papers.bib

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@misc{aggarwalApplicationQuantumScrambling2018,
  title = {Application of Quantum Scrambling in {{Rydberg}} Atom on {{IBM}} Quantum Computer},
  author = {Aggarwal, Daattavya and Raj, Shivam and Behera, Bikash K. and Panigrahi, Prasanta K.},
  year = 2018,
  month = jul,
  number = {arXiv:1806.00781},
  eprint = {1806.00781},
  primaryclass = {quant-ph},
  publisher = {arXiv},
  doi = {10.48550/arXiv.1806.00781},
  urldate = {2025-02-14},
  abstract = {Quantum scrambling measured by out-of-time-ordered correlator (OTOC) has an important role in understanding the physics of black holes and evaluating quantum chaos. It is known that Rydberg atom has been a general interest due to its extremely favourable properties for building a quantum simulator. Fast and efficient quantum simulators can be developed by studying quantum scrambling in related systems. Here we present a general quantum circuit to theoretically implement an interferometric protocol which is a technique proposed to measure OTOC functions. We apply this circuit to measure OTOC and hence the quantum scrambling in a simulation of two spin Ising spin model for Rydberg atom. We apply this method to both initial product and entangled states to compare the scrambling of quantum information in both cases. Finally we discuss other constructions where this technique can be applied.},
  archiveprefix = {arXiv},
  copyright = {All rights reserved},
  keywords = {Quantum Physics},
  preview = {quantum_scrambling.png},
}

@article{aggarwalMachineLearningSasakian2024,
  title = {Machine Learning {{Sasakian}} and {{G2}} Topology on Contact {{Calabi-Yau}} 7-Manifolds},
  author = {Aggarwal, Daattavya and He, Yang-Hui and Heyes, Elli and Hirst, Edward and S{\'a} Earp, Henrique N. and Silva, Tom{\'a}s S.R.},
  year = 2024,
  month = mar,
  journal = {Physics Letters B},
  volume = {850},
  pages = {138517},
  issn = {03702693},
  doi = {10.1016/j.physletb.2024.138517},
  urldate = {2025-02-14},
  abstract = {We propose a machine learning approach to study topological quantities related to the Sasakian and $G_2$-geometries of contact Calabi-Yau $7$-manifolds. Specifically, we compute datasets for certain Sasakian Hodge numbers and for the Crowley-N\"ordstrom invariant of the natural $G_2$-structure of the $7$-dimensional link of a weighted projective Calabi-Yau $3$-fold hypersurface singularity, for 7549 of the 7555 possible $\mathbb{P}^4(\textbf{w})$ projective spaces. These topological quantities are then machine learnt with high performance scores, where learning the Sasakian Hodge numbers from the $\mathbb{P}^4(\textbf{w})$ weights alone, using both neural networks and a symbolic regressor which achieve $R^2$ scores of 0.969 and 0.993 respectively. Additionally, properties of the respective Gr\"obner bases are well-learnt, leading to a vast improvement in computation speeds which may be of independent interest. The data generation and analysis further induced novel conjectures to be raised.},
  copyright = {All rights reserved},
  langid = {english},
  preview = {machine learning G2.jpeg},
}

@inproceedings{gangopadhyayGeneralizedBooleanFunctions2019,
  title = {Generalized {{Boolean Functions}} and {{Quantum Circuits}} on {{IBM-Q}}},
  booktitle = {2019 10th {{International Conference}} on {{Computing}}, {{Communication}} and {{Networking Technologies}} ({{ICCCNT}})},
  author = {Gangopadhyay, Sugata and Poonia, Vishvendra Singh and Aggarwal, Daattavya and Parekh, Rhea},
  year = 2019,
  month = jul,
  pages = {1--6},
  publisher = {IEEE},
  address = {Kanpur, India},
  doi = {10.1109/ICCCNT45670.2019.8944437},
  urldate = {2025-02-14},
  abstract = {We explicitly derive a connection between quantum circuits utilising IBM’s quantum gate set and multivariate quadratic polynomials over integers modulo 8. We demonstrate that the action of a quantum circuit over input qubits can be written as generalized Walsh-Hadamard transform. Here, we derive the polynomials corresponding to implementations of the Swap gate and Toffoli gate using IBM-Q gate set.},
  copyright = {https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html},
  isbn = {978-1-5386-5906-9},
  preview = {boolean_functions.jpeg},
}

@misc{mirjanicRemarkWeightedAverage2025a,
  title = {A Remark on Weighted Average Multiplicities in Prime Factorisation},
  author = {Mirjani{\'c}, Viktor and Aggarwal, Daattavya and Mishra, Challenger},
  year = 2025,
  month = oct,
  number = {arXiv:2510.06993},
  eprint = {2510.06993},
  primaryclass = {math},
  publisher = {arXiv},
  doi = {10.48550/arXiv.2510.06993},
  urldate = {2025-11-12},
  abstract = {We study a generalisation of the quality of an ABC triple that we call the weighted average multiplicity (WAM), in which the logarithmic heights of prime factors are raised to a complex exponent s. The WAM is connected to the standard ABC conjecture at s=1. We show that for real part of s less than 1, WAM is unbounded over ABC triples both for integers and polynomials. For real part greater than 1, we characterise a boundary beyond which WAM is holomorphic and bounded. In this region, we show that WAM is related to the multiplicity of the largest prime factor of the triple, a quantity that we connect with the original ABC conjecture and whose distribution we explore computationally.},
  archiveprefix = {arXiv},
  keywords = {Mathematics - Number Theory},
  preview = {weighted_average_multiplicity.png},
}

@misc{aggarwalDiscoveringMathematicalConcepts2026,
  title = {Discovering Mathematical Concepts through a Multi-Agent System},
  author = {Aggarwal, Daattavya and Kim, Oisin and Ek, Carl Henrik and Mishra, Challenger},
  year = 2026,
  month = mar,
  number = {arXiv:2603.04528},
  eprint = {2603.04528},
  primaryclass = {cs.AI},
  publisher = {arXiv},
  doi = {10.48550/arXiv.2603.04528},
  abstract = {Mathematical concepts emerge through an interplay of processes, including experimentation, efforts at proof, and counterexamples. In this paper, we present a new multi-agent model for computational mathematical discovery based on this observation. Our system, conceived with research in mind, poses its own conjectures and then attempts to prove them, making decisions informed by this feedback and an evolving data distribution. Inspired by the history of Euler's conjecture for polyhedra and an open challenge in the literature, we benchmark with the task of autonomously recovering the concept of homology from polyhedral data and knowledge of linear algebra. Our system completes this learning problem. Most importantly, the experiments are ablations, statistically testing the value of the complete dynamic and controlling for experimental setup. They support our main claim: that the optimisation of the right combination of local processes can lead to surprisingly well-aligned notions of mathematical interestingness.},
  archiveprefix = {arXiv},
  keywords = {Artificial Intelligence, Mathematics - History and Overview},
  preview = {topology_figure.jpg},
}