New high-performance computing architectures are becoming operative, in addition to
exascale computers. Quantum computers (QC) solve optimization problems with …

After the first detection of a gravitational wave in 2015, the number of successes achieved by
this innovative way of looking through the Universe has not stopped growing. However, the …

Quantum walks are promising tools based on classical random walks, with plenty of
applications such as many variants of optimization. Here we introduce the semiclassical …

Szegedy's quantum walk is an algorithm for quantizing a general Markov chain. It has plenty
of applications, such as many variants of optimizations. In order to check its properties in an …

The Markov chain Monte Carlo (MCMC) method, especially the Metropolis-Hastings (MH)
algorithm, is a widely used technique for sampling from a target probability distribution P on …

We compute the complexity for the mixed-state density operator derived from a one-
dimensional discrete-time quantum walk (DTQW). The complexity is computed using a two …

Advancements in gravitational-wave interferometers, particularly the next generation, are
poised to profoundly impact gravitational wave astronomy and multimessenger astrophysics …

We analyze the effect of a simple coin operator, built out of Bell pairs, in a 2d Discrete
Quantum Random Walk (DQRW) problem. The specific form of the coin enables us to find …

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 …

This thesis explores hybrid algorithms that combine classical and quantum computing to
enhance the performance of classical algorithms. Two approaches are studied: a hybrid …