arXiv subjects

Raghav G. Jha

Publications and source records attributed to Raghav G. Jha.

At least 37 records · Page 2Linked to original sources

arXiv2024

Continuous variable quantum computation of the $O(3)$ model in 1+1 dimensions

We formulate the $O(3)$ non-linear sigma model in 1+1 dimensions as a limit of a three-component scalar field theory restricted to the unit sphere in the large squeezing limit. This allows us to describe the model in terms of the continuous variable (CV) approach to quantum computing. We construct the ground state and excited states using the coupled-cluster Ansatz and find excellent agreement with the exact diagonalization results for a small number of lattice sites. We then present the simulation protocol for the time evolution of the model using CV gates and obtain numerical results using a photonic quantum simulator. We expect that the methods developed in this work will be useful for exploring interesting dynamics for a wide class of sigma models and gauge theories, as well as for simulating scattering events on quantum hardware in the coming decades.

quant-ph↗

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↗

arXiv2023

Tensor renormalization group study of 3D principal chiral model

We study the three-dimensional $SU(2)$ principal chiral model (PCM) using different tensor renormalization group methods based on the triad and anisotropic decomposition of the tensor. The tensor network representation is formulated based on the character expansion of the Boltzmann weight. We compare the average action obtained using these two tensor network algorithms and confirm that the resulting critical coupling and exponent are comparable with the recent estimations from the Monte Carlo methods.

hep-lat↗

arXiv2023

GPU-Acceleration of Tensor Renormalization with PyTorch using CUDA

We show that numerical computations based on tensor renormalization group (TRG) methods can be significantly accelerated with PyTorch on graphics processing units (GPUs) by leveraging NVIDIA's Compute Unified Device Architecture (CUDA). We find improvement in the runtime and its scaling with bond dimension for two-dimensional systems. Our results establish that the utilization of GPU resources is essential for future precision computations with TRG.

hep-lat↗

arXiv2023

Toward quantum computations of the $O(3)$ model using qumodes

We express the discrete 1+1-dimensional $O(3)$ non-linear sigma model (NL$σ$M) in a form well-suited for the continuous variable approach to quantum computing. Within the Schwinger boson formulation, we need two qumodes (quantum-mechanical oscillators) at each lattice site. We envision that it might be possible to reach the scaling regime of this model and observe asymptotic freedom on near-term photonic quantum devices in the coming decade.

hep-lat↗

arXiv2023

Notes on Quantum Computation and Information

We discuss fundamentals of quantum computing and information - quantum gates, circuits, algorithms, theorems, error correction, and provide collection of QISKIT programs and exercises for the interested reader.

quant-ph↗

arXiv2022

Non-perturbative phase structure of the bosonic BMN matrix model

We study the bosonic part of the BMN matrix model for wide ranges of temperatures, values of the deformation parameter, and numbers of colors $16 \leq N \leq 48$. Using lattice computations, we analyze phase transitions in the model, observing a single first-order transition from a uniform to a gapped phase for all values of the deformation parameter. We study the functional form of the dependence of the critical temperature on the deformation parameter, to describe how our results smoothly interpolate between the limits of the bosonic BFSS model and the gauged Gaussian model.

hep-lat↗

arXiv2022

Introduction to Monte Carlo for Matrix Models

We consider a wide range of matrix models and study them using the Monte Carlo technique in the large $N$ limit. The results we obtain agree with exact analytic expressions and recent numerical bootstrap methods for models with one and two matrices. We then present new results for several unsolved multi-matrix models where no other tool is yet available. In order to encourage an exchange of ideas between different numerical approaches to matrix models, we provide programs in Python that can be easily modified to study potentials other than the ones discussed. These programs were tested on a laptop and took between a few minutes to several hours to finish depending on the model, $N$, and the required precision.

hep-th↗

arXiv2022

Thermal phase structure of dimensionally reduced super-Yang--Mills

We present our current results from ongoing lattice investigations of the Berenstein--Maldacena--Nastase deformation of maximally supersymmetric Yang--Mills quantum mechanics. We focus on the thermal phase structure of this theory, which depends on both the temperature $T$ and the deformation parameter $μ$, through the dimensionless ratios $T / μ$ and $g = λ/ μ^3$ with $λ$ the 't Hooft coupling. We determine the critical $T / μ$ of the confinement transition for couplings $g$ that span three orders of magnitude, to connect weak-coupling perturbative calculations and large-$N$ dual supergravity predictions in the strong-coupling limit. Analyzing multiple lattice sizes up to $N_τ = 24$ and numbers of colors up to $N = 16$ allows initial checks of the large-$N$ continuum limit.

hep-lat↗

arXiv2022

Tensor renormalization of three-dimensional Potts model

We study the $q$-state Potts models on a cubic lattice in the thermodynamic limit using tensor renormalization group transformations with the triad approximation. By computing the thermodynamic potentials, we locate the first-order phase transitions for $10 < q \le 20$ which has not been explored using any method. We also examine the efficiency of the triad approximation method in obtaining the fixed-point tensor and comment on how this can be improved.

hep-lat↗

arXiv2021

Tensor renormalization group study of the 3d $O(2)$ model

We calculate thermodynamic potentials and their derivatives for the three-dimensional $O(2)$ model using tensor-network methods to investigate the well-known second-order phase transition. We also consider the model at non-zero chemical potential to study the Silver Blaze phenomenon, which is related to the particle number density at zero temperature. Furthermore, the temperature dependence of the number density is explored using asymmetric lattices. Our results for both zero and non-zero magnetic field, temperature, and chemical potential are consistent with those obtained using other methods.

hep-lat↗

arXiv2021

Large-$N$ limit of two-dimensional Yang--Mills theory with four supercharges

We study the two-dimensional Yang--Mills theory with four supercharges in the large-$N$ limit. By using thermal boundary conditions, we analyze the internal energy and the distribution of scalars. We compare their behavior to the maximally supersymmetric case with sixteen supercharges, which is known to admit a holographic interpretation. Our lattice results for the scalar distribution show no visible dependence on $N$ and the energy at strong coupling appears independent of temperature.

hep-lat↗

arXiv2020

Three-dimensional super-Yang--Mills theory on the lattice and dual black branes

In the large-$N$ and strong-coupling limit, maximally supersymmetric SU($N$) Yang--Mills theory in $(2 + 1)$ dimensions is conjectured to be dual to the decoupling limit of a stack of $N$ D$2$-branes, which may be described by IIA supergravity.We study this conjecture in the Euclidean setting using nonperturbative lattice gauge theory calculations.Our supersymmetric lattice construction naturally puts the theory on a skewed Euclidean 3-torus. Taking one cycle to have anti-periodic fermion boundary conditions, the large-torus limit is described by certain Euclidean black holes. We compute the bosonic action---the variation of the partition function---and compare our numerical results to the supergravity prediction as the size of the torus is changed, keeping its shape fixed. Our lattice calculations primarily utilize $N = 8$ with extrapolations to the continuum limit, and our results are consistent with the expected gravity behavior in the appropriate large-torus limit.

hep-th↗

arXiv2020

Positive Geometries for all Scalar Theories from Twisted Intersection Theory

We show that accordiohedra furnish polytopes which encode amplitudes for all massive scalar field theories with generic interactions. This is done by deriving integral formulae for the Feynman diagrams at tree level and integrands at one loop level in the planar limit using the twisted intersection theory of convex realizations of the accordiohedron polytopes.

hep-th↗

arXiv2020

Critical analysis of two-dimensional classical XY model

We consider the two-dimensional classical XY model on a square lattice in the thermodynamic limit using tensor renormalization group and precisely determine the critical temperature corresponding to the Berezinskii-Kosterlitz-Thouless (BKT) phase transition to be 0.89290(5) which is an improvement compared to earlier studies using tensor network methods.

hep-lat↗

arXiv2020

Finite $N$ unitary matrix model

We consider one-plaquette unitary matrix model at finite $N$ using exact expression of the partition function for both SU($N$) and U($N$) groups.

hep-lat↗

arXiv2020

Thermal phase structure of a supersymmetric matrix model

We present initial results from ongoing lattice investigations into the thermal phase structure of the Berenstein--Maldacena--Nastase deformation of maximally supersymmetric Yang--Mills quantum mechanics. The phase diagram of the theory depends on both the temperature $T$ and the deformation parameter $μ$, through the dimensionless ratios $T / μ$ and $g \equiv λ/ μ^3$ with $λ$ the 't Hooft coupling. Considering couplings $g$ that span three orders of magnitude, we reproduce the weak-coupling perturbative prediction for the deconfinement $T / μ$ and approach recent large-$N$ dual supergravity analyses in the strong-coupling limit. We are carrying out calculations with lattice sizes up to $N_τ = 24$ and numbers of colors up to $N = 16$, to allow initial checks of the large-$N$ continuum limit.

hep-lat↗

arXiv2019

Tensor renormalization group study of the non-Abelian Higgs model in two dimensions

We study the $SU(2)$ gauge-Higgs model in two Euclidean dimensions using the tensor renormalization group (TRG) approach. We derive a tensor formulation for this model in the unitary gauge and compare the expectation values of different observables between TRG and Monte Carlo simulations finding excellent agreement between the two methods. In practice we find the TRG method to be far superior to Monte Carlo simulation for calculations of the Polyakov loop correlation function which is used to extract the static quark potential.

hep-lat↗