We develop three new methods to implement any Linear Combination of Unitaries (LCU), a
powerful quantum algorithmic tool with diverse applications. While the standard LCU …

Estimating the volume of a convex body is a central problem in convex geometry and can be
viewed as a continuous version of counting. We present a quantum algorithm that estimates …

Spatial search by a discrete-time quantum walk can find a marked node on any ergodic,
reversible Markov chain P quadratically faster than its classical counterpart, ie, in a time that …

We study a mixing condition for entangled Markov chains, so-called ψ-mixing property. We
prove that every entangled Markov chain, whose Markov operators satisfy the Markov …

This article presents a novel and succinct algorithmic framework via alternating quantum
walks, unifying quantum spatial search, state transfer and uniform sampling on a large class …

Continuous-time quantum walks have proven to be an extremely useful framework for the
design of several quantum algorithms. Often, the running time of quantum algorithms in this …

The framework of this thesis is fault-tolerant quantum algorithms. Grover's algorithm and
quantum walks are described in Chapter 2. We start by highlighting the central role that …

In this article, we undertake a detailed study of the limiting behavior of a three-state discrete-
time quantum walk on a one-dimensional lattice with generalized Grover coins. Two limit …

We introduce-projectors, using which we can sample from limiting distributions of continuous-
time quantum walks. The standard algorithm for sampling from a distribution that is close to …

In the present paper, we introduce a class of F-stochastic operators on a finite-dimensional
simplex, each of which is regular, ascertaining that the species distribution in the succeeding …