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This thesis explores the application of the Symmetry-Breaking/Symmetry-Restoration methodology on quantum computers to better approximate a Hamiltonian's ground state energy within a variational framework in many-body physics. This involves…
Quantum computing is a promising approach to harnessing strong correlation in molecular systems; however, current devices only allow for hybrid quantum-classical algorithms with a shallow circuit depth, such as the variational quantum…
We propose a scheme to restore spatial symmetry of Hamiltonian in the variational-quantum-eigensolver (VQE) algorithm for which the quantum circuit structures used usually break the Hamiltonian symmetry. The symmetry-adapted VQE scheme…
The study of spontaneous supersymmetry breaking (SSB) on the lattice is obstructed by a severe sign problem. Quantum computing provides a promising alternative approach. In particular, properties of supersymmetry relate SSB to the…
Symmetry-breaking transitions are a well-understood phenomenon of closed quantum systems in quantum optics, condensed matter, and high energy physics. However, symmetry breaking in open systems is less thoroughly understood, in part due to…
Quantum chemistry calculations on a quantum computer frequently suffer from symmetry breaking: the situation when a state of assumed spin and number of electrons is contaminated with contributions of undesired symmetry. The situation may…
Symmetry is a cornerstone of quantum mechanics and materials theory, underpinning the classification of electronic states and the emergence of complex phenomena such as magnetism and superconductivity. While symmetry breaking in density…
We propose an extended version of the symmetry-adapted variational-quantum-eigensolver (VQE) and apply it to a two-component Fermi-Hubbard model on a bipartite lattice. In the extended symmetry-adapted VQE method, the Rayleigh quotient for…
Investigations of emergent symmetry breaking phenomena occurring in small finite-size systems are reviewed, with a focus on the strongly correlated regime of electrons in two-dimensional semicoductor quantum dots and trapped ultracold…
It is commonly known that the dephasing in open quantum systems is due to the establishment of bipartite correlations with ambient environments, which are typically difficult to be fully characterized. Recently, a new approach of average…
Ensembles of quantum chaotic systems are expected to exhibit energy eigenvalues with random-matrix-like level repulsion between pairs of energies separated by less than the inverse Thouless time. Recent research has shown that exact and…
The review considers the peculiarities of symmetry breaking and symmetry transformations and the related physical effects in finite quantum systems. Some types of symmetry in finite systems can be broken only asymptotically. However, with a…
Simulating the Hubbard model is of great interest to a wide range of applications within condensed matter physics, however its solution on classical computers remains challenging in dimensions larger than one. The relative simplicity of…
The emerging field of quantum simulation of many-body systems is widely recognized as a very important application of quantum computing. A crucial step towards its realization in the context of many-electron systems requires a rigorous…
We consider a quantum many-body system on a lattice with a continuous symmetry which exhibits a spontaneous symmetry breaking in its infinite volume ground states, but in which the order operator does not commute with the Hamiltonian. A…
The Variational Quantum Eigensolver (VQE) is a method of choice to solve the electronic structure problem for molecules on near-term gate-based quantum computers. However, the circuit depth is expected to grow significantly with problem…
A quantum system governed by a non-Hermitian Hamiltonian may exhibit zero temperature phase transitions that are driven by interactions, just as its Hermitian counterpart, raising the fundamental question how non-Hermiticity affects quantum…
We demonstrate the importance of symmetries in Variational Quantum Eigensolver (VQE) algorithms to prepare the ground or specific low-lying states of quantum Hamiltonians. We examine two spin problems, one with random all-to-all couplings…
Simulation of chemical reactions on quantum computing platforms using quantum classical hybrid algorithms such as the Variational Quantum Eigensolver (VQE) is challenged by the need for a reaction consistent treatment of electron…
The variational quantum-classical algorithms are the most promising approach for achieving quantum advantage on near-term quantum simulators. Among these methods, the variational quantum eigensolver has attracted a lot of attention in…