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Recently there has been significant interest in using causal modelling techniques to understand the structure of physical theories. However, the notion of `causation' is limiting - insisting that a physical theory must involve causal…
Quantum supermaps provide a framework in which higher order quantum processes can act on lower order quantum processes. In doing so, they enable the definition and analysis of new quantum protocols and causal structures. Recently, key…
Certain many-particle Hardy inequalities are derived in a simple and systematic way using the so-called ground state representation for the Laplacian on a subdomain of $\mathbb{R}^n$. This includes geometric extensions of the standard Hardy…
The performance of computational methods for many-body physics and chemistry is strongly dependent on the choice of basis used to cast the problem; hence, the search for better bases and similarity transformations is important for progress…
We show that quantum theory allows for transformations of black boxes that cannot be realized by inserting the input black boxes within a circuit in a pre-defined causal order. The simplest example of such a transformation is the classical…
The development of tailored materials for specific applications is an active field of research in chemistry, material science and drug discovery. The number of possible molecules that can be obtained from a set of atomic species grow…
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 rotations play in quantum algorithms, explaining Grover's,…
Motivated by algorithmic problems arising in quantum field theories whose dynamical variables are geometric in nature, we provide a quantum algorithm that efficiently approximates the colored Jones polynomial. The construction is based on…
Loop-tree duality (LTD) allows to express virtual contributions in terms of phase-space integrals, thus leading to a direct mapping with real radiation terms. We review the basis of the method and describe its application to regularize…
Classical algorithms for predicting the equilibrium geometry of strongly correlated molecules require expensive wave function methods that become impractical already for few-atom systems. In this work, we introduce a variational quantum…
We report on a new method for the numerical evaluation of loop integrals, based on the Feynman Tree Theorem. The loop integrals are replaced by phase-space integration over fictitious extra on-shell particles. This integration can be…
L-infinity morphisms are studied from the point of view of perturbative quantum field theory, as generalizations of Feynman expansions. The connection with the Hopf algebra approach to renormalization is exploited. Using the coalgebra…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
In a recent paper \cite{ft} a new powerful method to calculate Feynman diagrams was proposed. It consists in setting up a Taylor series expansion in the external momenta squared. The Taylor coefficients are obtained from the original…
The capacity to custom tailor the properties of quantum matter and materials is a central requirement for enlarging their range of possible functionalities. A particularly promising route is the use of driving protocols to engineer specific…
In this educational paper, we will discuss calculations on the hydrogen molecule both on classical and quantum computers. In the former case, we will discuss the calculation of molecular integrals that can then be used to calculate…
Quantum computing promises exponential improvements in solving large systems of partial differential equations (PDE), which forms a bottleneck in high-resolution computational fluid dynamics (CFD) simulations, in, among others, aerospace…
Quantum computation of vibrational properties of molecules is a promising platform to obtain computational advantages for computational chemistry. However, fault-tolerant quantum computations of vibrational properties remain a relatively…
In this contribution we deal with several issues one encounters when trying to couple quantum matter to classical gravitational fields. We start with a general background discussion and then move on to two more technical sections. In the…
Elaborating on the novel formulation of the loop-tree duality, we introduce the Mathematica package Lotty that automates the latter at multi-loop level. By studying the features of Lotty and recalling former studies, we discuss that the…