arXiv subjects

Nuno F. Loureiro

Publications and source records attributed to Nuno F. Loureiro.

At least 19 recordsLinked to original sources

arXiv2026

On the numerical limitations of dual Koopman von Neumann embeddings for solving conservative nonlinear ordinary differential equations on quantum computers

The simulation of nonlinear ordinary differential equations on quantum computers is inherently challenging, as quantum gates are linear operators on qubit states. In this paper, we put forth a Koopman-von Neumann (KvN) operator based algorithm for solving nonlinear ordinary differential equations on a quantum computer which overcomes the innate limitations of quantum operations. In this approach, a Liouville probability density is embedded into a wavefunction, the evolution of which is governed by an operator dual to the Koopman operator. The trajectories corresponding to the nonlinear differential equations are reconstructed from the average value of Koopman observables evaluated through quantum measurements. We specifically evaluate the computational limitations of solving nonlinear equations within this Liouville embedding framework. An Ehrenfest-type estimate is derived that relates the reconstruction error to the covariance of the transported density, highlighting the competition between linear stretching and Hessian-induced folding.This leads to a key stability criterion, which depends on the local Ehrenfest-Reynolds number. We discuss the effects of measurement-induced errors including those due to Hadamard-test sampling, amplitude estimation, and bias due to covariance in probabilistic Grover-type inference on the evaluation of trajectories. The limiting bounds on the accuracy of quantum computations are numerically verified for the Lotka-Volterra system and for the quartic oscillator. We observe a rapid growth in computational errors when the Ehrenfest-Reynolds number approaches the predicted threshold. The bounds resulting from our analysis provide key guidelines for selecting the width of the initial Gaussian probability distribution associated with a system of nonlinear ordinary differential equations.

quant-ph↗

arXiv2026

Counter-streaming heat-flux closure for electron-only collisionless magnetic reconnection

In electron-only collisionless magnetic reconnection (MR), a regime of growing importance in turbulent space plasmas, electrons develop strongly non-Maxwellian distributions that invalidate conventional fluid closures based on assumptions of near local thermodynamic equilibrium. Using particle-in-cell (PIC) simulations, we identify the physical origin of the electron heat-flux: counter-streaming between electron sub-populations originating from opposite sides of the current sheet, with each sub-population remaining approximately adiabatic. This insight yields a novel fluid closure, which we implement in fluid simulations using two adiabatic electron fluids initialized on opposite sides of the current sheet. The fluid simulations capture the heat-flux, reconnecting current density, thermal pressure, and bulk flows as observed in PIC, within a reduced fluid description that conventional single-electron-fluid models fundamentally cannot reproduce. The closure is most accurate at low $β_{\text{Reconn.}}$ and $B_{\text{Guide}}/B_{\text{Reconn.}}$, regimes relevant to Earth's magnetotail, where it establishes counter-streaming as the physical origin of heat-flux in electron-only collisionless MR and enables its computationally efficient fluid modeling.

physics.plasm-ph↗

arXiv2026

Efficient quantum algorithm for dissipative nonlinear differential equations

Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the linearity of quantum mechanics has limited analogous progress for the nonlinear case. Despite this obstacle, we develop a quantum algorithm for dissipative quadratic $n$-dimensional ordinary differential equations. Assuming $R < 1$, where $R$ is a parameter characterizing the ratio of the nonlinearity and forcing to the linear dissipation, this algorithm has complexity $T^2 q~\mathrm{poly}(\log T, \log n, \log 1/ε)/ε$, where $T$ is the evolution time, $ε$ is the allowed error, and $q$ measures decay of the solution. This is an exponential improvement over the best previous quantum algorithms, whose complexity is exponential in $T$. While exponential decay precludes efficiency, driven equations can avoid this issue despite the presence of dissipation. Our algorithm uses the method of Carleman linearization, for which we give a novel convergence theorem. This method maps a system of nonlinear differential equations to an infinite-dimensional system of linear differential equations, which we discretize, truncate, and solve using the forward Euler method and the quantum linear system algorithm. We also provide a lower bound on the worst-case complexity of quantum algorithms for general quadratic differential equations, showing that the problem is intractable for $R \ge \sqrt{2}$. Finally, we discuss potential applications, showing that the $R < 1$ condition can be satisfied in realistic epidemiological models and giving numerical evidence that the method may describe a model of fluid dynamics even for larger values of $R$.

quant-ph↗

arXiv2026

Quantum algorithm for anisotropic diffusion and convection equations with vector norm scaling

In this work, we tackle the resolution of partial differential equations (PDEs) on digital quantum computers. Two fundamental PDEs are addressed: the anisotropic diffusion equation and the anisotropic convection equation. We present a quantum numerical scheme consisting of three steps: quantum state preparation, evolution with diagonal operators, and measurement of observables of interest. The evolution step relies on a high-order centered finite difference and a product formula approximation, also known as Trotterization. We provide novel vector-norm analysis to bound the different sources of error. We prove that the number of time-steps required in the evolution can be reduced by a factor $Θ(16^n)$ for the diffusion equation, and $Θ(4^n)$ for the convection equation, where $n$ is the number of qubits per dimension, an exponential reduction compared to the previously established operator-norm analysis.

quant-ph↗

arXiv2025

Effects of Multi-scale Coupling on Particle Acceleration and Energy Partition in Magnetic Reconnection

The interplay between kinetic and macroscopic scales during magnetic reconnection is investigated using particle-in-cell simulations of magnetic island coalescence in the strongly-magnetized, relativistic pair plasma regime. For large system sizes, secondary current sheet formation and downstream turbulence driven by the reconnection outflows dominate the global energy dissipation so that it is causally connected, but spatially and temporally de-coupled from the primary reconnecting current sheet. When compared to simulations of an isolated, force-free current sheet, these dynamics activate additional particle acceleration channels which are responsible for a significant population of the non-thermal particles, modifying the particle energy spectra.

physics.plasm-ph↗

arXiv2025

Trotter-based quantum algorithm for solving transport equations with exponentially fewer time-steps

The extent to which quantum computers can simulate physical phenomena and solve the partial differential equations (PDEs) that govern them remains a central open question. In this work, one of the most fundamental PDEs is addressed: the multidimensional transport equation with space- and time-dependent coefficients. We present a quantum numerical scheme based on three steps: quantum state preparation, evolution, and measurement of relevant observables. The evolution step combines a high-order centered finite difference with a time-splitting scheme based on product formula approximations, also known as Trotterization. We introduce novel vector-norm analysis and prove that the number of time-steps can be reduced by a factor exponential in the number of qubits compared to previously established operator-norm analysis, thereby significantly lowering the projected computational resources. We also present efficient quantum circuits and numerical simulations that confirm the predicted vector-norm scaling. We report results on real quantum hardware for the one-dimensional convection equation, and solve a non-linear ordinary differential equation via its associated Liouville equation, a particular case of transport equations. This work provides a practical framework for efficiently simulating transport phenomena on quantum computers, with potential applications in plasma physics, molecular gas dynamics and non-linear dynamical systems, including chaotic systems.

quant-ph↗

arXiv2025

Current sheet formation under radiative cooling

We present a simple, analytically solvable MHD model of current sheet formation through X-point collapse under optically thin radiative cooling. Our results show that cooling accelerates the collapse of the X-point along the inflows, but strong cooling can arrest or even reverse the current sheet elongation in the outflow direction. Hence, we detail a modification to the radiatively-cooled Sweet-Parker model developed by Uzdensky & McKinney (2011) to allow for varying current sheet length. The steady-state solution shows that when radiative cooling dominates compressional heating, the current sheet length is shorter than the system size, with an increased reconnection rate compared to the classical Sweet-Parker rate. The model and subsequent results lay out the groundwork for a more complete theoretical understanding of magnetic reconnection in regimes dominated by optically thin radiative cooling.

physics.plasm-ph↗

arXiv2025

Role of ion acoustic instability in magnetic reconnection

We report on a first-principles numerical study of magnetic reconnection in plasmas with different initial ion-to-electron temperature ratios. In cases where this ratio is significantly below unity, we observe intense wave activity in the diffusion region, driven by the ion-acoustic instability. Our analysis shows that the dominant macroscopic effect of this instability is to drive substantial ion heating. In contrast to earlier studies reporting significant anomalous resistivity, we find that anomalous contributions due to the ion-acoustic instability are minimal. These results shed light on the dynamical impact of this instability on reconnection processes, offering new insights into the fundamental physics governing collisionless reconnection.

physics.plasm-ph↗

arXiv2025

Electron-only reconnection and inverse magnetic-energy transfer at sub-ion scales

We derive, and validate numerically, an analytical model for electron-only magnetic reconnection applicable to strongly magnetized plasmas. Our model predicts sub-ion-scale reconnection rates significantly higher than those pertaining to large-scale reconnection, aligning with recent observations and simulations. We apply this reconnection model to the problem of inverse magnetic energy transfer at sub-ion scales. We derive time-dependent scaling laws for the magnetic energy decay and the typical magnetic structure dimensions that differ from those previously found in the MHD regime. These scaling laws are validated via two- and three-dimensional simulations, demonstrating that sub-ion scale magnetic fields can reach large, system-size scales via successive coalescence.

physics.plasm-ph↗

arXiv2024

A Two-dimensional Numerical Study of Ion-Acoustic Turbulence

We investigate the linear and nonlinear evolution of the ion-acoustic instability in a collisionless plasma via two-dimensional (2D2V) Vlasov-Poisson numerical simulations. We initialize the system in a stable state and gradually drive it towards instability with an imposed, weak external electric field, thus avoiding super-critical initial conditions that are physically unrealizable. The nonlinear evolution of ion-acoustic turbulence (IAT) is characterized in detail, including the particles' distribution functions, particle heating, (two-dimensional) wave spectrum, and the resulting anomalous resistivity. An important result is that no steady saturated nonlinear state is ever reached in our simulations: strong ion heating suppresses the instability, which implies that the anomalous resistivity associated with IAT is transient and short-lived. Electron-acoustic waves (EAWs) are triggered during the late nonlinear evolution of the system, caused by strong modifications to the particle distribution induced by IAT.

physics.plasm-ph↗

arXiv2023

A transport-like approach to turbulence-mediated magnetic reconnection

A transport-like framework for the study of magnetic reconnection mediated by self-driven turbulence is proposed, based on timescale separation between the reconnection time and the characteristic timescale of the turbulent fluctuations which arise in the reconnection layer. We argue that the mean fields remain on MHD scales even in collisionless cases. These observations provide theoretical justification for an efficient computational approach to this problem, which we discuss.

physics.plasm-ph↗

arXiv2023

Magnetogenesis in a collisionless plasma: from Weibel instability to turbulent dynamo

We report on a first-principles numerical and theoretical study of plasma dynamo in a fully kinetic framework. By applying an external mechanical force to an initially unmagnetized plasma, we develop a self-consistent treatment of the generation of ``seed'' magnetic fields, the formation of turbulence, and the inductive amplification of fields by the fluctuation dynamo. Driven large-scale motions in an unmagnetized, weakly collisional plasma are subject to strong phase mixing, which leads to the development of thermal pressure anisotropy. This anisotropy triggers the Weibel instability, which produces filamentary ``seed'' magnetic fields on plasma-kinetic scales. The plasma is thereby magnetized, enabling efficient stretching and folding of the fields by the plasma motions and the development of Larmor-scale kinetic instabilities such as the firehose and mirror. The scattering of particles off the associated microscale magnetic fluctuations provides an effective viscosity, regulating the field morphology and turbulence. During this process, the seed field is further amplified by the fluctuation dynamo until they reach energy equipartition with the turbulent flow. By demonstrating that equipartition magnetic fields can be generated from an initially unmagnetized plasma through large-scale turbulent flows, this work has important implications for the origin and amplification of magnetic fields in the intracluster and intergalactic mediums.

astro-ph.HE↗

arXiv2023

A quantum algorithm for the linear Vlasov equation with collisions

The Vlasov equation is a nonlinear partial differential equation that provides a first-principles description of the dynamics of plasmas. Its linear limit is routinely used in plasma physics to investigate plasma oscillations and stability. In this work, we present a quantum algorithm that simulates the linearized Vlasov equation with and without collisions, in the one-dimensional, electrostatic limit. Rather than solving this equation in its native spatial and velocity phase-space, we adopt an efficient representation in the dual space yielded by a Fourier-Hermite expansion. The Fourier-Hermite representation is exponentially more compact, thus yielding a classical algorithm that can match the performance of a previously proposed quantum algorithm for this problem. This representation results in a system of linear ordinary differential equations which can be solved with well-developed quantum algorithms: Hamiltonian simulation in the collisionless case, and quantum ODE solvers in the collisional case. In particular, we demonstrate that a quadratic speedup in system size is attainable.

physics.plasm-ph↗

arXiv2022

Intermittency and electron heating in kinetic-Alfvén-wave turbulence

We report analytical and numerical investigations of sub-ion-scale turbulence in low-beta plasmas, focusing on the spectral properties of the fluctuations and electron heating. In the isothermal limit, the numerical results strongly support a description of the turbulence as a critically-balanced Kolmogorov-like cascade of kinetic Alfvén wave fluctuations, as amended by Boldyrev & Perez (Astrophys. J. Lett. 758, L44 (2012)) to include intermittent effects. When the constraint of isothermality is removed (i.e., with the inclusion of electron kinetic physics), the energy spectrum is found to steepen due to electron Landau damping, which is enabled by the local weakening of advective nonlinearities around current sheets, and yields significant energy dissipation via a velocity-space cascade. The use of a Hermite-polynomial representation to express the velocity-space dependence of the electron distribution function allows us to obtain an analytical, lowest-order solution for the Hermite moments of the distribution, which is borne out by numerical simulations.

astro-ph.HE↗

arXiv2022

Hybrid Quantum-Classical Algorithm for Hydrodynamics

A new model of nonlinear charged quantum relativistic fluids is presented. This model can be discretized into Discrete Time Quantum Walks (DTQWs), and a new hybrid (quantum-classical) algorithm for implementing these walks on NISQ devices is proposed. High resolution (up to $N=2^{17}$ grid points) hybrid numerical simulations of relativistic and non-relativistic hydrodynamical shocks on current IBM NISQs are performed with this algorithm and shown to reproduce equivalent simulations on classical computers. This work demonstrates that nonlinear fluid dynamics can be simulated on NISQs, and opens the door to simulating other, quantum and non-quantum fluids, including plasmas, with more general quantum walks and quantum automata.

quant-ph↗

arXiv2021

Dynamic Phase Alignment in Navier-Stokes Turbulence

In Navier-Stokes turbulence, energy and helicity injected at large scales are subject to a joint direct cascade, with both quantities exhibiting a spectral scaling $\propto k^{-5/3}$. We demonstrate via direct numerical simulations that the two cascades are compatible due to the existence of a strong scale-dependent phase alignment between velocity and vorticity fluctuations, with the phase alignment angle scaling as $\cosα_k\propto k^{-1}$.

physics.flu-dyn↗

arXiv2021

Statistical description of coalescing magnetic islands via magnetic reconnection

The physical picture of interacting magnetic islands provides a useful paradigm for certain plasma dynamics in a variety of physical environments, such as the solar corona, the heliosheath, and the Earth's magnetosphere. In this work, we derive an island kinetic equation to describe the evolution of the island distribution function (in area and in flux of islands) subject to a collisional integral designed to account for the role of magnetic reconnection during island mergers. This equation is used to study the inverse transfer of magnetic energy through the coalescence of magnetic islands in 2D. We solve our island kinetic equation numerically for three different types of initial distribution: delta-distribution, Gaussian and power-law distribution. The time evolution of several key quantities is found to agree well with our analytical predictions: magnetic energy decays as $\tilde t^{-1}$, the number of islands decreases as $\tilde t^{-1}$, and the averaged area of islands grows as $\tilde t$, where $\tilde t$ is the time normalized to the characteristic reconnection time scale of islands. General properties of the distribution function and the magnetic energy spectrum are also studied.

physics.plasm-ph↗

arXiv2021

Spontaneous magnetization of collisionless plasma through the action of a shear flow

We study in a fully kinetic framework the generation of seed magnetic fields through the Weibel instability driven in an initially unmagnetized plasma by a large-scale shear force. We develop an analytical model that describes the development of thermal pressure anisotropy via phase mixing, the ensuing exponential growth of magnetic fields in the linear Weibel stage, and its saturation when the seed magnetic fields become strong enough to instigate gyromotion of particles and thereby inhibit their free-streaming. The predicted scaling dependencies of the saturated seed fields on key parameters (e.g., ratio of system scale to electron skin depth, the forcing amplitude) are confirmed by 3D and 2D particle-in-cell simulations using an electron-positron plasma. This work demonstrates the spontaneous magnetization of a collisionless plasma through large-scale motions as simple as a shear flow, and therefore has important implications for magnetogenesis in dilute astrophysical systems.

physics.plasm-ph↗