In this article we provide a review of geometrical methods employed in the analysis of
quantum phase transitions and non-equilibrium dissipative phase transitions. After a …

Geometric and holonomic quantum computation utilizes intrinsic geometric properties of
quantum-mechanical state spaces to realize quantum logic gates. Since both geometric …

Measures are introduced to quantify the degree of superposition in mixed states with respect
to orthogonal decompositions of the Hilbert space of a quantum system. These …

A novel approach based on the Uhlmann curvature is introduced for the investigation of non-
equilibrium steady-state quantum phase transitions (NESS-QPTs). Equilibrium phase …

We show that the geometric phase of the ground state in the XY model obeys scaling
behavior in the vicinity of a quantum phase transition. In particular we find that the geometric …

The rise of quantum information science has opened up a new venue for applications of the
geometric phase (GP), as well as triggered new insights into its physical, mathematical, and …

The main challenges in achieving high-fidelity quantum gates are to reduce the influence of
control errors caused by imperfect Hamiltonians and the influence of decoherence caused …

Open quantum systems is the study of quantum dynamics of the system of interest, taking
into account the effects of the ambient environment. It is ubiquitous in the sense that any …

Geometric phase is a key player in many areas of quantum science and technology. In this
review article, several foundational aspects of quantum geometric phases and their relations …

Large-scale quantum computers are hard to construct because quantum systems easily lose
their coherence through interaction with the environment. Researchers have tried to avoid …