Related papers: Quantum Projector Method on Curved Manifolds
Many-body states described by a Schr\"{o}dinger equation include states of overlapping waves of non-vanishing interaction energies. These peculiar states formed in many-body transitions remain in asymptotic regions, and lead a new component…
In this article, the following results are obtained: the process of a randomly wandering particle having a size and a continuous trajectory of motion is considered; (b) based on the study of this probabilistic process, a derivation of the…
We develop a novel approach aimed at solving the equations of motion of open quantum many-body systems. It is based on a combination of generalized wave function trajectories and matrix product states. We introduce an adaptive quantum…
A unified approach, for solving a wide class of single and many-body quantum problems, commonly encountered in literature is developed based on a recently proposed method for finding solutions of linear differential equations. Apart from…
We describe quantum-field-theoretical (QFT) techniques for mapping quantum problems onto c-number stochastic problems. This approach yields results which are identical to phase-space techniques [C.W. Gardiner, {\em Quantum Noise} (1991)]…
Quantum random walks use interference to obtain faster state space exploration, which can be used for algorithmic purposes. Photonic technologies provide a natural platform for many recent experimental demonstrations. Here we analyze…
Dynamics of a state of interest coupled to a non-Markovian environment is studied for the first time by concatenating the non-Markovian quantum state diffusion (QSD) equation and the Feshbach projection operator partitioning technique. An…
Variational quantum calculations have borrowed many tools and algorithms from the machine learning community in the recent years. Leveraging great expressive power and efficient gradient-based optimization, researchers have shown that trial…
The Variational Monte Carlo method has recently seen important advances through the use of neural network quantum states. While more and more sophisticated ans\"atze have been designed to tackle a wide variety of quantum many-body problems,…
Quantum state preparation in high-dimensional systems is an essential requirement for many quantum-technology applications. The engineering of an arbitrary quantum state is, however, typically strongly dependent on the experimental platform…
We derive an exact equation of motion for the reduced density matrices of individual subsystems of quantum many-body systems of any lattice dimension and arbitrary system size. Our projection operator based theory yields a highly efficient…
We propose and demonstrate a method for quantum-state tomography of qudits encoded in the quantum polarization of $N$-photon states. This is achieved by distributing $N$ photons nondeterministically into three paths and their subsequent…
In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step towards this objective, the following question is being…
We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the…
Constrained optimization plays a crucial role in the fields of quantum physics and quantum information science and becomes especially challenging for high-dimensional complex structure problems. One specific issue is that of quantum process…
Continuous-time quantum walk is one of the alternative approaches to quantum computation, where a universal set of quantum gates can be achieved by scattering a quantum walker on some specially-designed structures embedded in a sparse graph…
We introduce a new way of generating the quantum geometric phase by making the initial base state index dependent on space-time curvature. We prove that the resulting Schr\"odinger equation is identical to the trace form of the Einstein…
Quantum states defined over a parameter space form a Grassmann manifold. To capture the geometry of the associated gauge structure, gauge-invariant quantities are essential. We employ the projector of a multilevel system to quantify the…
Many-body quantum-mechanical scattering problem is solved asymptotically when the size of the scatterers (inhomogeneities) tends to zero and their number tends to infinity. A method is given for calculation of the number of small…
We develop a projective quantum Monte Carlo algorithm of the Hirsch-Fye type for obtaining ground state properties of the Anderson impurity model. This method is employed to solve the self-consistency equations of dynamical mean field…