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We analyze topological phase transitions and higher Berry curvature in one-dimensional quantum spin systems, using a framework that explicitly incorporates the symmetry group action on the parameter space. Based on a $G$-compatible…
Control Barrier Function Quadratic Programs (CBF-QPs) have become a central tool for real-time safety-critical control due to their applicability to general control-affine systems and their ability to enforce constraints through…
A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions…
Matrix Product States (MPSs) provide a powerful framework to study and classify gapped quantum phases --symmetry-protected topological (SPT) phases in particular--defined in one dimensional lattices. On the other hand, it is natural to…
A generic method to investigate many-body continuous-variable systems is pedagogically presented. It is based on the notion of matrix product states (so-called MPS) and the algorithms thereof. The method is quite versatile and can be…
Spectral properties of the Hamiltonian function which characterizes a trapped ion are investigated. In order to study semiclassical dynamics of trapped ions, coherent state orbits are introduced as sub-manifolds of the quantum state space,…
Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of…
In recent years, a close connection between the description of open quantum systems, the input-output formalism of quantum optics, and continuous matrix product states in quantum field theory has been established. So far, however, this…
We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space, formulated entirely within a discrete phase space. Starting from the discrete Wigner function defined on $\mathbb{Z}_d…
Constrained Motion Planning (CMP) aims to find a collision-free path between the given start and goal configurations on the kinematic constraint manifolds. These problems appear in various scenarios ranging from object manipulation to…
Sequential dynamical systems (SDS) are used to model a wide range of processes occurring on graphs or networks. The dynamics of such discrete dynamical systems is completely encoded by their phase space, a directed graph whose vertices and…
While phases and phase transitions are conventionally described by local order parameters in real space, we present a unified framework characterizing the phase transition through the geometry of configuration space defined by the…
Starting from the geometric description of quantum systems, we propose a novel approach to time-independet dissipative quantum processes according to which the energy is dissipated but the coherence of the states is preserved. Our proposal…
We propose and develop a measurement scheme for quantum field theory (QFT) in curved spacetimes, in which the QFT of interest, the "system", is dynamically coupled to another, the "probe", in a compact spacetime region. Measurements of…
In this article, we study quantum critical phenomena in surfaces of symmetry-protected topological matter, i.e. surface topological quantum criticality. A generic phase boundary of gapless surfaces in a symmetry-protected state shall be a…
A matrix product state formulation of the multiconfiguration time-dependent Hartree (MPS-MCTDH) theory is presented. The Hilbert space that is spanned by the direct products of the phonon degree of freedoms, which is linearly parameterized…
The evolution of squeezed coherent states (CSs) of motion for trapped ions is investigated by applying the time dependent variational principle (TDVP) for the Schr\"{o}dinger equation. The method is applied in case of Paul and combined…
Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been…
Reliable trajectory-based nonadiabatic quantum dynamics methods at the atomic level are critical for understanding many important processes in real systems. The paper reports latest progress of nonadiabatic field (NaF), a conceptually novel…
Quantum walks are versatile simulators of topological phases and phase transitions as observed in condensed matter physics. Here, we utilize a step dependent coin in quantum walks and investigate what topological phases we can simulate with…