Related papers: Point-group symmetry analysis of many-electron wav…
Symmetry is an important and unifying notion in many areas of physics. In quantum mechanics, it is possible to eliminate degrees of freedom from a system by leveraging symmetry to identify the possible physical transitions. This allows us…
We consider group-covariant positive operator valued measures (POVMs) on a finite dimensional quantum system. Following Neumark's theorem a POVM can be implemented by an orthogonal measurement on a larger system. Accordingly, our goal is to…
The numerical renormalization group method is used to investigate zero temperature phase transitions in quantum impurity systems, in particular in the particle-hole symmetric soft-gap Anderson model. The model displays two stable phases…
Quantum computers promise to revolutionize our ability to simulate molecules, and cloud-based hardware is becoming increasingly accessible to a wide body of researchers. Algorithms such as Quantum Phase Estimation and the Variational…
This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…
Quantum machine learning algorithms, the extensions of machine learning to quantum regimes, are believed to be more powerful as they leverage the power of quantum properties. Quantum machine learning methods have been employed to solve…
We propose a fast and non-destructive spectroscopic method for single molecular ions that implements quantum logic schemes between an atomic ion and the molecular ion of interest. Our proposal relies on a hybrid coherent manipulation of the…
This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum…
Modeling many-body quantum systems with strong interactions is one of the core challenges of modern physics. A range of methods has been developed to approach this task, each with its own idiosyncrasies, approximations, and realm of…
Generally, the first step in modeling molecular magnets involves obtaining the low-lying eigenstates of a Heisenberg exchange Hamiltonian which conserves total spin and belongs usually to a non-Abelian point group. In quantum chemistry, it…
Quantum systems of indistinguishable particles are commonly described using the formalism of second quantisation, which relies on the assumption that any admissible quantum state must be either symmetric or anti-symmetric under particle…
We study a quantum-mechanical system of three particles in a one-dimensional box with two-particle harmonic interactions. The symmetry of the system is described by the point group $D_{3d}$. Group theory greatly facilitates the application…
Quantum chemistry provides key applications for near-term quantum computing, but these are greatly complicated by the presence of noise. In this work we present an efficient ansatz for the computation of two-electron atoms and molecules…
Energy spectroscopy is a powerful tool with diverse applications across various disciplines. The advent of programmable digital quantum simulators opens new possibilities for conducting spectroscopy on various models using a single device.…
We devise an efficient algorithm for the symbolic calculation of irreducible angular momentum and spin (LS) eigenspaces within the $n$-fold antisymmetrized tensor product $\wedge^n V_u$, where $n$ is the number of electrons and $u =…
A modified version of the Multicluster Dynamic Model of nuclei is proposed to construct completely antisymmetrized wave functions of multicluster systems. An overlap kernel operator is introduced to renormalize the total wave function after…
Many quantal many-body methods that aim at the description of self-bound nuclear or mesoscopic electronic systems make use of auxiliary wave functions that break one or several of the symmetries of the Hamiltonian in order to include…
Understanding complex chemical systems -- such as biomolecules, catalysts, and novel materials -- is a central goal of quantum simulations. Near-term strategies hinge on the use of variational quantum eigensolver (VQE) algorithms combined…
Simulations of energy loss and hadronization are essential for understanding a range of phenomena in non-equilibrium strongly-interacting matter. We establish a framework for performing such simulations on a quantum computer and apply it to…
This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions and star-products, following a technique developed earlier, {\it viz\/,} using the unitary…