Quantum Hamiltonian simulation (QHS) is one of the fundamental quantum sub-routines in quantum physics and quantum computing. QHS prepares a unitary approximately within some error bound for a given Hamiltonian. It has immense applications in science and engineering, from solving linear systems of equations to finding the ground state energy of an atomic configuration. We focus on the algorithmic side of the QHS problem for different practical Hamiltonian systems (such as signal processing, communication, and chemistry) and analyse their performance. Further, we look for interesting applications where these algorithms may bring some quantum advantage. One of the exciting research problems is to simulate the potential energy Hamiltonian on a practical quantum computer for some atomic configuration. Given a 1-dimensional potential energy function (of an arbitrary nature), we propose a Quantum polynomial approximate encoding algorithm that can offer a complexity improvement over the existing Hadamard basis encoding with complexity for some qubit size.

In this work, drawing inspiration from the type of noise present in real hardware, we study the output distribution of random quantum circuits under practical non-unital noise sources with constant noise rates. We show that even in the presence of unital sources like the depolarizing channel, the distribution, under the combined noise channel, never resembles a maximally entropic distribution at any depth. To show this, we prove that the output distribution of such circuits never anticoncentrates — meaning it is never too "flat"— regardless of the depth of the circuit. This is in stark contrast to the behavior of noiseless random quantum circuits or those with only unital noise, both of which anticoncentrate at sufficiently large depths. As consequences, our results have interesting algorithmic implications on both the hardness and easiness of noisy random circuit sampling, since anticoncentration is a critical property exploited by both state-of-the-art classical hardness and easiness results.

We discuss Bose's notion of indistinguishability at the combinatorial level as introduced by him in his seminal 1924 paper. We further describe its extension in a quantum mechanical setting and discuss various quantum statistics (including Bose and Fermi) describing N identical and indistinguishable particles. We also show how the theory of symmetric functions can be utilised to express the partition functions for all such statistics in terms of Schur functions.

From quantum computation to communication, design of quantum devices and peripheral technology relies strongly on the interaction of light with matter. This requires not only modelling these interactions at the microscopic level but also seeking appropriate solutions at different operational regime. In this talk, we informally look at a few approaches that can be used to study such light-matter interactions. These range from rate equations, cluster expansion and quantum trajectories to study condensates of light to tensor-network methods to design spin-ensemble based quantum memories.

Metamaterials are artificial materials consisting of micro or nano composites which exhibit properties different from their components in sub-wavelength regime. These materials are finding applications in several areas such as sensing, sub-diffractive imaging, negative refractive index materials, perfect absorption, Huygen’s lens and quantum technologies. More recently all-dielectric metamaterials have been garnering much attention due to the reduction in the dissipative losses which their metallic counterparts suffer from. Our research involves understanding the light-matter interactions in all-dielectric materials using simulations and designing reconfigurable multi-functional dielectric devices for applications in sensing, energy harvesting and quantum technologies. In the talk, I will briefly discuss the overview of our research area and give details of some recent findings on tunable soft-metamaterials.