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Roland Katz

Publications and source records attributed to Roland Katz.

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Solving nonlinear differential equations on noisy $156$-qubit quantum computers

In this paper, we report on the resolution of nonlinear differential equations using IBM's quantum platform. More specifically, we demonstrate that the hybrid classical-quantum algorithm H-DES successfully solves a one-dimensional material deformation problem and the inviscid Burgers' equation on IBM's 156-qubit quantum computers. These results constitute a step toward performing physically relevant simulations on present-day Noisy Intermediate-Scale Quantum (NISQ) devices.

quant-ph

H-DES: a Quantum-Classical Hybrid Differential Equation Solver

In this article, we introduce an original hybrid quantum-classical algorithm based on a variational quantum algorithm for solving systems of differential equations. The algorithm relies on a spectral decomposition of the trial functions that are encoded directly in the quantum states generated by different parametrized circuits, and transforms the task of solving the differential equations into an optimization problem. We first describe the principle of the algorithm from a theoretical point of view. We provide a detailed pseudo-code of the algorithm, on which we elaborate preliminary elements for a complexity analysis to highlight some of its scaling properties. We apply our algorithm to a set of examples, running on emulators and real hardware showcasing its applicability across diverse sets of differential equations. We discuss the advantages of our method and potential avenues for further exploration and refinement.

quant-ph

Quarkonium dynamics in the quantum Brownian regime with non-abelian quantum master equations

We present numerical solutions in a one-dimensional setting of quantum master equations that have been recently derived. We focus on the dynamics of a single heavy quark-antiquark pair in a Quark-Gluon Plasma in thermal equilibrium, in the so-called quantum Brownian regime where the temperature of the plasma is large in comparison with the spacing between the energy levels of the $Q\bar{Q}$ system. The one-dimensional potential used in the calculations has been adjusted so as to produce numbers that are relevant for the phenomenology of the charmonium. The equations are solved using different initial states and medium configurations. Various temperature regimes are studied and the effects of screening and collisions thoroughly analyzed. Technical features of the equations are analyzed. The contributions of the different operators that control the evolution are discussed as a function of the temperature. Some phenomenological consequences are addressed.

hep-ph

One-dimensional complex potentials for quarkonia in a quark-gluon plasma

Master equations of the Lindblad type have recently been derived to describe the dynamics of quarkonium states in the quark-gluon plasma. Because their full resolution in three dimensions is very challenging, the equations are often reduced to one dimension. The main ingredient of these equations is the complex potential that describes the binding of the heavy quark-antiquark pairs and their interactions with the medium. In this work, we propose a one-dimensional complex potential parameterized to reproduce at best two key properties -- the temperature-dependent masses of the eigenstates and their decay widths -- of a three-dimensional lattice QCD inspired potential. Their spectral decompositions are calculated to check their compatibility with the positivity of the master equations.

hep-ph

System size scan of D meson $R_\text{AA}$ and $v_n$ using PbPb, XeXe, ArAr, and OO collisions at LHC

Experimental measurements indicate no suppression (e.g. $R_\text{pPb} \sim 1$) but a surprisingly large D meson $v_2$ was measured in pPb collisions. In order to understand these results we use Trento+v-USPhydro+DAB-MOD to make predictions and propose a system size scan at the LHC involving $^{208}$PbPb, $^{129}$XeXe, $^{40}$ArAr, and $^{16}$OO collisions. We find that the nuclear modification factor approaches unity as the system size is decreased, but nonetheless, in the 0-10% most central collisions $v_2\{2\}$ is roughly equivalent regardless of system size. These results arise from a rather non-trivial interplay between the shrinking path length and the enhancement of eccentricities in small systems at high multiplicity. Finally, we also find a surprising sensitivity of D mesons $v_2\{2\}$ in 0-10% at $p_T = 2-10$ GeV to the slight deformation of $^{129}$Xe recently found at LHC.

nucl-th

Heavy flavor dynamics across system size at the LHC

One of the fundamental signatures of the Quark Gluon Plasma has been the suppression of heavy flavor (specifically D mesons), which has been measured via the nuclear modification factor, $R_{AA}$ and azimuthal anisotropies, $v_n$, in large systems. However, multiple competing models can reproduce the same data for $R_{AA}$ to $v_n$. In this talk we break down the competing effects that conspire together to successfully reproduce $R_{AA}$ and $v_n$ in experimental data using Trento+v-USPhydro+DAB-MOD. Then using our best fit model we make predictions for $R_{AA}$ and $v_n$ across system size for $^{208}PbPb$, $^{129}XeXe$, $^{40}ArAr$, and $^{16}OO$ collisions. We find that 0--10\% centrality has a non-trivial interplay between the system size and eccentricities such that system size effects are masked in $v_2$ whereas in 30--50\% centrality the eccentricities are approximately constant across system size and, therefore, is a better centrality class to study D meson dynamics across system size.

nucl-th

D meson sensitivity to a system size scan at LHC

Experimental measurements in pA collisions indicate no D meson suppression ($R_{\rm pPb} \sim 1$) but a surprisingly large $v_2$. To better understand these results we propose a system size scan at the LHC involving $^{16}$OO, $^{40}$ArAr, $^{129}$XeXe and $^{208}$PbPb collisions. Using Trento+ v-USPhydro+DAB-MOD to make predictions, we find that the $R_{\rm AA}$ tends towards unity when the system size is decreased, but nonetheless, in the most central collisions $v_2\{2\}$ is almost independent of the colliding system. These results are analyzed in light of path length and initial eccentricity variations.

nucl-th

DAB-MOD sensitivity study of heavy flavor $R_{AA}$ and azimuthal anisotropies based on beam energy, initial conditions, hadronization, and suppression mechanisms

Heavy flavor probes provide important information about the in-medium properties of the quark-gluon plasma produced in heavy-ion collisions. In this work, we investigate the effects of 2D+1 event-by-event fluctuating hydrodynamic backgrounds on the nuclear suppression factor and momentum anisotropies of heavy flavor mesons and non-photonic electrons. Using the state-of-the-art D and B mesons modular simulation code (called "DAB-MOD"), we perform a systematic comparison of different transport equations in the same background, including a few energy loss models --- with and without energy loss fluctuations --- and a relativistic Langevin model with different drag parametrizations. We present the resulting D and B mesons $R_{AA}$, $v_2$, $v_3$, and $v_4$ as well as multi-particle cumulants, in AuAu collisions at $\sqrt{s_\text{NN}}=200\, \text{GeV}$ and PbPb collisions at $\sqrt{s_\text{NN}}=2.76 \, \text{TeV}$ and $\sqrt{s_\text{NN}}=5.02 \, \text{TeV}$, and compare them to the available experimental data. The $v_2\{4\}/v_2\{2\}$ ratio, which is known to be a powerful probe of the initial conditions and flow fluctuations in the soft sector, is also studied in the context of heavy flavor. We also investigate the correlations between the transverse anisotropies of heavy mesons and all charged particles to better understand how heavy quarks couple to the hydrodynamically expanding quark-gluon plasma. We study the influence that different initial conditions and the implementation of heavy-light quark coalescence has on our results.

nucl-th

Sensitivity of D meson azimuthal anisotropies to system size and nuclear structure

Recent experimental data at the Large Hadron Collider (LHC) confirmed that the soft sector azimuthal anisotropies in central XeXe collisions are sensitive to deformations in the wave function of the Xenon nucleus. Additionally, the CMS experiment found that D meson flow is slightly suppressed compared to other particle species when considering quark number scaling in small systems of pPb compared to PbPb. In this talk we used the D and B Mesons Modular (DAB-MOD) code coupled to Trento+v-USPhydro to calculate the $R_{AA}$ and $v_n$'s of D mesons using different energy loss models and Langevin techniques. Comparing D mesons $R_{AA}$ and $v_n$ in PbPb to XeXe collisions it is found that in central collisions D meson azimuthal anisotropies are sensitive to details in the nuclear structure wave function of Xenon. Additionally, we find that in mid-central collisions the smaller system size of XeXe suppresses D meson flow.

nucl-th

Heavy-flavor dynamics in event-by-event viscous hydrodynamic backgrounds

We investigate the effects of (2+1)d event-by-event fluctuating hydrodynamic backgrounds on the nuclear modification factor and momentum anisotropies of heavy-flavor mesons. Using the state-of-the-art D and B mesons modular simulation code (the so-called DAB-mod), updated recently with heavy-light quark coalescence, we perform a systematic comparison of different transport equations, including two energy loss models and a relativistic Langevin model with two drag parametrizations. We present the resulting D$^0$ meson $R_{AA}$, $v_2$ and $v_3$, using the multiparticle cumulant method, in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV and compare them to the latest experimental data. We investigate the $v_2\{4\}/v_2\{2\}$ ratio as a function of centrality for different initial conditions (MCKLN vs. Trento) and different system geometries and sizes (coming from Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV, spherical and prolate Xe-Xe collisions at $\sqrt{s_{\rm NN}}=5.44$ TeV).

nucl-th

Event-by-event $v_n$ correlations of soft hadrons and heavy mesons in heavy ion collisions

In this paper heavy quark energy loss models are embedded in full event-by-event viscous hydrodynamic simulations to investigate the nuclear suppression factor and azimuthal anisotropy of D$^0$ mesons in PbPb collisions at 5.02 TeV in the $p_T$ range 8-40 GeV. In our model calculations, the $R_\text{AA}$ of D$^0$ mesons is consistent with experimental data from the CMS experiment. We present the first calculations of heavy flavor cumulants $v_2\{2\}$ and $v_3\{2\}$ (and also discuss $v_2\{4\}$), which is also consistent with experimental data. Event-shape engineering techniques are used to compute the event-by-event correlation between the soft hadron $v_n$ and the heavy meson $v_n$. We predict a linear correlation between these observables on an event-by-event basis.

nucl-th

Event-by-event $v_n$ correlations of soft hadrons and heavy mesons in heavy ion collisions

Combining event-by-event hydrodynamics with heavy quark energy loss we compute correlations between the heavy and soft sectors for elliptic and triangular flow harmonics $v_2$ and $v_3$ of D$^0$ mesons in PbPb collisions at $2.76$ TeV and $5.02$ TeV. Our results indicate that $v_3$ is strongly influenced by the fragmentation temperature and that it builds up later than $v_2$ during the evolution of the system.

nucl-th

The Schrödinger-Langevin equation with and without thermal fluctuations

The Schrödinger-Langevin (SL) equation is considered as an effective open quantum system formalism suitable for phenomenological applications involving a quantum subsystem interacting with a thermal bath. We focus on two open issues relative to its solutions: the stationarity of the excited states of the non-interacting subsystem when one considers the dissipation only and the thermal relaxation toward asymptotic distributions with the additional stochastic term. We first show that a proper application of the Madelung/polar transformation of the wave function leads to a non zero damping of the excited states of the quantum subsystem. We then study analytically and numerically the SL equation ability to bring a quantum subsystem to the thermal equilibrium of statistical mechanics. To do so, concepts about statistical mixed states and quantum noises are discussed and a detailed analysis is carried with two kinds of noise and potential. We show that within our assumptions the use of the SL equation as an effective open quantum system formalism is possible and discuss some of its limitations.

quant-ph

Upsilon suppression in the Schrödinger-Langevin approach

We treat the question of bottomonia suppression in ultrarelativistic heavy ion collisions (URHIC) as a dynamical open quantum problem, tackled for the first time using the Schrödinger-Langevin equation. Coupling this equation to the EPOS2 event generator, predictions are made for the nuclear modification factor of $Υ(1S)$ and $Υ(2S)$.

hep-ph

Semi-classical approach to $J/ψ$ suppression in high energy heavy-ion collisions

We study the heavy quark/antiquark pair dynamics in strongly-coupled quark gluon plasma. A semi-classical approach, based on the Wigner distribution and Langevin dynamics, is applied to a color screened $c{\bar c}$ pair, in a hydrodynamically cooling fireball, to evaluate the total $J/ψ$ suppression at both RHIC and LHC energies. Although its limitation is observed, this approach results to a $J/ψ$ suppression of around 0.30 at RHIC and 0.25 at LHC.

hep-ph