arXiv subjects

Abhishek Agarwal

Publications and source records attributed to Abhishek Agarwal.

At least 37 records · Page 2Linked to original sources

arXiv2021

Krylov variational quantum algorithm for first principles materials simulations

We propose an algorithm to obtain Green's functions as a continued fraction on quantum computers, which is based on the construction of the Krylov basis using variational quantum algorithms, and included in a Lanczos iterative scheme. This allows the integration of quantum algorithms with first principles material science simulations, as we demonstrate within the dynamical mean-field theory (DMFT) framework. DMFT enables quantitative predictions for strongly correlated materials, and relies on the calculation of Green's functions. On conventional computers the exponential growth of the Hilbert space with the number of orbitals limits DMFT to small systems. Quantum computers open new avenues and can lead to a significant speedup in the computation of expectation values required to obtain the Green's function. We apply our Krylov variational quantum algorithm combined with DMFT to the charge transfer insulator La$_{2}$CuO$_4$ using a quantum computing emulator, and show that with 8 qubits it predicts the correct insulating material properties for the paramagnetic phase. We therefore expect that the method is ideally suited to perform simulations for real materials on near term quantum hardware.

quant-ph↗

arXiv2021

Holomorphicity, Vortex Attachment, Gauge Invariance and the Fractional Quantum Hall Effect

A gauge invariant reformulation of nonrelativistic fermions in background magnetic fields is used to obtain the Laughlin and Jain wave functions as exact results in Mean Field Theory (MFT). The gauge invariant framework trades the U(1) gauge symmetry for an emergent holomorphic symmetry and fluxes for vortices. The novel holomorphic invariance is used to develop an analytical method for attaching vortices to particles. Vortex attachment methods introduced in this paper are subsequently employed to construct the Read operator within a second quantized framework and obtain the Laughlin and Jain wave functions as exact results entirely within a mean-field approximation. The gauge invariant framework and vortex attachment techniques are generalized to the case of spherical geometry and spherical counterparts of Laughlin and Jain wave functions are also obtained exactly within MFT.

hep-th↗

arXiv2020

Minimum Hardware Requirements for Hybrid Quantum-Classical DMFT

We numerically emulate noisy intermediate-scale quantum (NISQ) devices and determine the minimal hardware requirements for two-site hybrid quantum-classical dynamical mean-field theory (DMFT). We develop a circuit recompilation algorithm which significantly reduces the number of quantum gates of the DMFT algorithm and find that the quantum-classical algorithm converges if the two-qubit gate fidelities are larger than 99%. The converged results agree with the exact solution within 10%, and perfect agreement within noise-induced error margins can be obtained for two-qubit gate fidelities exceeding 99.9%. By comparison, the quantum-classical algorithm without circuit recompilation requires a two-qubit gate fidelity of at least 99.999% to achieve perfect agreement with the exact solution. We thus find quantum-classical DMFT calculations can be run on the next generation of NISQ devices if combined with the recompilation techniques developed in this work.

quant-ph↗

arXiv2020

Learning a generative model for robot control using visual feedback

We introduce a novel formulation for incorporating visual feedback in controlling robots. We define a generative model from actions to image observations of features on the end-effector. Inference in the model allows us to infer the robot state corresponding to target locations of the features. This, in turn, guides motion of the robot and allows for matching the target locations of the features in significantly fewer steps than state-of-the-art visual servoing methods. The training procedure for our model enables effective learning of the kinematics, feature structure, and camera parameters, simultaneously. This can be done with no prior information about the robot, structure, and cameras that observe it. Learning is done sample-efficiently and shows strong generalization to test data. Since our formulation is modular, we can modify components of our setup, like cameras and objects, and relearn them quickly online. Our method can handle noise in the observed state and noise in the controllers that we interact with. We demonstrate the effectiveness of our method by executing grasping and tight-fit insertions on robots with inaccurate controllers.

cs.RO↗

arXiv2020

Group Testing with Runlength Constraints for Topological Molecular Storage

Motivated by applications in topological DNA-based data storage, we introduce and study a novel setting of Non-Adaptive Group Testing (NAGT) with runlength constraints on the columns of the test matrix, in the sense that any two 1's must be separated by a run of at least d 0's. We describe and analyze a probabilistic construction of a runlength-constrained scheme in the zero-error and vanishing error settings, and show that the number of tests required by this construction is optimal up to logarithmic factors in the runlength constraint d and the number of defectives k in both cases. Surprisingly, our results show that runlength-constrained NAGT is not more demanding than unconstrained NAGT when d=O(k), and that for almost all choices of d and k it is not more demanding than NAGT with a column Hamming weight constraint only. Towards obtaining runlength-constrained Quantitative NAGT (QNAGT) schemes with good parameters, we also provide lower bounds for this setting and a nearly optimal probabilistic construction of a QNAGT scheme with a column Hamming weight constraint.

cs.IT↗

arXiv2019

EDUQA: Educational Domain Question Answering System using Conceptual Network Mapping

Most of the existing question answering models can be largely compiled into two categories: i) open domain question answering models that answer generic questions and use large-scale knowledge base along with the targeted web-corpus retrieval and ii) closed domain question answering models that address focused questioning area and use complex deep learning models. Both the above models derive answers through textual comprehension methods. Due to their inability to capture the pedagogical meaning of textual content, these models are not appropriately suited to the educational field for pedagogy. In this paper, we propose an on-the-fly conceptual network model that incorporates educational semantics. The proposed model preserves correlations between conceptual entities by applying intelligent indexing algorithms on the concept network so as to improve answer generation. This model can be utilized for building interactive conversational agents for aiding classroom learning.

cs.AI↗

arXiv2019

Online Convex Matrix Factorization with Representative Regions

Matrix factorization (MF) is a versatile learning method that has found wide applications in various data-driven disciplines. Still, many MF algorithms do not adequately scale with the size of available datasets and/or lack interpretability. To improve the computational efficiency of the method, an online (streaming) MF algorithm was proposed in Mairal et al. [2010]. To enable data interpretability, a constrained version of MF, termed convex MF, was introduced in Ding et al. [2010]. In the latter work, the basis vectors are required to lie in the convex hull of the data samples, thereby ensuring that every basis can be interpreted as a weighted combination of data samples. No current algorithmic solutions for online convex MF are known as it is challenging to find adequate convex bases without having access to the complete dataset. We address both problems by proposing the first online convex MF algorithm that maintains a collection of constant-size sets of representative data samples needed for interpreting each of the basis (Ding et al. [2010]) and has the same almost sure convergence guarantees as the online learning algorithm of Mairal et al. [2010]. Our proof techniques combine random coordinate descent algorithms with specialized quasi-martingale convergence analysis. Experiments on synthetic and real world datasets show significant computational savings of the proposed online convex MF method compared to classical convex MF. Since the proposed method maintains small representative sets of data samples needed for convex interpretations, it is related to a body of work in theoretical computer science, pertaining to generating point sets (Blum et al. [2016]), and in computer vision, pertaining to archetypal analysis (Mei et al. [2018]). Nevertheless, it differs from these lines of work both in terms of the objective and algorithmic implementations.

cs.LG↗

arXiv2019

Antiparticles as particles: QED$_{2+1}$ and composite Fermions at $ν= \frac{1}{2}$

We present a continuum operator map that inverts the role of particles and antiparticles in three dimensional QED. This is accomplished by the attachment of specific holomorphic Wilson lines to Dirac fermions. We show that this nonlocal map provides a continuum realization of Son's composite fermions at $ν= \frac{1}{2}$. The inversion of Landau levels and the Dirac-cone--composite-Fermion duality is explicitly demonstrated for the case of slowly varying magnetic fields. The role of Maxwell-terms as well as the connection of this construction to a gauge-invariant formulation of 3D gauge theories is also elaborated upon.

hep-th↗

arXiv2019

Linear Programming Approximations for Index Coding

Index coding, a source coding problem over broadcast channels, has been a subject of both theoretical and practical interest since its introduction (by Birk and Kol, 1998). In short, the problem can be defined as follows: there is an input $\textbf{x} \triangleq (\textbf{x}_1, \dots, \textbf{x}_n)$, a set of $n$ clients who each desire a single symbol $\textbf{x}_i$ of the input, and a broadcaster whose goal is to send as few messages as possible to all clients so that each one can recover its desired symbol. Additionally, each client has some predetermined "side information," corresponding to certain symbols of the input $\textbf{x}$, which we represent as the "side information graph" $\mathcal{G}$. The graph $\mathcal{G}$ has a vertex $v_i$ for each client and a directed edge $(v_i, v_j)$ indicating that client $i$ knows the $j$th symbol of the input. Given a fixed side information graph $\mathcal{G}$, we are interested in determining or approximating the "broadcast rate" of index coding on the graph, i.e. the fewest number of messages the broadcaster can transmit so that every client gets their desired information. Using index coding schemes based on linear programs (LPs), we take a two-pronged approach to approximating the broadcast rate. First, extending earlier work on planar graphs, we focus on approximating the broadcast rate for special graph families such as graphs with small chromatic number and disk graphs. In certain cases, we are able to show that simple LP-based schemes give constant-factor approximations of the broadcast rate, which seem extremely difficult to obtain in the general case. Second, we provide several LP-based schemes for the general case which are not constant-factor approximations, but which strictly improve on the prior best-known schemes.

cs.IT↗

arXiv2018

Novel Impossibility Results for Group-Testing

In this work we prove non-trivial impossibility results for perhaps the simplest non-linear estimation problem, that of {\it Group Testing} (GT), via the recently developed Madiman-Tetali inequalities. Group Testing concerns itself with identifying a hidden set of $d$ defective items from a set of $n$ items via $t$ {disjunctive/pooled} measurements ("group tests"). We consider the linear sparsity regime, i.e. $d = δn$ for any constant $δ>0$, a hitherto little-explored (though natural) regime. In a standard information-theoretic setting, where the tests are required to be non-adaptive and a small probability of reconstruction error is allowed, our lower bounds on $t$ are the {\it first} that improve over the classical counting lower bound, $t/n \geq H(δ)$, where $H(\cdot)$ is the binary entropy function. As corollaries of our result, we show that (i) for $δ\gtrsim 0.347$, individual testing is essentially optimal, i.e., $t \geq n(1-o(1))$; and (ii) there is an {adaptivity gap}, since for $δ\in (0.3471,0.3819)$ known {adaptive} GT algorithms require fewer than $n$ tests to reconstruct ${\cal D}$, whereas our bounds imply that the best nonadaptive algorithm must essentially be individual testing of each element. Perhaps most importantly, our work provides a framework for combining combinatorial and information-theoretic methods for deriving non-trivial lower bounds for a variety of non-linear estimation problems.

cs.IT↗

arXiv2018

Combinatorial Alphabet-Dependent Bounds for Locally Recoverable Codes

Locally recoverable (LRC) codes have recently been a focus point of research in coding theory due to their theoretical appeal and applications in distributed storage systems. In an LRC code, any erased symbol of a codeword can be recovered by accessing only a small number of other symbols. For LRC codes over a small alphabet (such as binary), the optimal rate-distance trade-off is unknown. We present several new combinatorial bounds on LRC codes including the locality-aware sphere packing and Plotkin bounds. We also develop an approach to linear programming (LP) bounds on LRC codes. The resulting LP bound gives better estimates in examples than the other upper bounds known in the literature. Further, we provide the tightest known upper bound on the rate of linear LRC codes with a given relative distance, an improvement over the previous best known bounds.

cs.IT↗

arXiv2017

Gauge-invariant Variables and Entanglement Entropy

The entanglement entropy (EE) of gauge theories in three spacetime dimensions is analyzed using manifestly gauge-invariant variables defined directly in the continuum. Specifically, we focus on the Maxwell, Maxwell-Chern-Simons (MCS), and nonabelian Yang-Mills theories. Special attention is paid to the analysis of edge modes and their contribution to EE. The contact term is derived without invoking the replica method and its physical origin is traced to the phase space volume measure for the edge modes. The topological contribution to the EE for the MCS case is calculated. For all the abelian cases, the EE presented in this paper agrees with known results in the literature. The EE for the nonabelian theory is computed in a gauge-invariant gaussian approximation, which incoprorates the dynamically generated mass gap. A formulation of the contact term for the nonabelian case is also presented.

hep-th↗

arXiv2017

Estimation of Sparsity via Simple Measurements

We consider several related problems of estimating the 'sparsity' or number of nonzero elements $d$ in a length $n$ vector $\mathbf{x}$ by observing only $\mathbf{b} = M \odot \mathbf{x}$, where $M$ is a predesigned test matrix independent of $\mathbf{x}$, and the operation $\odot$ varies between problems. We aim to provide a $Δ$-approximation of sparsity for some constant $Δ$ with a minimal number of measurements (rows of $M$). This framework generalizes multiple problems, such as estimation of sparsity in group testing and compressed sensing. We use techniques from coding theory as well as probabilistic methods to show that $O(D \log D \log n)$ rows are sufficient when the operation $\odot$ is logical OR (i.e., group testing), and nearly this many are necessary, where $D$ is a known upper bound on $d$. When instead the operation $\odot$ is multiplication over $\mathbb{R}$ or a finite field $\mathbb{F}_q$, we show that respectively $Θ(D)$ and $Θ(D \log_q \frac{n}{D})$ measurements are necessary and sufficient.

cs.IT↗

arXiv2016

Security in Locally Repairable Storage

In this paper we extend the notion of {\em locally repairable} codes to {\em secret sharing} schemes. The main problem that we consider is to find optimal ways to distribute shares of a secret among a set of storage-nodes (participants) such that the content of each node (share) can be recovered by using contents of only few other nodes, and at the same time the secret can be reconstructed by only some allowable subsets of nodes. As a special case, an eavesdropper observing some set of specific nodes (such as less than certain number of nodes) does not get any information. In other words, we propose to study a locally repairable distributed storage system that is secure against a {\em passive eavesdropper} that can observe some subsets of nodes. We provide a number of results related to such systems including upper-bounds and achievability results on the number of bits that can be securely stored with these constraints.

cs.IT↗

arXiv2016

Bounds on the Rate of Linear Locally Repairable Codes over Small Alphabets

Locally repairable codes (LRC) have recently been a subject of intense research due to theoretical appeal and their application in distributed storage systems. In an LRC, any coordinate of a codeword can be recovered by accessing only few other coordinates. For LRCs over small alphabet (such as binary), the optimal rate-distance trade-off is unknown. In this paper we provide the tightest known upper bound on the rate of linear LRCs of a given relative distance, an improvement over any previous result, in particular \cite{cadambe2013upper}.

cs.IT↗

arXiv2016

Local Partial Clique Covers for Index Coding

Index coding, or broadcasting with side information, is a network coding problem of most fundamental importance. In this problem, given a directed graph, each vertex represents a user with a need of information, and the neighborhood of each vertex represents the side information availability to that user. The aim is to find an encoding to minimum number of bits (optimal rate) that, when broadcasted, will be sufficient to the need of every user. Not only the optimal rate is intractable, but it is also very hard to characterize with some other well-studied graph parameter or with a simpler formulation, such as a linear program. Recently there have been a series of works that address this question and provide explicit schemes for index coding as the optimal value of a linear program with rate given by well-studied properties such as local chromatic number or partial clique-covering number. There has been a recent attempt to combine these existing notions of local chromatic number and partial clique covering into a unified notion denoted as the local partial clique cover (Arbabjolfaei and Kim, 2014). We present a generalized novel upper-bound (encoding scheme) - in the form of the minimum value of a linear program - for optimal index coding. Our bound also combines the notions of local chromatic number and partial clique covering into a new definition of the local partial clique cover, which outperforms both the previous bounds, as well as beats the previous attempt to combination. Further, we look at the upper bound derived recently by Thapa et al., 2015, and extend their $n$-$\mathsf{GIC}$ (Generalized Interlinked Cycle) construction to $(k,n)$-$\mathsf{GIC}$ graphs, which are a generalization of $k$-partial cliques.

cs.IT↗

arXiv2015

Fermions, Mass-Gap and Landau Levels: Gauge invariant Hamiltonian for QCD in D=2+1

A gauge-invariant reformulation of QCD in three spacetime dimensions is presented within a Hamiltonian formalism, extending previous work to include fermion fields in the adjoint and fundamental representations. A priori there are several ways to define the gauge-invariant versions of the fermions; a consistent prescription for choosing the fermionic variables is presented. The fermionic contribution to the volume element of the gauge orbit space and the gluonic mass-gap is computed exactly and this contribution is shown to be closely related to the mechanism for induction of Chern-Simons terms by parity-odd fermions. The consistency of the Hamiltonian scheme with known results on index theorems, Landau Levels and renormalization of Chern-Simons level numbers is shown in detail. We also comment on the fermionic contribution to the volume element in relation to issues of confinement and screening.

hep-th↗

arXiv2014

Scattering Amplitudes of Massive N=2 Gauge Theories in Three Dimensions

We study the scattering amplitudes of mass-deformed Chern-Simons theories and Yang-Mills-Chern-Simons theories with N=2 supersymmetry in three dimensions. In particular, we derive the on-shell supersymmetry algebras which underlie the scattering matrices of these theories. We then compute various 3 and 4-point on-shell tree-level amplitudes in these theories. For the mass-deformed Chern-Simons theory, odd-point amplitudes vanish and we find that all of the 4-point amplitudes can be encoded elegantly in superamplitudes. For the Yang-Mills-Chern-Simons theory, we obtain all of the 4-point tree-level amplitudes using a combination of perturbative techniques and algebraic constraints and we comment on difficulties related to computing amplitudes with external gauge fields using Feynman diagrams. Finally, we propose a BCFW recursion relation for mass-deformed theories in three dimensions and discuss the applicability of this proposal to mass-deformed N=2 theories.

hep-th↗