Related papers: Geometric properties of evolutionary graph states …
The study of quantum systems evolving from initial states to distinguishable, orthogonal final states is important for information processing applications such as quantum computing and quantum metrology. However, for most unitary evolutions…
We analyze composed quantum systems consisting of $k$ subsystems, each described by states in the $n$-dimensional Hilbert space. Interaction between subsystems can be represented by a graph, with vertices corresponding to individual…
In optimal quantum-mechanical evolutions, motion can take place along paths of minimal length within an optimal time frame. Alternatively, optimal evolutions may occur along established paths without any waste of energy resources and…
Three new graph invariants are introduced which may be measured from a quantum graph state and form examples of a framework under which other graph invariants can be constructed. Each invariant is based on distinguishing a different number…
The possibilities of curvature of space-time in the metric of quantum states are investigated. The curvature of the metric corresponding to a wave function of Hydrogen atom is determined. Also, Einstein tensor is described for a given…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
Quantum counting is a key quantum algorithm that aims to determine the number of marked elements in a database. This algorithm is based on the quantum phase estimation algorithm and uses the evolution operator of Grover's algorithm because…
For a quantum walk on a graph, there exist many kinds of operators for the discrete-time evolution. We give a general relation between the characteristic polynomial of the evolution matrix of a quantum walk on edges and that of a kind of…
We present the results of a numerical simulation aimed at understanding the nature of the `c = 1 barrier' in two dimensional quantum gravity. We study multiple Ising models living on dynamical $\phi^3$ graphs and analyse the behaviour of…
We study relations between the ground-state energy of a quantum graph Hamiltonian with attractive $\delta$ coupling at the vertices and the graph geometry. We derive a necessary and sufficient condition under which the energy increases with…
We theoretically study the geometric effect of quantum dynamical evolution in the presence of a nonequilibrium noisy environment. We derive the expression of the time dependent geometric phase in terms of the dynamical evolution and the…
Graph structures are ubiquitous throughout the natural sciences. Here we consider graph-structured quantum data and describe how to carry out its quantum machine learning via quantum neural networks. In particular, we consider training data…
We follow up on previous work which found that commonly used graph evolution moves lead to conserved quantities that can be expressed in terms of the braiding of the graph in its embedding space. We study non-embedded graphs under three…
We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge…
Calibrating the role of entanglement in quantum algorithms is a crucial task in the development of quantum computing. Most existing studies have primarily focused on how the static properties of entanglement-such as its magnitude and…
Graph states are the main computational building blocks of measurement-based computation and a useful tool for error correction in the gate model architecture. The graph states form a class of quantum states which are eigenvectors for the…
We present a graph theory-based method to characterise flow defects and structural shifts in condensed matter. We explore the connection between dynamical properties, particularly the recently introduced concept of ''softness'', and…
Quantum Graphity (QG) is a model of emergent geometry in which space is represented by a dynamical graph. The graph evolves under the action of a Hamiltonian from a high-energy pre-geometric state to a low-energy state in which geometry…
The evolution of $N$ spin-$1/2$ system with all-range Ising-type interaction is considered. For this system we study the entanglement of one spin with the rest spins. It is shown that the entanglement depends on the amount of spins and the…
Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic…