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Quantum SENiority-based Subspace Expansion (Q-SENSE) is a hybrid quantum-classical algorithm that interpolates between the Variational Quantum Eigensolver (VQE) and Configuration Interaction (CI) methods. It constructs Hamiltonian matrix…
Our aim in this thesis is to use the language of deformation-quantization to understand certain quantized algebras by looking at properties of the corresponding commutative ones, and conversely to obtain results about the commutative…
The quantization of a single particle without spin in an appropriate curved space-time is considered. The Hamilton formalism on reduced space for a particle in a curved space-time is constructed and the main aspects of quantization scheme…
We consider three different approaches to analyze the quantum mechanical problems in multi-well potentials: i) the standard matrix diagonalization technique in the basis sets of harmonic oscillator eigenfunctions or plain waves; ii) the…
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…
Many problems in linear algebra -- such as those arising from non-Hermitian physics and differential equations -- can be solved on a quantum computer by processing eigenvalues of the non-normal input matrices. However, the existing Quantum…
Inspired by the success of Boltzmann Machines based on classical Boltzmann distribution, we propose a new machine learning approach based on quantum Boltzmann distribution of a transverse-field Ising Hamiltonian. Due to the non-commutative…
Subspace diagonalisation methods have appeared recently as promising means to access the ground state and some excited states of molecular Hamiltonians by classically diagonalising small matrices, whose elements can be efficiently obtained…
I present a method of performing geometric quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UTC). I also show that by using this method…
Within the framework of Quantum Reduced Loop Gravity we quantize the Hamiltonian for a gauge vector field. The regularization can be performed using tools analogous to the ones adopted in full Loop Quantum Gravity, while the matrix elements…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
The variational quantum eigensolver (VQE) combines classical and quantum resources in order simulate classically intractable quantum states. Amongst other variables, successful VQE depends on the choice of variational ansatz for a problem…
In many condensed-matter systems, it is very useful to introduce a quasi-particle approach, which is based on some sort of linearization around a suitable background state. In order to be a systematic and controlled approximation, this…
In this brief review we describe the idea of holonomic quantum computation. The idea of geometric phase and holonomy is introduced in a general way and we provide few examples that should help the reader understand the issues involved.
Quasiparticle band structures are fundamental for understanding strongly correlated electron systems. While solving these structures accurately on classical computers is challenging, quantum computing offers a promising alternative.…
The numerical version of the Hamilton-Jacobi quantization method, recently proposed, is applied to the one dimensional quartic oscillator. A suitable quantization condition is formulated and various energy levels and wave functions are…
We apply the quantum Hamilton-Jacobi formalism, naturally defined in the complex domain, to a number of complex Hamiltonians, characterized by discrete parity and time reversal (PT) symmetries and obtain their eigenvalues and…
The relevance in Physics of non-Hermitian operators with real eigenvalues is being widely recognized not only in quantum mechanics but also in other areas, such as quantum optics, quantum fluid dynamics and quantum field theory. %stochastic…
We review results about entanglement (or modular) Hamiltonians of quantum many-body systems in field theory and statistical mechanics models, as well as recent applications in the context of quantum information and quantum simulation.
We study the tunneling between two quantum Hall systems, along a quasi one-dimensional interface. A detailed analysis relates microscopic parameters, characterizing the potential barrier, with the effective field theory model for the…