Related papers: Geometric properties of evolutionary graph states …
Graphene, a two-dimensional material with tunable electronic properties, holds significant importance in condensed matter physics and material science. In this study, we analyze the curvature of graphene's ground-state energy dispersion…
The evolution of certain pair state in a quantum network with isomorphic branches, governed by the Heisenberg $XY$ Hamiltonian, depends solely on the local structure, and it remains unaffected even if the global structure is altered. All…
Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting…
In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the…
Recent work suggests that topological features of certain quantum gravity theories can be interpreted as particles, matching the known fermions and bosons of the first generation in the Standard Model. This is achieved by identifying…
Quantum computers can sometimes exponentially outperform classical ones, but only for problems with sufficient structure. While it is well known that query problems with full permutation symmetry can have at most polynomial quantum speedup…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…
We initiate a systematic study of quantum properties of finite graphs, namely, quantum asymmetry, quantum symmetry, and quantum isomorphism. We define the Schmidt alternative for a class of graphs, which reveals to be a useful tool for…
We introduce two novel evolutionary formulations of the problem of coloring the nodes of a graph. The first formulation is based on the relationship that exists between a graph's chromatic number and its acyclic orientations. It views such…
Graph states are a class of multi-partite entangled quantum states that are ubiquitous in quantum information. We study equivalence relations between graph states under local unitaries (LU) to obtain distinguishing methods both in local and…
We study the electronic and magnetic properties of multilayer quantum dots (MQDs) of graphite in the nearest-neighbor approximation of tight-binding model. We calculate the electronic density of states and orbital susceptibility of the…
In this series of papers we aim to provide a mathematically comprehensive framework to the Hamiltonian pictures of quantum field theory in curved spacetimes. Our final goal is to study the kinematics and the dynamics of the theory from the…
The symmetries of a finite graph are described by its automorphism group; in the setting of Woronowicz's quantum groups, a notion of a quantum automorphism group has been defined by Banica capturing the quantum symmetries of the graph. In…
We consider quantum metrology for unitary evolutions generated by parameter-dependent Hamiltonians. We focus on the unitary evolutions generated by the Ising Hamiltonian that describes the dynamics of a one-dimensional chain of spins with…
We present an information geometric analysis of entropic speeds and entropy production rates in geodesic evolution on manifolds of parametrized quantum states. These pure states emerge as outputs of suitable su(2; C) time-dependent…
In this article the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is…
Ground-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert…
Multi-qubit quantum states corresponding to bipartite graphs $G(U,V,E)$ are examined. These states are constructed by applying $CNOT$ gates to an arbitrary separable multi-qubit quantum state. The entanglement distance of the resulting…
The phase space for a system of $n$ qubits is a discrete grid of $2^{n} \times 2^{n}$ points, whose axes are labeled in terms of the elements of the finite field $\Gal{2^n}$ to endow it with proper geometrical properties. We analyze the…
Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…