Research
FOR STUDENTS: If you'd like to work on a research project, please contact me. Until I get a position, I cannot write a reference letter for your future applications. If you are still interested, I'd love to talk and discuss potential projects. In my research, I am broadly interested in various problems related to lattice gauge theory, tensor networks, qubits and qumodes approach to quantum computing, matrix models, computational complexity theory, variational algorithms like conventional VQE and d-sparse VQE, Hamiltonian simulation, and quantum chaos in random systems.
In my Ph.D., I focused exclusively on supersymmetric gauge theories as non-perturbative formulations of string theory through gauge/gravity duality. I'm interested in studying finite-temperature maximally supersymmetric gauge theories using Monte Carlo (MC) methods to test and understand non-extremal black p-branes in dual supergravity (SUGRA). This numerical approach provides a tool for potential non-trivial checks of the AdS/CFT conjecture
and explore away from the classical SUGRA and planar limit.
About seven years ago, I started exploring the tensor network renormalization group
methods to study lower-dimensional gauge theories
and spin models with continuous or discrete symmetries.
Since the tensor network methods are computationally expensive in higher dimensions,
one of my other recent interests is also exploring different algorithms
which will enable us to study a wide range of
statistical models with sufficient accuracy.
A long-term goal is to compute critical exponents in 3d
models by going close to the QFT limit and comparing it to the results
from the well-established conformal bootstrap program and MC method.
Another direction is to study models that are affected by sign problem
in conventional Monte Carlo methods, such as those at finite chemical potential
or with a topological term.
Due to increased interest related to
quantum architectures around the world and its potential applications in Physics, my focus in the last several years has focused on
available/near-term quantum devices and applications of quantum
computation to quantum many-body problems. Quantum computation and especially a proper
understanding of digitization of gauge and spin models is one of the problems I am interested in.
My projects also focus on the continuous variable (CV) approach to
quantum computing but I also work on qubit based algorithms and simulation.
In the CV approach, unlike the qubits, the quantum information and
unitary transformations are written in terms of bosonic operators which have infinite-
dimensional Hilbert space (suitably truncated). I wrote a small review several years ago,
please refer to it on arXiv --
here .
The material in this article is based on lectures given at Rensselaer Polytechnic Institute (RPI) Summer School
in June 2022, Hampton University Graduate Studies (HUGS) program and Quantum Computing Bootcamp at Jefferson Lab in June 2023.
Around the World
Notes and Learning Resources
- Notes on path integral approach to QM due to Dirac/Feynman (read here, May 2013)
- Short introduction to large N limit of gauge theories (read here, November 2017)
- Tensor networks, Entanglement, and Holography ( In progress! )
- Introduction to Quantum Computing ( Check on arXiv )
- Short review on holographic matrix models + fuzzy spheres (read here, December 2018)
- Some scratch notes on Data Science and Machine Learning (read here)
- Some notes on topological field theory (TFT) (read here, April 2015)
- A brief review of lattice supersymmetry (read here, December 2014)
- Note on SUSY quantum mechanics (read here, August 2014)
- Short note on ABJM integrability and 3d SYM (read here, September 2019)
- Compilation of important $\mathcal{L}, \mathcal{H}$ of models in Physics (read here, August 2019)
- Tensor network lectures at RPI (using Python) (read here, June 2020)
- Some worked out QFT problems in five parts from back in 2014-2015 (1, 2, 3, 4, 5, 6)
- Textbook by Polyakov on gauge fields and strings ( PDF here)
- Textbook by Baxter on exactly solvable models ( PDF here)
- Aspects of Symmetry by Coleman ( PDF here)
- About 100+ advanced Physics e-books available on my GitHub. See README for details. (Click this link)
Talks
(see CV for detailed description and PDFs)
- Thermal state preparation and dynamics of random all-to-all fermionic model (July 17, 2024) - Talk at Massachusetts Institute of Technology (MIT), C2QA meeting, Boston, USA
- Introduction to tensor networks (29-30 April, 2 May 2024) - University of Pretoria, South Africa
- Quantum computing for quantum many-body systems (17 April, 2024) - William & Mary, VA, USA
- Approaches to universal quantum computing for spin and gauge models (16 April, 2024) - University of Iowa
- Random dense Hamiltonians on current noisy quantum computers (28 March, 2024) - University of Maryland
- Extracting some Physics with IBM's 127-qubit quantum processor (13 March, 2024) - Jefferson Lab
- Real-time dynamics of SYK model on a noisy quantum computer (05 March, 2024) - Workshop on 'Toward quantum simulation of gauge/gravity duality and lattice gauge theory', Queen Mary University of London (Online) (PDF)
- SYK model on a noisy quantum computer (06 February, 2024) - Indian Institute of Science (IISc), Bangalore, India (PDF)
- Quantum Computation of the O(3) model using qumodes (02 August, 2023) - Lattice 2023, Fermilab, USA
- Computation with Quantum Mechanics (June 20, 2023) - Set of two lectures at Quantum Computation Bootcamp, Jefferson Lab, USA
- Can quantum computation improve our understanding of quantum fields? (June 7, 2023) - Set of two lectures at HUGS 2023 Summer School, Jefferson Lab, USA
- Non-linear sigma models using quantum computation (May 30, 2023) at C2QA Meeting, New York City, USA
- Introduction to Quantum Computing methods in Physics (April 27, 2023) at Tata Institute, Mumbai, India (Online) (PDF)
- Aspects of Classical and Quantum Computing of Quantum Many-Body Systems (February 10, 2023) at Ashoka University (Online) (PDF)
- Classical computation using tensor networks and quantum computation with qubits and qumodes (November 14, 2022) at Jefferson Lab, USA
- Application of tensor methods to real-space renormalization and real-time study of field theories (October 31, 2022) at Brookhaven National Lab, USA (Online)
- New tools for old problems in spin and gauge models on the lattice (October 12, 2022) at IIT Hyderabad, India (Online)
- Some old problems on the lattice using tensors (August 26, 2022) at NUMSTRINGS 2022 conference at ICTS, India
- Introduction to Quantum Computation using QISKIT (June 21 and 22, 2022) at Rensselaer Polytechnic Institute, Troy, USA (Online)
- New approach to continuous spin models in two and three dimensions (May 17, 2022) at APTCP, Pohang, South Korea (Online)
- Holography with large matrices on the lattice (March 24, 2022) at UNAM, Mexico City, Mexico
- Large N matrix models using Monte Carlo and Bootstrap (February 22, 2022) at University of Surrey, UK (Online)
- Introduction to tensor networks and spin systems (January 11, 2022) at Azim Premji University, Bengaluru, India (Online)
- Tensor networks and spin models (December 7, 2021) - at Indian Institute of Science Education and Research (IISER), Mohali, India (Online) (PDF)
- Real-space tensor renormalization for spin models in three dimensions - November 19, 2021 at Perimeter Institute
- Solving matrix models at large and finite N (June 28 and 29, 2021) - Two lectures for Summer School 2021 at Rensselaer Polytechnic Institute, USA (Online due to COVID-19 pandemic) (PDF)
- Holographic gauge theories on the lattice - June 23, 2021 at Dublin Institute for Advanced Studies, Dublin, Ireland (Online via Zoom due to COVID-19 pandemic) (PDF)
- Old and new methods for new and old problems in Physics - March 8, 2021 at Indian Institute of Technology (IIT) Madras (Online via Zoom due to COVID-19 pandemic) (PDF)
- Probing holographic dualities with lattice supersymmetric Yang-Mills theories - February 25, 2021 at Massachusetts Institute of Technology (Online via Zoom due to COVID-19 pandemic) (PDF) (YouTube)
- New tool for old problems — Tensor network approach to spin models and gauge theories - October 14, 2020 at University of Liverpool, UK (Online via Zoom due to COVID-19 pandemic) (PDF)
- Tensor Networks: Algorithm & Applications — June 10 and 11, 2020 – Two lectures [1.5 hours each] for CyberTraining Summer School 2020 at Rensselaer Polytechnic Institute, USA (Online due to COVID-19 pandemic) (PDF)
- Holographic aspects of supersymmetric gauge theories – October 4, 2019 - Perimeter Institute
- Numerical Approaches to Holography — August 28, 2019 - Seminar at Ashoka University, Sonipat, India (PDF)
- Numerical Approaches to Holography — August 08, 2019 - Seminar at Indian Institute of Science Education and Research (IISER), Mohali, India
- Holography, large $N$, and supersymmetry on the lattice — April 02, 2019 - Ph.D. thesis defense (PDF)
- Fundamentals of Quantum Entropy — March 29, 2019
- Holographic dualities and tensor renormalization group study of gauge theories — March 11, 2019 - Interdisciplinary Quantum Fields and Strings + Tensor Networks Initiative invited talk at Perimeter Institute (PDF) (PIRSA)
- Matrix Models — December 7, 2018 - Theory HEP Group talk at Syracuse University
- Lattice gravity and scalar fields — July 23, 2018 at Annual Lattice Conference 2018, Michigan, USA (PDF)
- Supersymmetry breaking and gauge/gravity duality on the lattice — April 06, 2018 - Lattice beyond Standard Model 2018 at UC Boulder, Colorado (PDF)
- Large $N$ gauge theories — March 09, 2018 - Theory HEP Group talk at Syracuse University
- Recent results from lattice supersymmetry in $2 \le d < 4$ dimensions — January 31, 2018 - NUMSTRINGS I conference at ICTS, Bangalore (PDF) (YouTube)
- Testing gauge/gravity duality using lattice simulations — July 22, 2017 at Annual Lattice Conference 2017 , Granada, Spain (PDF)
- Testing holography through lattice simulations — April 04, 2017 at Quantum Gravity, String theory, and Holography conference at Yukawa Institute for Theoretical Physics, Kyoto, Japan (PDF)
- Maximally supersymmetric Yang-Mills and dual gravitational theories — October 07, 2016 - Theory HEP Group talk at Syracuse University
- Supersymmetry on the lattice — April 17, 2016 at the APS 2016 Meeting, Salt Lake City, Utah, USA (PDF)
- Lattice studies of $ \mathcal{N} = (8,8)$ SYM - April 08, 2016 — Theory HEP Group talk at Syracuse University
Data Science Stuff
Publications
Last updated: 2024, August 03. Please check iNSPIRE-HEP for the most up to date publication list. To download list of papers as a single file PDF, click PDF here
- Quantum computation of SU(2) lattice gauge theory with continuous variables (arXiv)
- Sparsity dependence of Krylov state complexity in the SYK model (arXiv)
- Thermal state preparation of the SYK model using a variational quantum algorithm (arXiv)
- SU(2) principal chiral model with tensor renormalization group on a cubic lattice (arXiv)
- Phase diagram of generalized XY model using tensor renormalization group (arXiv)
- Hamiltonian simulation of minimal holographic sparsified SYK model (arXiv)
- Tensor renormalization group study of 3D principal chiral model (arXiv)
- Phase diagram of two-dimensional $SU(N)$ super-Yang--Mills theory with four supercharges (arXiv)
- Sachdev-Ye-Kitaev model on a noisy quantum computer (arXiv)
- Continuous variable quantum computation of the O(3) model in 1+1 dimensions (arXiv)
- Toward quantum computations of the O(3) model using qumodes (arXiv)
- GPU-Acceleration of Tensor Renormalization with PyTorch using CUDA (arXiv)
- Notes on Quantum Computation and Information (arXiv)
- Supersymmetric Wilson loops on the lattice in the large $N$ limit (Springer) (Published in EPJ-ST)
- Non-perturbative phase structure of the bosonic BMN matrix model (arXiv)
- Thermal phase structure of dimensionally reduced super-Yang--Mills (arXiv)
- Tensor renormalization of three-dimensional Potts model (arXiv)
- Introduction to Monte Carlo for Matrix Models (arXiv)
- Large-$N$ limit of two-dimensional Yang--Mills theory with four supercharges (arXiv)
- Tensor renormalization group study of the 3d O(2) model (arXiv)
- Three-dimensional super-Yang–Mills theory on the lattice and dual black branes (arXiv)
- Positive geometries for all scalar theories from twisted intersection theory (arXiv)
- Critical analysis of two-dimensional classical XY model using tensor renormalization group (arXiv)
- Thermal phase structure of a supersymmetric matrix model (arXiv)
- Finite $N$ unitary matrix models (arXiv)
- Tensor renormalization group study of the non-Abelian Higgs model in two dimensions (arXiv)
- Lattice quantum gravity with scalar fields (arXiv)
- The properties of D1-branes from lattice super Yang–Mills theory using gauge/gravity duality (arXiv)
- On the removal of the trace mode in lattice $\mathcal{N} = 4$ super Yang-Mills theory (arXiv)
- Nonperturbative study of dynamical SUSY breaking in $\mathcal{N} = (2,2)$ Yang-Mills theory (arXiv)
- Truncation of lattice $\mathcal{N} = 4$ super Yang-Mills
- Testing the holographic principle using lattice simulations (arXiv)
- Testing holography using the lattice with super-Yang-Mills theory on a 2-torus (arXiv)