publications

2025

1. A Remark on Weighted Average Multiplicities in Prime Factorisation

   Viktor Mirjanić, Daattavya Aggarwal, and Challenger Mishra

   Oct 2025

   Abs DOI

   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.

2024

1. Machine Learning Sasakian and G2 Topology on Contact Calabi-Yau 7-Manifolds

   Daattavya Aggarwal, Yang-Hui He, Elli Heyes, and 3 more authors

   Physics Letters B, Mar 2024

   Abs DOI

   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-Nördstrom 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 \mathbbP^4(\textbfw) projective spaces. These topological quantities are then machine learnt with high performance scores, where learning the Sasakian Hodge numbers from the \mathbbP^4(\textbfw) 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 Gröbner 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.

2019

1. Generalized Boolean Functions and Quantum Circuits on IBM-Q

   Sugata Gangopadhyay, Vishvendra Singh Poonia, Daattavya Aggarwal, and 1 more author

   In 2019 10th International Conference on Computing, Communication and Networking Technologies (ICCCNT), Jul 2019

   Abs DOI

   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.

2018

1. Application of Quantum Scrambling in Rydberg Atom on IBM Quantum Computer

   Daattavya Aggarwal, Shivam Raj, Bikash K. Behera, and 1 more author

   Jul 2018

   Abs DOI

   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.