Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2601.14399

Differentiable quantum-trajectory simulation of Lindblad dynamics for QGP transport-coefficient inference

Lukas Heinrich, Tom Magorsch

physics.comp-phhep-exhep-phnucl-exquant-phSubmitted Jan 20, 2026• Announced Jan 22, 2026• 0 citations
arXivHTMLPDF

Abstract

We study parameter estimation for the transport coefficients of the quark-gluon plasma by differentiating open-quantum-system-based Monte Carlo simulations of quarkonium suppression. The underlying simulator requires solving a Lindblad equation in a large Hilbert space, which makes parameter estimation computationally expensive. We approach the problem using gradient-based optimization. Specifically, we apply the score-function gradient estimator to differentiate through discrete jump sampling in the Monte Carlo wave-function algorithm used to solve the Lindblad equation. The resulting stochastic gradient estimator exhibits sufficiently low variance and can still be estimated in an embarrassingly parallel manner, enabling efficient scaling of the simulations. We implement this gradient estimator in the existing open-source quarkonium suppression code QTraj. To demonstrate its utility for parameter estimation, we infer the two transport coefficients $\hatκ$ and $\hatγ$ using gradient-based optimization on synthetic nuclear modification factor data.

Comments
13 pages, 4 figures

Related papers

Quantum simulation of bottomonium dynamics in the quark-gluon plasma via the Lindblad equation

Linyuan Wei, Jin Hu, Anping Huang +2 more

Quantum computing provides a powerful framework for simulating real-time dynamics in open quantum systems, offering key advantages for modeling heavy-quarkonium transport in high-energy nuclear collisions. In this work, we perform quantum simulations of the isotropic next-to-leading-order Lindblad equation for bottomonium in the quark-gluon plasma using a reduced spherical coordinate representation. We discretize operators and wavefunctions, map the physical state onto qubits, and execute time evolution via parameterized quantum gate operations. By extracting the $Υ(1S)$ survival probability, we quantitatively isolate the color-octet contribution, demonstrating that its overall impact is small in the final production of the bottomonium ground state $Υ(1S)$ in the hot QCD medium at temperatures accessible at the Large Hadron Collider. Additionally, we have further optimized the quantum simulation algorithm for the Lindblad equation. The improved algorithm requires only a single ancillary qubit to realize the Lindblad evolution, thereby minimizing the circuit significantly.

arXiv:2608.06754•Aug 7, 2026•0 citations

General Lindblad equation for quarkonium evolution in a quark-gluon plasma

Aoumeur Daddi Hammou, Jean-Paul Blaizot, Pol Bernard Gossiaux +1 more

Accurate modelling and understanding of quarkonium production in ultrarelativistic heavy ion collisions requires a formalism that preserves the quantum properties of microscopic $\bar{Q}Q$ systems while treating the interaction of such pairs with the quark-gluon plasma (QGP). The open quantum system approach has recently emerged as one of the most fruitful schemes to meet such requirements. However, the quantum master equations obtained so far in this context are derived assuming a strict ordering between the QGP temperature $T$ and the $\bar{Q}Q$ energy gaps ($ΔE$) of the quarkonia bound states. This limits their predictive power since, as the QGP expands and cools down, the system traverse all regimes between the quantum Brownian motion (QBM) regime for $T\gtrsim ΔE$ to the quantum optical (QO) regime for $ΔE\gtrsim T$. In this paper, we derive and present a more general non-abelian quantum master equation of the Lindblad type, which does not suffer from these limitations and thus allows to faithfully describe the quantum evolution of the $Q\bar{Q}$ pairs during the whole QGP-evolution. We also provide some illustration of the key quantities governing this equation.

nucl-thCross-listedarXiv:2608.15347•Aug 18, 2026

Quantum Trajectories for Time-Local Non-Lindblad Master Equations

Tobias Becker, Ché Netzer, André Eckardt

For the efficient simulation of open quantum systems, we often use quantum jump trajectories given by pure states that evolve stochastically to unravel the dynamics of the underlying master equation. In the Markovian regime, when the dynamics is described by a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, this procedure is known as Monte Carlo wave function approach. However, beyond ultraweak system-bath coupling, the dynamics of the system is not described by an equation of GKSL type, but rather by the Redfield equation, which can be brought into pseudo-Lindblad form. Here, negative dissipation strengths prohibit the conventional approach. To overcome this problem, we propose a pseudo-Lindblad quantum trajectory (PLQT) unraveling. It does not require an effective extension of the state space, like other approaches, except for the addition of a single classical bit. We test the PLQT for the eternal non-Markovian master equation for a single qubit and an interacting Fermi-Hubbard chain coupled to a thermal bath and discuss its computational effort compared to solving the full master equation.

arXiv:2306.14876•Physical Review Letters•Oct 17, 2023•11 citations

Quantum simulation of open quantum systems in heavy-ion collisions

Wibe Albert de Jong, Mekena Metcalf, James Declan Mulligan +3 more

We present a framework to simulate the dynamics of hard probes such as heavy quarks or jets in a hot, strongly coupled quark-gluon plasma (QGP) on a quantum computer. Hard probes in the QGP can be treated as open quantum systems governed in the Markovian limit by the Lindblad equation. However, due to large computational costs, most current phenomenological calculations of hard probes evolving in the QGP use semiclassical approximations of the quantum evolution. Quantum computation can mitigate these costs and offers the potential for a fully quantum treatment with exponential speed-up over classical techniques. We report a simplified demonstration of our framework on IBM Q quantum devices and apply the random identity insertion method to account for cnot depolarization noise, in addition to measurement error mitigation. Our work demonstrates the feasibility of simulating open quantum systems on current and near-term quantum devices, which is of broad relevance to applications in nuclear physics, quantum information, and other fields.

arXiv:2010.03571•Physical review. D/Physical review. D.•Sep 7, 2021•52 citations

Quantum Brownian motion of a heavy quark pair in the quark-gluon plasma

Takahiro Miura, Yukinao Akamatsu, Masayuki Asakawa +1 more

In this paper we study the real-time evolution of heavy quarkonium in the quark-gluon plasma (QGP) on the basis of the open quantum systems approach. In particular, we shed light on how quantum dissipation affects the dynamics of the relative motion of the quarkonium state over time. To this end we present a novel nonequilibrium master equation for the relative motion of quarkonium in a medium, starting from Lindblad operators derived systematically from quantum field theory. In order to implement the corresponding dynamics, we deploy the well established quantum state diffusion method. In turn we reveal how the full quantum evolution can be cast in the form of a stochastic nonlinear Schr\"odinger equation. This for the first time provides a direct link from quantum chromodynamics to phenomenological models based on nonlinear Schr\"odinger equations. Proof of principle simulations in one dimension show that dissipative effects indeed allow the relative motion of the constituent quarks in a quarkonium at rest to thermalize. Dissipation turns out to be relevant already at early times well within the QGP lifetime in relativistic heavy ion collisions.

arXiv:1908.06293•Physical review. D/Physical review. D.•Feb 11, 2020•61 citations

From the universal Lindblad equation to Boltzmann equations: in-QGP quarkonium dynamics

Aoumeur Daddi Hammou, Pol Bernard Gossiaux

Recently, a set of coupled singlet-octet universal Lindblad equations (ULEs) was derived within the framework of non-relativistic QCD (NRQCD) to describe quarkonium dynamics in the quark-gluon plasma (QGP). These equations provide a unified quantum description spanning the quantum Brownian and quantum optical regimes. In this work, we further develop this framework and establish its connection with semiclassical transport. We first derive the universal Lindblad equations within the potential non-relativistic QCD (pNRQCD) effective field theory and show that they coincide with the small-dipole limit of the NRQCD ULEs. We then derive the semiclassical limit of the NRQCD ULEs, obtaining a set of coupled singlet-octet Boltzmann equations. To our knowledge, this is the first derivation of Boltzmann transport equations directly from the universal Lindblad framework. The resulting equations are valid beyond the small-dipole approximation, allowing the evolution of heavy-quark pairs from compact to widely separated configurations. Taking their small-dipole limit allows a direct comparison with the Boltzmann equations of Yao et al. [Phys. Rev. D 99, 096028 (2019)], which were derived within pNRQCD from the Davies secular equation, relying on the rotating-wave approximation (RWA). While the singlet equations are found to be in near-complete agreement, the octet equation contains an additional collision term describing transitions within the continuum of octet scattering states, which is absent from the RWA-based derivation. Finally, we derive the leading quantum correction to the singlet Boltzmann equation. Our results establish a more general and systematic theoretical foundation for the semiclassical transport description of quarkonium in the QGP.

hep-phCross-listedarXiv:2608.17372•Aug 19, 2026
We study parameter estimation for the transport coefficients of the quark-gluon plasma by differentiating open-quantum-system-based Monte Carlo simulations of quarkonium suppression. The underlying simulator requires solving a Lindblad equation in a large Hilbert space, which makes parameter estimation computationally expensive. We approach the problem using gradient-based optimization. Specifically, we apply the score-function gradient estimator to differentiate through discrete jump sampling in the Monte Carlo wave-function algorithm used to solve the Lindblad equation. The resulting stochastic gradient estimator exhibits sufficiently low variance and can still be estimated in an embarrassingly parallel manner, enabling efficient scaling of the simulations. We implement this gradient estimator in the existing open-source quarkonium suppression code QTraj. To demonstrate its utility for parameter estimation, we infer the two transport coefficients κ^\hatκκ^ and γ^\hatγγ^​ using gradient-based optimization on synthetic nuclear modification factor data.
Quantum computing provides a powerful framework for simulating real-time dynamics in open quantum systems, offering key advantages for modeling heavy-quarkonium transport in high-energy nuclear collisions. In this work, we perform quantum simulations of the isotropic next-to-leading-order Lindblad equation for bottomonium in the quark-gluon plasma using a reduced spherical coordinate representation. We discretize operators and wavefunctions, map the physical state onto qubits, and execute time evolution via parameterized quantum gate operations. By extracting the Υ(1S)Υ(1S)Υ(1S) survival probability, we quantitatively isolate the color-octet contribution, demonstrating that its overall impact is small in the final production of the bottomonium ground state Υ(1S)Υ(1S)Υ(1S) in the hot QCD medium at temperatures accessible at the Large Hadron Collider. Additionally, we have further optimized the quantum simulation algorithm for the Lindblad equation. The improved algorithm requires only a single ancillary qubit to realize the Lindblad evolution, thereby minimizing the circuit significantly.
Accurate modelling and understanding of quarkonium production in ultrarelativistic heavy ion collisions requires a formalism that preserves the quantum properties of microscopic QˉQ\bar{Q}QQˉ​Q systems while treating the interaction of such pairs with the quark-gluon plasma (QGP). The open quantum system approach has recently emerged as one of the most fruitful schemes to meet such requirements. However, the quantum master equations obtained so far in this context are derived assuming a strict ordering between the QGP temperature TTT and the QˉQ\bar{Q}QQˉ​Q energy gaps (ΔEΔEΔE) of the quarkonia bound states. This limits their predictive power since, as the QGP expands and cools down, the system traverse all regimes between the quantum Brownian motion (QBM) regime for T≳ΔET\gtrsim ΔET≳ΔE to the quantum optical (QO) regime for ΔE≳TΔE\gtrsim TΔE≳T. In this paper, we derive and present a more general non-abelian quantum master equation of the Lindblad type, which does not suffer from these limitations and thus allows to faithfully describe the quantum evolution of the QQˉQ\bar{Q}QQˉ​ pairs during the whole QGP-evolution. We also provide some illustration of the key quantities governing this equation.
For the efficient simulation of open quantum systems, we often use quantum jump trajectories given by pure states that evolve stochastically to unravel the dynamics of the underlying master equation. In the Markovian regime, when the dynamics is described by a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, this procedure is known as Monte Carlo wave function approach. However, beyond ultraweak system-bath coupling, the dynamics of the system is not described by an equation of GKSL type, but rather by the Redfield equation, which can be brought into pseudo-Lindblad form. Here, negative dissipation strengths prohibit the conventional approach. To overcome this problem, we propose a pseudo-Lindblad quantum trajectory (PLQT) unraveling. It does not require an effective extension of the state space, like other approaches, except for the addition of a single classical bit. We test the PLQT for the eternal non-Markovian master equation for a single qubit and an interacting Fermi-Hubbard chain coupled to a thermal bath and discuss its computational effort compared to solving the full master equation.
We present a framework to simulate the dynamics of hard probes such as heavy quarks or jets in a hot, strongly coupled quark-gluon plasma (QGP) on a quantum computer. Hard probes in the QGP can be treated as open quantum systems governed in the Markovian limit by the Lindblad equation. However, due to large computational costs, most current phenomenological calculations of hard probes evolving in the QGP use semiclassical approximations of the quantum evolution. Quantum computation can mitigate these costs and offers the potential for a fully quantum treatment with exponential speed-up over classical techniques. We report a simplified demonstration of our framework on IBM Q quantum devices and apply the random identity insertion method to account for cnot depolarization noise, in addition to measurement error mitigation. Our work demonstrates the feasibility of simulating open quantum systems on current and near-term quantum devices, which is of broad relevance to applications in nuclear physics, quantum information, and other fields.
In this paper we study the real-time evolution of heavy quarkonium in the quark-gluon plasma (QGP) on the basis of the open quantum systems approach. In particular, we shed light on how quantum dissipation affects the dynamics of the relative motion of the quarkonium state over time. To this end we present a novel nonequilibrium master equation for the relative motion of quarkonium in a medium, starting from Lindblad operators derived systematically from quantum field theory. In order to implement the corresponding dynamics, we deploy the well established quantum state diffusion method. In turn we reveal how the full quantum evolution can be cast in the form of a stochastic nonlinear Schr\"odinger equation. This for the first time provides a direct link from quantum chromodynamics to phenomenological models based on nonlinear Schr\"odinger equations. Proof of principle simulations in one dimension show that dissipative effects indeed allow the relative motion of the constituent quarks in a quarkonium at rest to thermalize. Dissipation turns out to be relevant already at early times well within the QGP lifetime in relativistic heavy ion collisions.
Recently, a set of coupled singlet-octet universal Lindblad equations (ULEs) was derived within the framework of non-relativistic QCD (NRQCD) to describe quarkonium dynamics in the quark-gluon plasma (QGP). These equations provide a unified quantum description spanning the quantum Brownian and quantum optical regimes. In this work, we further develop this framework and establish its connection with semiclassical transport. We first derive the universal Lindblad equations within the potential non-relativistic QCD (pNRQCD) effective field theory and show that they coincide with the small-dipole limit of the NRQCD ULEs. We then derive the semiclassical limit of the NRQCD ULEs, obtaining a set of coupled singlet-octet Boltzmann equations. To our knowledge, this is the first derivation of Boltzmann transport equations directly from the universal Lindblad framework. The resulting equations are valid beyond the small-dipole approximation, allowing the evolution of heavy-quark pairs from compact to widely separated configurations. Taking their small-dipole limit allows a direct comparison with the Boltzmann equations of Yao et al. [Phys. Rev. D 99, 096028 (2019)], which were derived within pNRQCD from the Davies secular equation, relying on the rotating-wave approximation (RWA). While the singlet equations are found to be in near-complete agreement, the octet equation contains an additional collision term describing transitions within the continuum of octet scattering states, which is absent from the RWA-based derivation. Finally, we derive the leading quantum correction to the singlet Boltzmann equation. Our results establish a more general and systematic theoretical foundation for the semiclassical transport description of quarkonium in the QGP.