arXiv subjects

Ermal Rrapaj

Publications and source records attributed to Ermal Rrapaj.

At least 37 records · Page 2Linked to original sources

arXiv2025

Collective Neutrino Oscillations in Three Flavors on Qubit and Qutrit Processors

Collective neutrino flavor oscillations are of primary importance in understanding the dynamic evolution of core-collapse supernovae and subsequent terrestrial detection, but also among the most challenging aspects of numerical simulations. This situation is complicated by the quantum many-body nature of the problem due to neutrino-neutrino interactions which demands a quantum treatment. An additional complication is the presence of three flavors, which often is approximated by the electron flavor and a heavy lepton flavor. In this work, we provide both qubit and qutrit encodings for all three flavors, and develop optimized quantum circuits for the time evolution and analyze the Trotter error. We conclude our study with a hardware experiment of a system of two neutrinos with superconducting hardware: the IBM Torino device for qubits and AQT device for qutrits. We find that error mitigation greatly helps in obtaining a signal consistent with simulations. While hardware results are comparable at this stage, we expect the qutrit setup to be more convenient for large-scale simulations since it does not suffer from probability leakage into nonphsycial qubit space, unlike the qubit setup.

quant-ph↗

arXiv2024

HATT: Hamiltonian Adaptive Ternary Tree for Optimizing Fermion-to-Qubit Mapping

This paper introduces the Hamiltonian-Adaptive Ternary Tree (HATT) framework to compile optimized Fermion-to-qubit mapping for specific Fermionic Hamiltonians. In the simulation of Fermionic quantum systems, efficient Fermion-to-qubit mapping plays a critical role in transforming the Fermionic system into a qubit system. HATT utilizes ternary tree mapping and a bottom-up construction procedure to generate Hamiltonian aware Fermion-to-qubit mapping to reduce the Pauli weight of the qubit Hamiltonian, resulting in lower quantum simulation circuit overhead. Additionally, our optimizations retain the important vacuum state preservation property in our Fermion-to-qubit mapping and reduce the complexity of our algorithm from $O(N^4)$ to $O(N^3)$. Evaluations and simulations of various Fermionic systems demonstrate $5\sim20\%$ reduction in Pauli weight, gate count, and circuit depth, alongside excellent scalability to larger systems. Experiments on the Ionq quantum computer also show the advantages of our approach in noise resistance in quantum simulations.

quant-ph↗

arXiv2024

Comprehensive Performance Modeling and System Design Insights for Foundation Models

Generative AI, in particular large transformer models, are increasingly driving HPC system design in science and industry. We analyze performance characteristics of such transformer models and discuss their sensitivity to the transformer type, parallelization strategy, and HPC system features (accelerators and interconnects). We utilize a performance model that allows us to explore this complex design space and highlight its key components. We find that different transformer types demand different parallelism and system characteristics at different training regimes. Large Language Models are performant with 3D parallelism and amplify network needs only at pre-training scales with reduced dependence on accelerator capacity and bandwidth. On the other hand, long-sequence transformers, representative of scientific foundation models, place a more uniform dependence on network and capacity with necessary 4D parallelism. Our analysis emphasizes the need for closer performance modeling of different transformer types keeping system features in mind and demonstrates a path towards this. Our code is available as open-source.

cs.LG↗

arXiv2024

Restricted Boltzmann Machines Propagators for Auxiliary Field Diffusion Monte Carlo

The auxiliary field diffusion Monte Carlo method uses imaginary-time projection techniques to accurately solve the ground-state wave function of atomic nuclei and infinite nuclear matter. In this work, we present a novel representation of the imaginary-time propagator based on restricted Boltzmann machines. We test its accuracy against the routinely employed Hubbard-Stratonovich transformations by evaluating ground-state energies and single-particle densities of selected light nuclei. This analysis paves the way for incorporating more realistic nuclear potentials in the auxiliary field diffusion Monte Carlo method, including isospin-dependent spin-orbit terms and cubic spin-isospin operators, which characterize accurate phenomenological and chiral effective field theory Hamiltonians.

nucl-th↗

arXiv2024

Exact block encoding of imaginary time evolution with universal quantum neural networks

We develop a constructive approach to generate quantum neural networks capable of representing the exact thermal states of all many-body qubit Hamiltonians. The Trotter expansion of the imaginary-time propagator is implemented through an exact block encoding by means of a unitary, restricted Boltzmann machine architecture. Marginalization over the hidden-layer neurons (auxiliary qubits) creates the non-unitary action on the visible layer. Then, we introduce a unitary deep Boltzmann machine architecture, in which the hidden-layer qubits are allowed to couple laterally to other hidden qubits. We prove that this wave function ansatz is closed under the action of the imaginary-time propagator and, more generally, can represent the action of a universal set of quantum gate operations. We provide analytic expressions for the coefficients for both architectures, thus enabling exact network representations of thermal states without stochastic optimization of the network parameters. In the limit of large imaginary time, the ansatz yields the ground state of the system. The number of qubits grows linearly with the system size and total imaginary time for a fixed interaction order. Both networks can be readily implemented on quantum hardware via mid-circuit measurements of auxiliary qubits. If only one auxiliary qubit is measured and reset, the circuit depth scales linearly with imaginary time and system size, while the width is constant. Alternatively, one can employ a number of auxiliary qubits linearly proportional to the system size, and circuit depth grows linearly with imaginary time only.

quant-ph↗

arXiv2024

Correlations and Distinguishability Challenges in Supernova Models: Insights from Future Neutrino Detectors

This paper explores core-collapse supernovae as crucial targets for neutrino telescopes, addressing uncertainties in their simulation results. We comprehensively analyze eighteen modern simulations and discriminate among supernova models using realistic detectors and interactions. A significant correlation between the total neutrino energy and cumulative counts, driven by massive lepton neutrinos and oscillations, is identified, particularly noticeable with the DUNE detector. Bayesian techniques indicate strong potential for model differentiation during a Galactic supernova event, with HK excelling in distinguishing models based on equation of state, progenitor mass, and mixing scheme.

astro-ph.HE↗

arXiv2023

Quantum information and quantum simulation of neutrino physics

In extreme astrophysical environments such as core-collapse supernovae and binary neutron star mergers, neutrinos play a major role in driving various dynamical and microphysical phenomena, such as baryonic matter outflows, the synthesis of heavy elements, and the supernova explosion mechanism itself. The interactions of neutrinos with matter in these environments are flavor-specific, which makes it of paramount importance to understand the flavor evolution of neutrinos. Flavor evolution in these environments can be a highly nontrivial problem thanks to a multitude of collective effects in flavor space, arising due to neutrino-neutrino ($ν$-$ν$) interactions in regions with high neutrino densities. A neutrino ensemble undergoing flavor oscillations under the influence of significant $ν$-$ν$ interactions is somewhat analogous to a system of coupled spins with long-range interactions among themselves and with an external field ('long-range' in momentum-space in the case of neutrinos). As a result, it becomes pertinent to consider whether these interactions can give rise to significant quantum correlations among the interacting neutrinos, and whether these correlations have any consequences for the flavor evolution of the ensemble. In particular, one may seek to utilize concepts and tools from quantum information science and quantum computing to deepen our understanding of these phenomena. In this article, we attempt to summarize recent work in this field. Furthermore, we also present some new results in a three-flavor setting, considering complex initial states.

nucl-th↗

arXiv2023

Chiral EFT calculation of neutrino reactions in warm neutron-rich matter

Neutrino scattering and absorption rates of relevance to supernovae and neutron star mergers are obtained from nuclear matter dynamical structure functions that encode many-body effects from nuclear mean fields and correlations. We employ nuclear interactions from chiral effective field theory to calculate the density, spin, isospin, and spin-isospin response functions of warm beta-equilibrium nuclear matter. We include corrections to the single-particle energies in the mean field approximation as well as vertex corrections resummed in the random phase approximation (RPA), including, for the first time, both direct and exchange diagrams. We find that correlations included through the RPA redistribute the strength of the response to higher energy for neutrino absorption and lower energy for antineutrino absorption. This tends to suppress the absorption rate of electron neutrinos across all relevant energy scales. In contrast, the inclusion of RPA correlations enhances the electron antineutrino absorption rate at low energy and supresses the rate at high energy. These effects are especially important at high-density and in the vicinity of the neutrino decoupling region. Implications for heavy element nucleosynthesis, electromagnetic signatures of compact object mergers, supernova dynamics, and neutrino detection from galactic supernovae are discussed briefly.

nucl-th↗

arXiv2023

Less is More! A slim architecture for optimal language translation

The softmax attention mechanism has emerged as a noteworthy development in the field of Artificial Intelligence research, building on the successes of Transformer-based architectures. However, their ever increasing sizes necessitate ever increasing computational memory, that limits their usage. We propose KgV, a sigmoid gating mechanism that, in conjunction with softmax attention, significantly boosts performance without increasing architecture size. To amend the size requirements, we leverage Tensor Chains to identify and prune the excess parameters. We find that such excess resides primarily within the embedding layer, and not in the output linear layer. To further improve embedding and significantly reduce parameters, we introduce H-SoftPOS, a hierarchical embedding layer which simultaneously enhances performance. Remarkably, on the WMT14 English-German validation set, our approach yields a threefold reduction in perplexity, surpassing the current state-of-the-art, while reducing parameter counts also by a factor of 3. When we further reduce the number of parameters up to sevenfold, we can still achieve a 21\% decrease in perplexity with respect to the baseline Transformer. To understand generalization capabilities, we conduct experiments on the 7 language pairs of the WMT17 dataset. Our method outperforms existing techniques in terms of test loss while simultaneously halving the number of parameters. Moreover, we observe a 70 times reduction in variance with respect to the prior state-of-the-art. In conclusion, our proposed method yields significant improvements in performance and much lower memory cost. We call the resulting architecture Anthe.

cs.CL↗

arXiv2023

Many-body collective neutrino oscillations: recent developments

Neutrino flavor transformations in core-collapse supernovae and binary neutron star mergers represent a complex and unsolved problem that is integral to our understanding of the dynamics and nucleosynthesis in these environments. The high number densities of neutrinos present in these environments can engender various collective effects in neutrino flavor transformations, driven either by neutrino-neutrino coherent scattering, or in some cases, through collisional (incoherent) interactions. An ensemble of neutrinos undergoing coherent scattering among themselves is an interacting quantum many-body system -- as such, there is a tantalising prospect of quantum entanglement developing between the neutrinos, which can leave imprints on their flavor evolution histories. Here, we seek to summarize recent progress that has been made towards understanding this phenomenon.

hep-ph↗

arXiv2022

Gate Based Implementation of the Laplacian with BRGC Code for Universal Quantum Computers

We study the gate-based implementation of the binary reflected Gray code (BRGC) and binary code of the unitary time evolution operator due to the Laplacian discretized on a lattice with periodic boundary conditions. We find that the resulting Trotter error is independent of system size for a fixed lattice spacing through the Baker-Campbell-Hausdorff formula. We then present our algorithm for building the BRGC quantum circuit. For an adiabatic evolution time $t$ with this circuit, and spectral norm error $ε$, we find the circuit cost (number of gates) and depth required are $\mc{O}(t^2 n A D /ε)$ with $n-3$ auxiliary qubits for a system with $2^n$ lattice points per dimension $D$ and particle number $A$; an improvement over binary position encoding which requires an exponential number of $n$-local operators. Further, under the reasonable assumption that $[T,V]$ bounds $Δt$, with $T$ the kinetic energy and $V$ a non-trivial potential, the cost of QFT (Quantum Fourier Transform ) implementation of the Laplacian scales as $\mc{O}\left(n^2\right)$ with depth $\mc{O}\left(n\right)$ while BRGC scales as $\mc{O}\left(n\right)$, giving an advantage to the BRGC implementation.

quant-ph↗

arXiv2022

Improving Schrödinger Equation Implementations with Gray Code for Adiabatic Quantum Computers

We reformulate the continuous space Schrödinger equation in terms of spin Hamiltonians. For the kinetic energy operator, the critical concept facilitating the reduction in model complexity is the idea of position encoding. Binary encoding of position produces a Heisenberg-like model and yields exponential improvement in space complexity when compared to classical computing. Encoding with a binary reflected Gray code, and a Hamming distance 2 Gray code yields the additional effect of reducing the spin model down to the XZ and transverse Ising model respectively. We also identify the bijective mapping between diagonal unitaries and the Walsh series, producing the mapping of any real potential to a series of $k$-local Ising models through the fast Walsh transform. Finally, in a finite volume, we provide some numerical evidence to support the claim that the total time needed for adiabatic evolution is protected by the infrared cutoff of the system. As a result, initial state preparation from a free-field wavefunction to an interacting system is expected to exhibit polynomial time complexity with volume and constant scaling with respect to lattice discretization for all encodings. For the Hamming distance 2 Gray code, the evolution starts with the transverse Hamiltonian before introducing penalties such that the low lying spectrum reproduces the energy levels of the Laplacian. The adiabatic evolution of the penalty Hamiltonian is therefore sensitive to the ultraviolet scale. It is expected to exhibit polynomial time complexity with lattice discretization, or exponential time complexity with respect to the number of qubits given a fixed volume.

quant-ph↗

arXiv2022

Entanglement and correlations in fast collective neutrino flavor oscillations

Collective neutrino oscillations play a crucial role in transporting lepton flavor in astrophysical settings like supernovae and neutron star binary merger remnants, which are characterized by large neutrino densities. In these settings, simulations in the mean-field approximation show that neutrino-neutrino interactions can overtake vacuum oscillations and give rise to fast collective flavor evolution on time-scales $t\proptoμ^{-1}$, with $μ$ proportional to the local neutrino density. In this work, we study the full out-of-equilibrium flavor dynamics in simple multi-angle geometries displaying fast oscillations in the mean field linear stability analysis. Focusing on simple initial conditions, we analyze the production of pair correlations and entanglement in the complete many-body-dynamics as a function of the number $N$ of neutrinos in the system, for up to thousands of neutrinos. Similarly to simpler geometries with only two neutrino beams, we identify three regimes: stable configurations with vanishing flavor oscillations, marginally unstable configurations with evolution occurring on long time scales $τ\approxμ^{-1}\sqrt{N}$, and unstable configurations showing flavor evolution on short time scales $τ\approxμ^{-1}\log(N)$. We present evidence that these fast collective modes are generated by the same dynamical phase transition which leads to the slow bipolar oscillations, establishing a connection between these two phenomena and explaining the difference in their time scales. We conclude by discussing a semi-classical approximation which reproduces the entanglement entropy at short to medium time scales and can be potentially useful in situations with more complicated geometries where classical simulation methods starts to become inefficient.

astro-ph.HE↗

arXiv2022

Sphaleron Transition Rates and the Chiral Magnetic Effect

The chiral magnetic effect is a novel quantum phenomenon proposed for high-energy nuclear collisions but which has yet to be observed. We quantify the axial charge relaxation time, due to sphalerons, which enters in simulations of this effect. An extrapolation of weak coupling calculations of the sphaleron rate yields rather different relaxation times than strong coupling AdS/CFT calculations. The AdS/CFT relaxation time is the larger one of the two by an order of magnitude, but the weak coupling relaxation time may not be reliable because it is only marginally bigger than the microscopic thermalization time. The role of quark masses has yet to be accurately assessed.

hep-ph↗

arXiv2021

Prediction and compression of lattice QCD data using machine learning algorithms on quantum annealer

We present regression and compression algorithms for lattice QCD data utilizing the efficient binary optimization ability of quantum annealers. In the regression algorithm, we encode the correlation between the input and output variables into a sparse coding machine learning algorithm. The trained correlation pattern is used to predict lattice QCD observables of unseen lattice configurations from other observables measured on the lattice. In the compression algorithm, we define a mapping from lattice QCD data of floating-point numbers to the binary coefficients that closely reconstruct the input data from a set of basis vectors. Since the reconstruction is not exact, the mapping defines a lossy compression, but, a reasonably small number of binary coefficients are able to reconstruct the input vector of lattice QCD data with the reconstruction error much smaller than the statistical fluctuation. In both applications, we use D-Wave quantum annealers to solve the NP-hard binary optimization problems of the machine learning algorithms.

hep-lat↗

arXiv2021

Lossy compression of statistical data using quantum annealer

We present a new lossy compression algorithm for statistical floating-point data through a representation learning with binary variables. The algorithm finds a set of basis vectors and their binary coefficients that precisely reconstruct the original data. The optimization for the basis vectors is performed classically, while binary coefficients are retrieved through both simulated and quantum annealing for comparison. A bias correction procedure is also presented to estimate and eliminate the error and bias introduced from the inexact reconstruction of the lossy compression for statistical data analyses. The compression algorithm is demonstrated on two different datasets of lattice quantum chromodynamics simulations. The results obtained using simulated annealing show 3.5 times better compression performance than the algorithms based on a neural-network autoencoder and principal component analysis. Calculations using quantum annealing also show promising results, but performance is limited by the integrated control error of the quantum processing unit, which yields large uncertainties in the biases and coupling parameters. Hardware comparison is further studied between the previous generation D-Wave 2000Q and the current D-Wave Advantage system. Our study shows that the Advantage system is more likely to obtain low-energy solutions for the problems than the 2000Q.

quant-ph↗

arXiv2021

Inference of neutrino flavor evolution through data assimilation and neural differential equations

The evolution of neutrino flavor in dense environments such as core-collapse supernovae and binary compact object mergers constitutes an important and unsolved problem. Its solution has potential implications for the dynamics and heavy-element nucleosynthesis in these environments. In this paper, we build upon recent work to explore inference-based techniques for estimation of model parameters and neutrino flavor evolution histories. We combine data assimilation, ordinary differential equation solvers, and neural networks to craft an inference approach tailored for non-linear dynamical systems. Using this architecture, and a simple two-neutrino, two-flavor model, we test various optimization algorithms with the help of four experimental setups. We find that employing this new architecture, together with evolutionary optimization algorithms, accurately captures flavor histories in the four experiments. This work provides more options for extending inference techniques to large numbers of neutrinos.

astro-ph.HE↗

arXiv2021

Exact representations of many body interactions with RBM neural networks

Restricted Boltzmann Machines (RBM) are simple statistical models defined on a bipartite graph which have been successfully used in studying more complicated many-body systems, both classical and quantum. In this work, we exploit the representation power of RBMs to provide an exact decomposition of many-body contact interactions into one-body operators coupled to discrete auxiliary fields. This construction generalizes the well known Hirsch's transform used for the Hubbard model to more complicated theories such as Pionless EFT in nuclear physics, which we analyze in detail. We also discuss possible applications of our mapping for quantum annealing applications and conclude with some implications for RBM parameter optimization through machine learning.

nucl-th↗