arXiv subjects

Wolfgang Unger

Publications and source records attributed to Wolfgang Unger.

At least 19 recordsLinked to original sources

arXiv2025

Quantum sampling on a quantum annealer for large volumes in the strong coupling limit for gauge group U(3)

In our previous studies [1, 2], we confirmed that a quantum annealer can be used for importance sampling of gauge theories. In this paper, we extend the previous results to larger 2-dimensional and 4-dimensional lattices to generate ensembles for U(3) gauge theory in the strong coupling limit. We make use of the D-Wave quantum annealer to generate histograms for sub-lattices, and use the Metropolis-Hastings algorithm to determine thermodynamic observables and their dependence on the physical parameters on large volumes. We benchmark our results to those obtained from classical Monte Carlo simulations.

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arXiv2025

The chiral critical point from the strong coupling expansion

The strong coupling expansion for staggered fermions allows for Monte Carlo simulations using a dual representation. It has a mild sign problem for low values of the inverse gauge coupling $β$, hence the phase diagram in the full $μ_B - T$ plane can be evaluated. We have extended this framework to include $\mathcal{O}(β)$ and $\mathcal{O}(β^2)$ corrections, by mapping the degrees of freedom to a vertex model. We present results on the $β$-dependence of the chiral critical point from those simulations.

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arXiv2024

Quantum computational resources for lattice QCD in the strong-coupling limit

We consider the strong coupling limit of lattice QCD with massless staggered quarks and study the resource requirements for quantum simulating the theory in its Hamiltonian formulation. The bosonic Hilbert space of the color-singlet degrees of freedom grows quickly with the number of quark flavors, making it a suitable testing ground for resource considerations across different platforms. In particular, in addition to the standard model of computation with qubits, we consider mapping the theory to qudits $(d>2)$ and qumodes, as used on trapped-ion systems and photonic devices, respectively.

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arXiv2023

Chiral Transition via Strong Coupling Expansion

We investigate the chiral transition of $U(3)$ lattice gauge theory based on the strong coupling expansion. A generalized vertex model with vertices and weights derived from the tensor network approach of the dual representation of lattice QCD with staggered fermions is used and the configurations are sampled by the Metropolis algorithm. We study the chiral transition in the chiral limit and focus on the dependence of the second-order chiral transition temperature $aT_c$ for different values of the lattice gauge coupling $β$. We compare different orders of truncations of the strong coupling expansion: $Ord(β^0)$, $Ord(β^1)$, and $Ord(β^2)$. We comment on the prospects of extending to $SU(3)$ at finite density.

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arXiv2023

Testing importance sampling on a quantum annealer for strong coupling SU(3) gauge theory

$SU(N_c)$ gauge theories in the strong coupling limit can be described by integer variables representing monomers, dimers and baryon loops. We demonstrate how the D-wave quantum annealer can perform importance sampling on $U(N_c)$ gauge theory in the strong coupling formulation of this theory. In addition to causing a sign problem in importance sampling, baryon loops induce a complex QUBO matrix which cannot be optimized by the D-Wave annealer. Instead we show that simulating the sign-problem free quenched action on the D-Wave is sufficient when combined with a sign reweighting method. As the first test on $SU(3)$ gauge theory, we simulate on $2 \times 2$ lattice and compare the results with its analytic solutions.

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arXiv2023

Quantum Gate Sets for Lattice QCD in the strong coupling limit: $N_f=1$

We derive the primitive quantum gate sets to simulate lattice quantum chromodynamics (LQCD) in the strong-coupling limit with one flavor of massless staggered quarks. This theory is of interest for studies at non-zero density as the sign problem can be overcome using Monte Carlo methods. In this work, we use it as a testing ground for quantum simulations. The key point is that no truncation of the bosonic Hilbert space is necessary as the theory is formulated in terms of color-singlet degrees of freedom (``baryons'' and ``mesons''). The baryons become static in the limit of continuous time and decouple, whereas the dynamics of the mesonic theory involves two qubits per lattice site. Lending dynamics also to the ``baryons'' simply requires to use the derived gate set in its controlled version.

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arXiv2023

$U(N)$ gauge theory in the strong coupling limit on a quantum annealer

Lattice QCD in the strong coupling regime can be formulated in dual variables which are integer-valued. It can be efficiently simulated for modest finite temperatures and finite densities via the worm algorithm, circumventing the finite density sign problem in this regime. However, the low temperature regime is more expensive to address. As the partition function is solely expressed in terms of integers, it can be cast as a combinatorial optimization problem that can be solved on a quantum annealer. We will first explain the setup of the system we want to study, and then present its reformulation suitable for a quantum annealer, and in particular the D-Wave. As a proof of concept, we present first results obtained on D-Wave for gauge group $U(1)$ and $U(3)$, and outline the next steps towards gauge groups $SU(3)$. We find that in addition, histogram reweighting greatly improves the accuracy of our observables when compared to analytic results.

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arXiv2023

Nuclear Liquid-Gas Transition in the Strong Coupling Regime of Lattice QCD

The nuclear liquid-gas transition from a gas of hadrons to a nuclear phase cannot be determined numerically from conventional lattice QCD due to the severe sign problem at large values of the baryon chemical potential. In the strong coupling regime of lattice QCD with staggered quarks, the dual formulation is suitable to address the nuclear liquid gas transition. We determine this first order transition at low temperatures and as a function of the quark mass and the inverse gauge coupling $β$. We also determine the baryon mass and discuss the nuclear interactions as a function of the quark mass, and compare to mean field results.

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arXiv2022

Towards Quantum Monte Carlo Simulations at non-zero Baryon and Isospin Density in the Strong Coupling Regime

The Hamiltonian formulation of Lattice QCD with staggered fermions in the strong coupling limit has no sign problem at non-zero baryon density and allows for Quantum Monte Carlo simulations. We have extended this formalism to two flavors, and after a resummation, there is no sign problem both for non-zero baryon and isospin chemical potential. We report on recent progress on the implementation of the Quantum Monte Carlo simulations.

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arXiv2022

Nuclear Transition in the Strong Coupling Limit

Lattice QCD at finite baryon chemical potential has the infamous sign problem which hinders Monte Carlo simulations. This can be remedied by a dual representation that makes the sign problem mild. In the strong coupling limit, the dual formulation with staggered quarks is well established. We have used this formulation to study the quark mass dependence of the baryon mass and the nuclear transition. This allows us to quantify the nuclear interaction. We have also compared our Monte Carlo results with mean field predictions.

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arXiv2022

Error reduction using machine learning on Ising worm simulation

We develop a method to improve on the statistical errors for higher moments using machine learning techniques. We present here results for the dual representation of the Ising model with an external field, derived via the high temperature expansion and simulated by the worm algorithm. We compare two ways of measuring the same set of observables, without and with machine learning: moments of the magnetization and the susceptibility can be improved by using the decision tree method to train the correlations between the higher moments and the second moment obtained from an integrated 2-point function. Those results are compared in small volumes to analytic predictions.

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arXiv2021

Hamiltonian Lattice QCD from Strong Coupling Expansion

We present generalizations of Hamiltonian Lattice QCD as derived from the continuous time limit of strong coupling lattice QCD: we discuss the flavor dependence and the effect of gauge corrections. This formalism can be applied at finite temperature and baryon density as well as isospin density and allows both for analytic and numeric investigations that are sign problem-free.

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arXiv2020

Strong Coupling Lattice QCD in the Continuous Time Limit

We present results for lattice QCD with staggered fermions in the limit of infinite gauge coupling, obtained from a worm-type Monte Carlo algorithm on a discrete spatial lattice but with continuous Euclidean time. This is obtained by sending both the anisotropy parameter $ξ=a_σ/a_τ$ and the number of time-slices $N_τ$ to infinity, keeping the ratio $aT=ξ/Nτ$ fixed. The obvious gain is that no continuum extrapolation $N_τ\rightarrow \infty$ has to be carried out. Moreover, the algorithm is faster and the sign problem disappears. We derive the continuous time partition function and the corresponding Hamiltonian formulation. We compare our computations with those on discrete lattices and study both zero and finite temperature properties of lattice QCD in this regime.

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arXiv2020

Gauge Corrections to Strong Coupling Lattice QCD on Anisotropic Lattices

Lattice QCD with staggered fermions can be formulated in dual variables to address the finite baryon density sign problem. In the past we have performed simulations in the strong coupling regime, including leading order gauge corrections. In order to vary the temperature for fixed $β$ it was necessary to introduce a bare anisotropy. In this talk we will extend our work to include results from a non-perturbative determination of the physical anisotropy $a_σ$/$a_τ= ξ(γ, β)$, which is necessary to unambiguously locate the critical end point and the first order line of the chiral transition.

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arXiv2019

Continuous Time Simulations of Strong Coupling LQCD at Finite Baryon Density

We study lattice QCD in the limit of infinite gauge coupling on a discrete spatial yet continuous Euclidean time lattice at finite baryon chemical potential $μ_B$. The continuous time framework is based on sending $N_τ\rightarrow \infty$ and the bare anisotropy to infinity while fixing the temperature in a non-perturbative setup. This leads to a sign problem free algorithm that allows us to study the whole $μ_B$-$T$ plane. We construct Taylor coefficients required for a Taylor expansion in the pressure at zero chemical potential and in the chiral limit. On that account, cumulants in the baryon number density are measured in various fashions to improve on accuracy. These calculations are based on our worm type Monte Carlo algorithm featuring a polymer resummation scheme and a histogram method.

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arXiv2019

On the $β$- and quark mass dependence of the nuclear transition in the strong coupling regime

Lattice QCD in a dual formulation with staggered fermions is well established in the strong coupling limit and allows to perform Monte Carlo simulations at finite baryon chemical potential. We have recently addressed the dependence of the nuclear critical end point as a function of the quark mass $am_q$, and separately as a function of the lattice gauge coupling $β$ in the chiral limit. Here we proceed to determine the dependence of the nuclear transition on both, $am_q$ and $β$, on isotropic lattices and attempt to pinpoint the critical end point for various $β$ where the sign problem is still manageable.

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arXiv2019

A new dual representation for staggered lattice QCD

We propose a new strategy to evaluate the partition function of lattice QCD with Wilson gauge action coupled to staggered fermions, based on a strong coupling expansion in the inverse bare gauge coupling $β= 2N/g^{2}$. Our method makes use of the recently developed formalism to evaluate the ${\rm SU}(N)$ $1-$link integrals and consists in an exact rewriting of the partition function in terms of a set of additional dual degrees of freedom which we call "Decoupling Operator Indices" (DOI). The method is not limited to any particular number of dimensions or gauge group ${\rm U}(N)$, ${\rm SU}(N)$. In terms of the DOI the system takes the form of a Tensor Network which can be simulated using Worm-like algorithms. Higher order $β$-corrections to strong coupling lattice QCD can be, in principle, systematically evaluated, helping to answer the question whether the finite density sign problem remains mild when plaquette contributions are included. Issues related to the complexity of the description and strategies for the stochastic evaluation of the partition function are discussed.

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arXiv2018

Thermodynamics at Strong Coupling on Anisotropic Lattices

Lattice QCD with staggered fermions at strong coupling has long been studied in a dual representation to circumvent the finite baryon density sign problem. Monte Carlo simulations at finite temperature and density require anisotropic lattices. Recent results that established the non-perturbative functional dependence between the bare anisotropy $γ$ and the physical anisotropy $a_s/a_t$ in the chiral limit are now extended to finite quark mass. We illustrate how the calibration of the anisotropy works and discuss the consequences of the anisotropy on thermodynamic observables. We also show first results on the energy density and pressure in the QCD phase diagram in the strong coupling regime.

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