Related papers: Tripartite connection condition for quantum graph …
The graph state formalism is a useful abstraction of entanglement. It is used in some multipartite purification schemes and it adequately represents universal resources for measurement-only quantum computation. We focus in this paper on the…
A fundamental problem in quantum information is to describe efficiently multipartite quantum states. An efficient representation in terms of graphs exists for several families of quantum states (graph, cluster, stabilizer states),…
Recently, a novel GHZ/W graphical calculus has been established to study and reason more intuitively about interacting quantum systems. The compositional structure of this calculus was shown to be well-equipped to sufficiently express…
We consider boundary conditions at the vertex of a star graph which make Schroedinger operators on the graph self-adjoint, in particular, the two-parameter family of such conditions invariant with respect to permutations of graph edges. It…
We consider the dynamics of relativistic spin-half particles in quantum graphs with transparent branching points. The system is modeled by combining the quantum graph concept with the one of transparent boundary conditions applied to the…
This work shows that minimizing the depth of a quantum circuit composed of commuting operations reduces to a vertex coloring problem on an appropriately constructed graph, where gates correspond to vertices and edges encode…
We analyze few-body quantum states with particular correlation properties imposed by the requirement of maximal bipartite entanglement for selected partitions of the system into two complementary parts. A novel framework to treat this…
We propose a method for constructing multi-qubit entangled quantum states representing weighted tripartite graphs. An expression for the entanglement distance for multi-qubit states corresponding to arbitrary tripartite graph structures is…
We consider an explicitly solvable model (formulated in the Riemannian geometry terms) for a stationary wave process in a specific thin domain with the Dirichlet boundary conditions on the boundary of the domain. The transition from the…
We study the transmission of a quantum particle along a straight input--output line to which a graph $\Gamma$ is attached at a point. In the point of contact we impose a singularity represented by a certain properly chosen scale-invariant…
This article comprehensively explores matrices and their prerequisites for achieving positive semidefiniteness. The study delves into a series of theorems concerning pure quantum states in the context of weighted graphs. The main objective…
Boundary conditions strongly affect the results of numerical computations for finite size inhomogeneous or incommensurate structures. We present a method which allows to deal with this problem, both for ground state and for critical…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
Five different versions of the three-dimensional (3D) reduction of the Bethe-Salpeter (BS) equation in the instantaneous approximation for kernel of BS equation for the two-fermion systems are formulated. The normalization condition for the…
We study the statistical properties of the scattering matrix associated with generic quantum graphs. The scattering matrix is the quantum analogue of the classical evolution operator on the graph. For the energy-averaged spectral form…
We study multi-qubit variational quantum states that can be considered as vertex- and edge-weighted graph. These states are constructed as single-layer variational circuits with $RX$ rotations and $RZZ$ entangling gates, corresponding to…
We consider the Dirac equation on periodic networks (quantum graphs). The self-adjoint quasi periodic boundary conditions are derived. The secular equation allowing us to find the energy spectrum of the Dirac particles on periodic quantum…
We consider the case of an integrable quantum spin chain with ``soliton non-preserving'' boundary conditions. This is the first time that such boundary conditions have been considered in the spin chain framework. We construct the transfer…
In this work, we present new connections between three types of quantum states: positive under partial transpose states, symmetric with positive coefficients states and invariant under realignment states. First, we obtain a common upper…
Quantum Singular Value Transformation (QSVT) is a state-of-the-art, near-optimal quantum algorithm that can be used for matrix inversion. The QSVT circuit is parameterized by a sequence of angles that must be pre-calculated classically,…