arXiv subjects

Muhammad Asaduzzaman

Publications and source records attributed to Muhammad Asaduzzaman.

32 records · Page 2Linked to original sources

arXiv2024

ZS4C: Zero-Shot Synthesis of Compilable Code for Incomplete Code Snippets using LLMs

Technical Q&A sites are valuable for software developers seeking knowledge, but the code snippets they provide are often uncompilable and incomplete due to unresolved types and missing libraries. This poses a challenge for users who wish to reuse or analyze these snippets. Existing methods either do not focus on creating compilable code or have low success rates. To address this, we propose ZS4C, a lightweight approach for zero-shot synthesis of compilable code from incomplete snippets using Large Language Models (LLMs). ZS4C operates in two stages: first, it uses an LLM, like GPT-3.5, to identify missing import statements in a snippet; second, it collaborates with a validator (e.g., compiler) to fix compilation errors caused by incorrect imports and syntax issues. We evaluated ZS4C on the StatType-SO benchmark and a new dataset, Python-SO, which includes 539 Python snippets from Stack Overflow across the 20 most popular Python libraries. ZS4C significantly outperforms existing methods, improving the compilation rate from 63% to 95.1% compared to the state-of-the-art SnR, marking a 50.1% improvement. On average, ZS4C can infer more accurate import statements (with an F1 score of 0.98) than SnR, with an improvement of 8.5% in the F1.

cs.SE↗

arXiv2024

Fermions, quantum gravity and holography in two dimensions

We study a model comprising $N$ flavors of Kähler Dirac fermion propagating on a triangulated two dimensional disk which is constrained to have a negative average bulk curvature. Dirichlet boundary conditions are chosen for the fermions. Quantum fluctuations of the geometry are included by summing over all possible triangulations consistent with these constraints. We show in the limit $N\to \infty$ that the partition function is dominated by a regular triangulation of two dimensional hyperbolic space. We use strong coupling expansions and Monte Carlo simulation to show that in this limit boundary correlators of the fermions have a power law dependence on boundary separation as one expects from holography. However we argue that this behavior breaks down for any finite number of massive fields in the thermodynamic limit and quantum fluctuations of the bulk geometry drive the theory into a non-holographic phase. In contrast, for massless fermions we find evidence that the boundary is conformal even for finite $N$. This is consistent with theoretical results in quantum Liouville theory.

hep-lat↗

arXiv2024

Sachdev-Ye-Kitaev model on a noisy quantum computer

We study the SYK model -- an important toy model for quantum gravity on IBM's superconducting qubit quantum computers. By using a graph-coloring algorithm to minimize the number of commuting clusters of terms in the qubitized Hamiltonian, we find the gate complexity of the time evolution using the first-order product formula for $N$ Majorana fermions is $\mathcal{O}(N^5 J^{2}t^2/ε)$ where $J$ is the dimensionful coupling parameter, $t$ is the evolution time, and $ε$ is the desired precision. With this improved resource requirement, we perform the time evolution for $N=6, 8$ with maximum two-qubit circuit depth of 343. We perform different error mitigation schemes on the noisy hardware results and find good agreement with the exact diagonalization results on classical computers and noiseless simulators. In particular, we compute return probability after time $t$ and out-of-time order correlators (OTOC) which is a standard observable of quantifying the chaotic nature of quantum systems.

quant-ph↗

arXiv2024

Simulating Field Theories with Quantum Computers

In this study, we investigate Trotter evolution in the Gross-Neveu and hyperbolic Ising models in two spacetime dimensions, using quantum computers. We identify different sources of errors prevalent in various quantum processing units and discuss challenges to scale up the size of the computation. We present benchmark results obtained on a variety of platforms and employ a range of error mitigation techniques to address coherent and incoherent noise. By comparing these mitigated outcomes with exact diagonalization results and density matrix renormalization group calculations, we assess the effectiveness of our approaches. Moreover, we demonstrate the implementation of an out-of-time-ordered correlator (OTOC) protocol using IBM's quantum computers.

quant-ph↗

arXiv2023

Tensor network representation of non-abelian gauge theory coupled to reduced staggered fermions

We show how to construct a tensor network representation of the path integral for reduced staggered fermions coupled to a non-abelian gauge field in two dimensions. The resulting formulation is both memory and computation efficient because reduced staggered fermions can be represented in terms of a minimal number of tensor indices while the gauge sector can be approximated using Gaussian quadrature with a truncation. Numerical results obtained using the Grassmann TRG algorithm are shown for the case of $SU(2)$ lattice gauge theory and compared to Monte Carlo results.

hep-lat↗

arXiv2023

Quantum Ising model on two dimensional anti-de Sitter space

This paper investigates the transverse Ising model on a discretization of two-dimensional anti-de Sitter space. We use classical and quantum algorithms to simulate real-time evolution and measure out-of-time-ordered correlators (OTOC). The latter can probe thermalization and scrambling of quantum information under time evolution. We compared tensor network-based methods both with simulation on gated-based superconducting quantum devices and analog quantum simulation using Rydberg arrays. While studying this system's thermalization properties, we observed different regimes depending on the radius of curvature of the space. In particular, we find a region of parameter space where the thermalization time depends only logarithmically on the number of degrees of freedom.

quant-ph↗

arXiv2022

Quantum Simulation of the N flavor Gross-Neveu Model

We discuss the use of quantum simulation to study an $N$ flavor theory of interacting relativistic fermions in(1+1) dimensions on NISQ era machines. The case of two flavors is particularly interesting as it can be mapped to the Hubbard model. We derive the appropriate qubit Hamiltonians and associated quantum circuits. We compare classical simulation and DMRG/TEBD calculations with the results of quantum simulation on various platforms for $N$=2 and 4. We demonstrate that the four steps of the calculations of real-time scattering can actually be implemented using current NISQ devices.

hep-lat↗

arXiv2022

Improved coarse-graining methods on two dimensional tensor networks including fermions

We show how to apply renormalization group algorithms incorporating entanglement filtering methods and a loop optimization to a tensor network which includes Grassmann variables which represent fermions in an underlying lattice field theory. As a numerical test a variety of quantities are calculated for two dimensional Wilson--Majorana fermions and for the two flavor Gross--Neveu model. The improved algorithms show much better accuracy for quantities such as the free energy and the determination of Fisher's zeros.

hep-lat↗

arXiv2022

Euclidean Dynamical Triangulations Revisited

We conduct numerical simulations of a model of four dimensional quantum gravity in which the path integral over continuum Euclidean metrics is approximated by a sum over combinatorial triangulations. At fixed volume the model contains a discrete Einstein-Hilbert term with coupling $κ$ and local measure term with coupling $β$ that weights triangulations according to the number of simplices sharing each vertex. We map out the phase diagram in this two dimensional parameter space and compute a variety of observables that yield information on the nature of any continuum limit. Our results are consistent with a line of first order phase transitions with a latent heat that decreases as $κ\to\infty$. We find a Hausdorff dimension along the critical line that approaches $D_H=4$ for large $κ$ and a spectral dimension that is consistent with $D_s=\frac{3}{2}$ at short distances. These results are broadly in agreement with earlier works on Euclidean dynamical triangulation models which utilize degenerate triangulations and/or different measure terms and indicate that such models exhibit a degree of universality.

hep-lat↗

arXiv2021

Scalar fields on fluctuating hyperbolic geometries

We present results on the behavior of the boundary-boundary correlation function of scalar fields propagating on discrete two-dimensional random triangulations representing manifolds with the topology of a disk. We use a gravitational action that includes a curvature squared operator, which favors a regular tessellation of hyperbolic space for large values of its coupling. We probe the resultant geometry by analyzing the propagator of a massive scalar field and show that the conformal behavior seen in the uniform hyperbolic space survives as the coupling approaches zero. The analysis of the boundary correlator suggests that holographic predictions survive, at least, weak quantum gravity corrections. We then show how such an $R^2$ operator might be induced as a result of integrating out massive lattice fermions and show preliminary result for boundary correlation functions that include the effects of this fermionic backreaction on the geometry.

hep-lat↗

arXiv2021

Holography for Ising spins on the hyperbolic plane

Motivated by the AdS/CFT correspondence, we use Monte Carlo simulation to investigate the Ising model formulated on tessellations of the two-dimensional hyperbolic disk. We focus in particular on the behavior of boundary-boundary correlators, which exhibit power-law scaling both below and above the bulk critical temperature indicating scale invariance of the boundary theory at any temperature. This conclusion is strengthened by a finite-size scaling analysis of the boundary susceptibility which yields a scaling exponent consistent with the scaling dimension extracted from the boundary correlation function. This observation provides evidence that the connection between continuum boundary conformal symmetry and isometries of the bulk hyperbolic space survives for simple interacting field theories even when the bulk is approximated by a discrete tessellation.

hep-lat↗

arXiv2021

Fast Clustering of Short Text Streams Using Efficient Cluster Indexing and Dynamic Similarity Thresholds

Short text stream clustering is an important but challenging task since massive amount of text is generated from different sources such as micro-blogging, question-answering, and social news aggregation websites. One of the major challenges of clustering such massive amount of text is to cluster them within a reasonable amount of time. The existing state-of-the-art short text stream clustering methods can not cluster such massive amount of text within a reasonable amount of time as they compute similarities between a text and all the existing clusters to assign that text to a cluster. To overcome this challenge, we propose a fast short text stream clustering method (called FastStream) that efficiently index the clusters using inverted index and compute similarity between a text and a selected number of clusters while assigning a text to a cluster. In this way, we not only reduce the running time of our proposed method but also reduce the running time of several state-of-the-art short text stream clustering methods. FastStream assigns a text to a cluster (new or existing) using the dynamically computed similarity thresholds based on statistical measure. Thus our method efficiently deals with the concept drift problem. Experimental results demonstrate that FastStream outperforms the state-of-the-art short text stream clustering methods by a significant margin on several short text datasets. In addition, the running time of FastStream is several orders of magnitude faster than that of the state-of-the-art methods.

cs.IR↗

arXiv2020

Tensor network formulation of two dimensional gravity

We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to two-dimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to gravity in a first-order formalism in which the local frame and spin connection are treated as independent fields. Recasting this lattice theory as a tensor network allows us to study the theory at strong coupling without encountering a sign problem. In two dimensions this tensor network is exactly soluble and we show that the system has a series of critical points that occur for pure imaginary coupling and are associated with first order phase transitions. We then augment the action with a Yang-Mills term which allows us to control the lattice spacing and show how to apply the TRG to compute the free energy and look for critical behavior. Finally we perform an analytic continuation in the gravity coupling in this extended model and show that its critical behavior in a certain scaling limit depends only on the topology of the underlying lattice. We also show how the lattice gauge theory can be naturally generalized to generate the Polyakov or Liouville action for two dimensional quantum gravity.

hep-lat↗

arXiv2020

Holography on tessellations of hyperbolic space

We compute boundary correlation functions for scalar fields on tessellations of two- and three-dimensional hyperbolic geometries. We present evidence that the continuum relation between the scalar bulk mass and the scaling dimension associated with boundary-to-boundary correlation functions survives the truncation of approximating the continuum hyperbolic space with a lattice.

hep-lat↗