking and its relation to magnetic monopoles. Specifically, we study the eigenvalue spectrum of the Dirac operator in the basis of fermionic zero modes in an SU(2) monopole background. We find that as the temperature approaches the deconfinement temperature $T_c$ from above, the eigenvalue spectrum has a finite density at $omega = 0$, indicating the presence of a chiral condensate. In addition, we find the critical scaling of the eigenvalue gap to be consistent with that of the correlation length in the 3d Ising model and the BEC transition of monopoles on the lattice.
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