Research

Quantum Computing

In recent years, advancements in quantum technology and algorithms have shown significant promise for leveraging quantum computers to surpass the constraints of classical computing when tackling these challenges, particularly for studying dynamical processes like scattering in the high-energy and high-inelasticity regimes, which are crucial for understanding time-dependent mechanisms like fragmentation, hadronization, and thermalization in QCD.

I am currently working on simulating scattering in lattice gauge theories in one spatial dimension on a quantum computer, with the eventual goal of quantumly simulating QCD. Creating initial scattering wave packets on a quantum computer is a necessary first step for quantum simulation of hadronic scattering processes. With my collaborators Zohreh Davoudi and Chung-Chun Hsieh, we have provided a comprehensive construction of a hadronic wave packet with a desired wave function directly in the interacting regime of confined Abelian lattice gauge theories in one spatial dimension, and demonstrated its viability by implementing the proposed algorithm on Quantinuum's quantum computer.

We are currently working on utilizing this method for preparing multi-particle initial scattering state and simulate particle collision dynamics on quantum computers.

Scattering wave packets of hadrons in gauge theories: Preparation on a quantum computer,
Z. Davoudi, C. C. Hsieh and S. V. Kadam, Quantum 8 (2024) 1520, arXiv:2402.00840 [quant-ph]

Hamiltonian formulation

Despite its successes, lattice QCD has several limitations when general finite-density and real-time quantities are concerned. Hamiltonian simulation of QCD is another non-perturbative method of solving QCD that, by its nature, does not suffer from those limitations. The Hamiltonian formulation of QCD was discovered and developed around the same time as lattice QCD. However, it deals directly with the Hilbert space of QCD which scales exponentially in system sizes, and thus, the computational implementation of Hamiltonian simulation of QCD with the traditional computation methods was impractical. Recent developments in tensor network methods and the advent of quantum simulation and quantum computing have revived interest in the Hamiltonian simulation of QCD, since these tools allow for handling such systems with polynomial scaling in their respective computational resources. Even though a predictive non-perturbative Hamiltonian simulation of QCD is a distant future, theoretical developments in that direction are gaining interest. One of the challenges on its theoretical front is to find a computationally resource efficient formulation of the QCD Hamiltonian and its Hilbert space.

Towards that aim, I am working with my collaborators, Jesse Stryker and Indrakshi Raychowdhury on developing an alternate formulation of SU(3) lattice gauge theories called the loop-string-hadron (LSH) formulation. I am also interested in utilizing this formulation to better understand gauge theories.

Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks,
S. V. Kadam, I. Raychowdhury and J. R. Stryker, Phys. Rev. D 107, 094513 (2023), arXiv:2212.04490 [hep-lat]
Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: Gauge invariant Hilbert space of a trivalent vertex,
S. V. Kadam, A. Naskar I. Raychowdhury and J. R. Stryker, arXiv:2407.19181 [hep-lat]

Tensor Network

This is an ongoing work where we are using tensor networks to study non-Abelian lattice gauge theories in one spatial dimension. As the first step towards this goal, we have developed and benchmarked a matrix-product-state (MPS) ansatz for the SU(2) lattice gauge theory using the loop-string-hadron formulation. We computed static and dynamical observables in a SU(2) gauge theory in (1+1)D, pushing the boundary of existing studies.

Stay tuned for more updates . . .

Tensor-network toolbox for probing dynamics of non-Abelian gauge theories,
E. Mathew, N. Gupta, S. V. Kadam, A. Bapat, J. Stryker, Z. Davoudi and I. Raychowdhury,
PoS LATTICE2024 (2025) 472, Contribution to Lattice 2024, arXiv:2501.18301 [hep-lat]

Analog Simulation

I am currently involved in an ongoing project employing trapped-ion systems to simulate lattice field theories. Keep an eye out for forthcoming updates on our progress . . .

Lattice QCD

Quantum chromodynamics (QCD) describes the strong force and does not have the precise analytical predictive power at all energy scales. There exists a numerical method to solve QCD non-perturbatively from first principles known as lattice QCD. Lattice QCD is a lattice gauge theory in which QCD is formulated on a discrete space-time with a finite size, and the observables are calculated using the path integral formulation with an imaginary time. However, obtaining QCD predictions, especially for scattering processes, from numerical lattice QCD calculation is a non-trivial task. Nonetheless, one can use the finite size effects in lattice QCD for matching its numerical results to scattering amplitudes.

I am interested in analytically developing such prescriptions using the finite-volume formalism. I was involved in providing matching relations for predicting transition amplitudes of nuclear double beta decays, rare nuclear processes that offer insights into fundamental symmetries, from first-principles numerical lattice QCD.

Path from lattice QCD to the short-distance contribution to 0νββ decay with a light Majorana neutrino,
Z. Davoudi and S. V. Kadam, Phys. Rev. Lett. 126, 152003 (2021)
Two-neutrino double-β decay in pionless effective field theory from a Euclidean finite-volume correlation function,
Z. Davoudi and S. V. Kadam, Phys. Rev. D 102, 114521 (2020)
Extraction of low-energy constants of single- and double-β decays from lattice QCD: A sensitivity analysis,
Z. Davoudi and S. V. Kadam, Phys. Rev. D 105, 094502 (2022)

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