arXiv subjects

Indrakshi Raychowdhury

Publications and source records attributed to Indrakshi Raychowdhury.

At least 19 recordsLinked to original sources

arXiv2026

Dynamics of entanglement entropy for a locally monitored lattice gauge theory

The $1+1$ dimensional $Z_2$ gauge theory is the simplest model that allows for quantum computation or quantum simulation to probe the fundamental aspects of a gauge theory coupled with dynamical fermions. To reliably benchmark such a system, it is crucial to understand the non-unitary quantum dynamics arising from the underlying non-Hermitian evolution and to model the effects of quantum measurements. In this work, we study post-selected filtering dynamics of physical observables for a $\mathbb {Z} _2$ gauge theory. Tensor network calculations are performed to dynamically probe entanglement entropy at larger lattice sizes. We report that projective measurement of local and diagonal observables (electric and mass energy densities) in the computational basis demonstrates the absence of any measurement-induced phase transition like phenomenon, as indicated by the system-size independence of the late-time saturation value of the bipartite entanglement entropy.

quant-ph↗

arXiv2026

Effects of monitoring on entanglement dynamics for $1+1$D $\mathbb Z_2$ lattice gauge theory

The $(1+1)$-dimensional $\mathbb Z_2$ gauge theory is the simplest model that allows for quantum simulation to probe the fundamental aspects of a gauge theory coupled with dynamical fermions. To reliably benchmark such a system, it is crucial to understand the non-unitary quantum dynamics arising from effective non-Hermitian evolution and post-selected monitoring protocols. This work focuses on the post-selected non-Hermitian filtering dynamics of a $\mathbb Z_2$ gauge theory, where the non-Hermitian terms are associated with local and non-local gauge-invariant operators naturally present in the theory. We interpret the resulting dynamics as post-selected filtering, where different operator sectors are coupled to loss channels with different rates. This gives a unified framework for both the local electric flux and particle-number terms and the non-local mesonic hopping term. Tensor network calculations are performed to probe the effect of the filtering for larger lattice sizes (up to 256-site systems). Using Matrix Product State calculations, the dynamics of entanglement entropy are studied as a function of the filtering rate and the coupling constant. We find that, under both local and non-local filtering, the late-time saturation value of the bipartite entanglement entropy remains independent of system size, providing no evidence of a measurement-induced phase transition-like phenomenon in the post-selected dynamics across the range of filtering strengths, evolution times, and system sizes considered here.

quant-ph↗

arXiv2026

String-breaking statics and dynamics in a (1+1)D SU(2) lattice gauge theory

String breaking is at the core of hadronization models of relevance to particle colliders. Yet, studies of string-breaking dynamics rooted in quantum chromodynamics remain fundamentally challenging. Tensor networks enable sign-problem-free studies of static and dynamical properties of lattice gauge theories. In this work, we develop and apply a tensor-network toolkit based on the loop-string-hadron formulation of an SU(2) lattice gauge theory in 1+1 dimensions with dynamical fermions. We apply this toolkit to study static and dynamical aspects of strings and their breaking in this theory. The simple, gauge-invariant, and local structure of the loop-string-hadron states and constraints removes the need to impose non-Abelian constraints in the algorithm, and allows for a systematic computation of observables at increasingly large bosonic cutoffs, and toward the infinite-volume and continuum limits. Our study of static strings yields a determination of the string tension in the continuum and thermodynamic limits. Our study of dynamical string breaking, performed at a fixed lattice spacing and system size, illuminates underlying processes at play during the quench dynamics of a string. The loop, string, and hadron description offers a systematic and intuitive way to diagnose these processes, including string expansion and contraction, endpoint splitting and particle shower, chain scattering events, and inelastic processes resulting from string dissociation and recombination, and particle production. We relate these processes to several features of the dynamics, such as energy transport, entanglement-entropy production, and correlation spreading. This work opens the way to future tensor-network studies of string breaking and particle production in increasingly complex lattice gauge theories.

hep-lat↗

arXiv2026

Observation of Robust and Coherent Non-Abelian Hadron Dynamics on Noisy Quantum Processors

The real-time evolution of strongly interacting matter remains a frontier of fundamental physics, as classical simulations are hampered by exponential Hilbert space growth and rapid, unmanageable growth of quantum entanglement. This study reports the quantum simulation of hadron dynamics within a $(1+1)$-dimensional SU(2) lattice gauge theory using a 156-qubit IBM superconducting processor. Leveraging a hardware-efficient Loop-String-Hadron (LSH) encoding, we simulate the dynamics of the physical degrees of freedom on a $60$-site lattice in the weak-coupling regime, as a crucial step toward the continuum limit. The hardware data reveal confined meson propagation and early-time oscillations of the mesonic profile, from which we extract a breathing-mode frequency as a spectroscopic observable. Benchmarking against tensor-network simulations of the full LSH Hamiltonian and Pauli-propagation simulations of the noiseless circuit supports the validity of the physical approximation, the quantum algorithm and the observed dynamics within the accessible time window. These results show that physics-native encodings can enable scalable access to coherent non-Abelian real-time dynamics on noisy quantum hardware.

hep-lat↗

arXiv2025

Physicality oracle for SU(3) Loop-String-Hadron dynamics: a digital quantum circuit

Within the aim of understanding quantum chromodynamics through simulation, an increasingly studied approach is that of quantum computation and simulation. Challenges exist in encoding the minimal and physical degrees of freedom for a non-Abelian gauge theory and maintaining physical or gauge-invariant dynamics in a simulation. In this work, the Loop-String-Hadron (LSH) formulation of the 1+1-dimensional SU(3) lattice gauge theory is used to define an efficient mapping of SU(3) invariant degrees of freedom onto qubits. It is shown that the required number of qubits in the LSH basis is significantly reduced compared to its IRREP basis counterpart. While the non-Abelian Gauss laws of the SU(3) theory are automatically satisfied by the usage of LSH variables, the remnant constraints on the consistency of the flux numbers still exist. During time evolution, the noise can accumulate and take the state out of the sector of the Hilbert space where the constraint is satisfied. With this motivation, an oracle algorithm is constructed to be applied to the qubits for checking the local constraint at a given link. Costs in terms of qubit and gate number, and circuit depth, are found.

hep-lat↗

arXiv2025

Loop-string-hadron approach to SU(3) lattice Yang-Mills theory, II: Operator representation for the trivalent vertex

This work is the second installment of a series on the loop-string-hadron (LSH) approach to SU(3) lattice Yang-Mills theory. Here, we present the infinite-dimensional matrix representation for arbitrary gauge-invariant operators at a trivalent vertex, which results in a standalone framework for computations that supersedes the underlying Schwinger-boson framework. To that end, we present a partial summary of the commutation relations and use it to evaluate the result of applying any gauge-invariant operator on the LSH basis states introduced in Part I (arXiv:2407.19181). Classical calculations in the LSH basis run significantly faster than equivalent calculations performed using Schwinger bosons. A companion code script is provided, which implements the derived formulas and aims to facilitate rapid progress towards Hamiltonian-based calculations of quantum chromodynamics.

hep-lat↗

arXiv2025

Eigenstate Thermalization in 1+1-Dimensional SU(2) Lattice Gauge Theory Coupled with Dynamical Fermions

We test the eigenstate thermalization hypothesis (ETH) in 1+1-dimensional SU(2) lattice gauge theory (LGT) with one flavor of dynamical fermions. Using the loop-string-hadron framework of the LGT with a bosonic cut-off, we exactly diagonalize the Hamiltonian for finite size systems and calculate matrix elements (MEs) in the eigenbasis for both local and non-local operators. We analyze different indicators to identify the parameter space for quantum chaos at finite lattice sizes and investigate how the ETH behavior emerges in both the diagonal and off-diagonal MEs. Our investigations allow us to study various time scales of thermalization and the emergence of random matrix behavior, and highlight the interplays of the several diagnostics with each other. Furthermore, from the off-diagonal MEs, we extract a smooth function that is closely related to the spectral function for both local and non-local operators. We find numerical evidence of the spectral gap and the memory peak in the non-local operator case. Finally, we investigate aspects of subsystem ETH in the lattice gauge theory and identify certain features in the subsystem reduced density matrix that are unique to gauge theories.

hep-th↗

arXiv2025

Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: I. Hilbert space of a trivalent vertex

The construction of gauge invariant states of SU(3) lattice gauge theories has garnered new interest in recent years, but implementing them is complicated by the need for SU(3) Clebsch-Gordon coefficients. In the loop-string-hadron (LSH) approach to lattice gauge theories, the elementary excitations are strictly gauge invariant, and constructing the basis requires no knowledge of Clebsch-Gordon coefficients. Originally developed for SU(2), the LSH formulation was recently generalized to SU(3), but limited to one spatial dimension. In this work, we generalize the LSH approach to constructing the basis of SU(3) gauge invariant states at a trivalent vertex -- the essential building block to multidimensional space. A direct generalization from the SU(2) vertex yields a legitimate basis; however, in certain sectors of the Hilbert space, the naive LSH basis vectors so defined suffer from being nonorthogonal. The issues with orthogonality are directly related to the "missing label" or "outer multiplicity" problem associated with SU(3) tensor products, and may also be phrased in terms of Littlewood-Richardson coefficients or the need for a "seventh Casimir" operator. The states that are unaffected by the problem are orthonormalized in closed form. For the sectors that are afflicted, we discuss the nonorthogonal bases and their orthogonalization. A few candidates for seventh Casimir operators are readily constructed from the suite of LSH gauge-singlet operators. The diagonalization of a seventh Casimir represents one prescriptive solution toward obtaining a complete orthonormal basis, but a closed-form general solution remains to be found.

hep-lat↗

arXiv2025

Tensor-network toolbox for probing dynamics of non-Abelian gauge theories

Tensor-network methods enable probing dynamics of strongly interacting quantum many-body systems, including gauge theories, via Hamiltonian simulation, hence bypassing sign problems. They also have the potential to inform efficient quantum-simulation algorithms of the same theories. We develop and benchmark a matrix-product-state ansatz for the SU(2) lattice gauge theory using the loop-string-hadron formulation. This formulation has been demonstrated to be advantageous in Hamiltonian simulation of non-Abelian gauge theories. It is applicable to both SU(2) and SU(3) gauge groups, to periodic and open boundary conditions, and to 1+1 and higher dimensions. In this work, we report on progress in computing static and dynamical observables in a SU(2) gauge theory in (1+1)D, pushing the boundary of existing studies.

hep-lat↗

arXiv2024

Protecting gauge symmetries in the the dynamics of SU(3) lattice gauge theories

Quantum simulation of the dynamics of a lattice gauge theory demands imposing on-site constraints. Ideally, the dynamics remain confined within the physical Hilbert space, where all the states satisfy those constraints. For non-Abelian gauge theories, implementing local constraints is non-trivial, as is keeping the dynamics confined in the physical Hilbert space, considering the erroneous quantum devices. SU(3) gauge group, albeit crucial for describing the strong interaction of nature, is notorious for studying via Hamiltonian simulation. This work presents a couple of symmetry protection protocols for simulating the exact dynamics of SU(3) gauge theory in $1+1$ dimension. The first protocol doesn't require imposing any local symmetry but relies on protecting global symmetries, which are Abelian with a preferred choice of framework, namely the loop-string-hadron framework. Generalization to a higher dimension is possible, however, the protection scheme needs to be local for that case but is still Abelian and thus advantageous. The symmetry protection schemes presented here are important steps towards quantum simulating the full theory of quantum chromodynamics.

hep-lat↗

arXiv2024

Entanglement of edge modes in (very) strongly correlated topological insulators

Identifying topological phases for a strongly correlated theory remains a non-trivial task, as defining order parameters, such as Berry phases, is not straightforward. Quantum information theory is capable of identifying topological phases for a theory that exhibits quantum phase transition with a suitable definition of order parameters that are related to different entanglement measures for the system. In this work, we study entanglement entropy for a bi-layer SSH model, both in the presence and absence of Hubbard interaction and at varying interaction strengths. For the free theory, edge entanglement acts as an order parameter, which is supported by analytic calculations and numerical (DMRG) studies. We calculate the symmetry-resolved entanglement and demonstrate the equipartition of entanglement for this model which itself acts as an order parameter when calculated for the edge modes. As the DMRG calculation allows one to go beyond the free theory, we study the entanglement structure of the edge modes in the presence of on-site Hubbard interaction for the same model. A sudden reduction of edge entanglement is obtained as interaction is switched on. The explanation for this lies in the change in the size of the degenerate subspaces in the presence and absence of interaction. We also study the signature of entanglement when the interaction strength becomes extremely strong and demonstrate that the edge entanglement remains protected. In this limit, the energy eigenstates essentially become a tensor product state, implying zero entanglement. However, a remnant entropy survives in the non-trivial topological phase which is exactly due to the entanglement of the edge modes.

cond-mat.str-el↗

arXiv2023

Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks

Towards the goal of quantum computing for lattice quantum chromodynamics, we present a loop-string-hadron (LSH) framework in 1+1 dimensions for describing the dynamics of SU(3) gauge fields coupled to staggered fermions. This novel framework was previously developed for an SU(2) lattice gauge theory in $d\leq3$ spatial dimensions and its advantages for classical and quantum algorithms have thus far been demonstrated in $d=1$. The LSH approach uses gauge invariant degrees of freedoms such as loop segments, string ends, and on-site hadrons, it is free of all nonabelian gauge redundancy, and it is described by a Hamiltonian containing only local interactions. In this work, the SU(3) LSH framework is systematically derived from the reformulation of Hamiltonian lattice gauge theory in terms of irreducible Schwinger bosons, including the addition of staggered quarks. Furthermore, the superselection rules governing the LSH dynamics are identified directly from the form of the Hamiltonian. The SU(3) LSH Hamiltonian with open boundary conditions has been numerically confirmed to agree with the completely gauge-fixed Hamiltonian, which contains long-range interactions and does not generalize to either periodic boundary conditions or to $d>1$.

hep-lat↗

arXiv2022

Protecting local and global symmetries in simulating 1+1-D non-abelian gauge theories

Efficient quantum simulation protocols for any quantum theories demand efficient protection protocols for its underlying symmetries. This task is nontrivial for gauge theories as it is involves local symmetry/invariance. For non-Abelian gauge theories, protecting all the symmetries generated by a set of mutually non-commuting generators, is particularly difficult. In this letter, a global symmetry-protection protocol is proposed. Using the novel loop-string-hadron formalism of non-Abelian lattice gauge theory, we numerically demonstrate that all of the local symmetries get protected even for large time by this global symmetry protection scheme. With suitable protection strength, the dynamics of a (1+1)-dimensional SU(2) lattice gauge theory remains confined in the physical Hilbert space of the theory even in presence of explicit local symmetry violating terms in the Hamiltonian that may occur in both analog and digital simulation schemes as an error. The whole scheme holds for SU(3) gauge theory as well.

hep-lat↗

arXiv2021

Towards Quantum Simulating Non-Abelian Gauge Theories

In this article, we review some of the recent developments towards the future goal of quantum computing or quantum simulating lattice QCD. This includes a novel theoretical framework developed for non-Abelian gauge theories that is the first necessary step towards this goal. We also review some immediate applications of this framework in the context of both digital and analog quantum simulations of SU(2) lattice gauge theory coupled with staggered fermions.

hep-lat↗

arXiv2020

Cold Atom Quantum Simulator for String and Hadron Dynamics in Non-Abelian Lattice Gauge Theory

We propose an analog quantum simulator for simulating real time dynamics of $(1+1)$-d non-Abelian gauge theory well within the existing capacity of ultracold atom experiments. The scheme calls for the realization of a two-state ultracold fermionic system in a 1-dimensional bipartite lattice, and the observation of subsequent tunneling dynamics. Being based on novel loop string hadron formalism of SU(2) lattice gauge theory, this simulation technique is completely SU(2) invariant and simulates accurate dynamics of physical phenomena such as string breaking and/or pair production. The scheme is scalable, and particularly effective in simulating the theory in weak coupling regime, and also bulk limit of the theory in strong coupling regime up to certain approximations. This paper also presents a numerical benchmark comparison of exact spectrum and real time dynamics of lattice gauge theory to that of the atomic Hamiltonian with experimentally realizable range of parameters.

hep-lat↗

arXiv2020

Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories

Hamiltonian formulation of lattice gauge theories (LGTs) is the most natural framework for the purpose of quantum simulation, an area of research that is growing with advances in quantum-computing algorithms and hardware. It, therefore, remains an important task to identify the most accurate, while computationally economic, Hamiltonian formulation(s) in such theories, considering the necessary truncation imposed on the Hilbert space of gauge bosons with any finite computing resources. This paper is a first step toward addressing this question in the case of non-Abelian LGTs, which further require the imposition of non-Abelian Gauss's laws on the Hilbert space, introducing additional computational complexity. Focusing on the case of SU(2) LGT in 1+1 D coupled to matter, a number of different formulations of the original Kogut-Susskind framework are analyzed with regard to the dependence of the dimension of the physical Hilbert space on boundary conditions, system's size, and the cutoff on the excitations of gauge bosons. The impact of such dependencies on the accuracy of the spectrum and dynamics is examined, and the (classical) computational-resource requirements given these considerations are studied. Besides the well-known angular-momentum formulation of the theory, the cases of purely fermionic and purely bosonic formulations (with open boundary conditions), and the Loop-String-Hadron formulation are analyzed, along with a brief discussion of a Quantum Link Model of the same theory. Clear advantages are found in working with the Loop-String-Hadron framework which implements non-Abelian Gauss's laws a priori using a complete set of gauge-invariant operators. Although small lattices are studied in the numerical analysis of this work, and only the simplest algorithms are considered, a range of conclusions will be applicable to larger systems and potentially to higher dimensions.

hep-lat↗

arXiv2020

Solving Gauss's Law on Digital Quantum Computers with Loop-String-Hadron Digitization

We show that using the loop-string-hadron (LSH) formulation of SU(2) lattice gauge theory (arXiv:1912.06133) as a basis for digital quantum computation easily solves an important problem of fundamental interest: implementing gauge invariance (or Gauss's law) exactly. We first discuss the structure of the LSH Hilbert space in $d$ spatial dimensions, its truncation, and its digitization with qubits. Error detection and mitigation in gauge theory simulations would benefit from physicality "oracles,'"so we decompose circuits that flag gauge invariant wavefunctions. We then analyze the logical qubit costs and entangling gate counts involved with the protocols. The LSH basis could save or cost more qubits than a Kogut-Susskind-type representation basis, depending on how the bases are digitized as well as the spatial dimension. The numerous other clear benefits encourage future studies into applying this framework.

hep-lat↗

arXiv2020

Loop, String, and Hadron Dynamics in SU(2) Hamiltonian Lattice Gauge Theories

The question of how to efficiently formulate Hamiltonian gauge theories is experiencing renewed interest due to advances in building quantum simulation platforms. We introduce a reformulation of an SU(2) Hamiltonian lattice gauge theory---a loop-string-hadron (LSH) formulation---that describes dynamics directly in terms of its loop, string, and hadron degrees of freedom, while alleviating several disadvantages of quantumly simulating the Kogut-Susskind formulation. This LSH formulation transcends the local loop formulation of $d+1$-dimensional lattice gauge theories by incorporating staggered quarks, furnishing the algebra of gauge-singlet operators, and being used to reconstruct dynamics between states that have Gauss's law built in to them. LSH operators are then factored into products of "normalized" ladder operators and diagonal matrices, priming them for classical or quantum information processing. Self-contained expressions of the Hamiltonian are given up to $d=3$. The LSH formalism makes little use of structures specific to SU(2) and its conceptual clarity makes it an attractive approach to apply to other non-Abelian groups like SU(3).

hep-lat↗