Quantum_Tech_Project_M_Tech_IISc

This repository contains my current research on quantum technology. My primary interest is in knowing "WHY" and "WHERE" Quantum-ness can be used as a resource in computation.

Advisor: Prof. Apoorva Patel, IISc Benagluru

Phase-I (August-November '23): Review of different domains of Quantum Computing

⭐ Quantum Complexity Theory (QCT)

Paper reviews

Forrelation: A problem that optimally separates quantum and classical computation [Aaronson-Ambianis 2015]. (Reviewed; see presentation folder)

Oracle separation of BQP and PH(Polynomial Hierarchy) [Raz-Tal 2018]. (Partially reviewed. Forrelation)

Verifiable Quantum Advantage without structure [Yamakawa-Zhandry 2022]. (Reviewed; see presentation folder)

⭐ Quantum Linear System Algorithms (QLSA)

Paper reviews

Efficient Quantum Algorithms for Dissipative Nonlinear Differential Equations [Jin-Peng Liu,..., Andrew Childs 2021]. (Reviewed; see presentation folder)

Further improving quantum algorithms for nonlinear differential equations via higher-order methods and rescaling [Costa, Pedro C. S.; Schleich, Philipp; Morales, Mauro E. S.; Berry, Dominic W. (2023)]

Towards provably efficient Quantum algorithms for large-scale Machine-learning models [Pre-print: JunyuLiu,.., Liang Jiang 2023] (Reviewed; see presentation folder)

⭐ Quantum Algorithms for Optimisation

Paper reviews

A review on Quantum Approximate Optimisation Algorithm (QAOA) and its variant [Kostas Blekos, ..., Alessandro Summer 2023] (Review Ongoing)

Quantum computing for finance: Nature Reviews Physics [Herman, ..., Alexeev 2023] (Review Ongoing)

⭐ Quantum Learning theory

Paper reviews

Quantum Learning of Concentrated Boolean Functions [Krishna Palem, Duc Hung Pham, M. V. Panduranga Rao (2022)] (Reviewed; see presentation folder)

Phase-II (December 23): Research Proposal with exact problem Statement

Exploring some possibilities to enhance the computational complexity of the quantum algorithm for the Reaction-Diffusion System proposed by Costa et al (2023).

We hypothesise there is some room for improvement if we replace the truncated Taylor series employed by Costa et al (2023) with a Chebyshev series-based method.

Phase-III (January- June 24): Working on the Proposal.

Finally, I have uploaded my findings to arXiv: https://arxiv.org/abs/2510.19855.

Special thanks to Dr Apoorva D. Patel at IISc Bengaluru.

I acknowledge Guoming Wang (https://arxiv.org/pdf/2509.07155) for (i) noticing one definitional error in the first version published on arxiv, and (ii) a suggestion for some improvement related to convergence criteria for the non-linear systems studied in my paper.