Related papers: Quantum walk informed variational algorithm design
The lackadaisical quantum walk is a discrete-time, coined quantum walk on a graph with a weighted self-loop at each vertex. It uses a generalized Grover coin and the flip-flop shift, which makes it equivalent to Szegedy's quantum Markov…
The physics of quantum walks on graphs is formulated in Hamiltonian language, both for simple quantum walks and for composite walks, where extra discrete degrees of freedom live at each node of the graph. It is shown how to map between…
Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or…
Quantum walks (QWs) represent pillars of quantum dynamics and information processing. They provide a powerful framework for simulating quantum transport, designing search algorithms, and enabling universal quantum computation. Several…
Quantum computing has the potential to solve complex problems faster and more efficiently than classical computing. It can achieve speedups by leveraging quantum phenomena like superposition, entanglement, and tunneling. Quantum walks (QWs)…
A fundamental problem in Quantum Information Processing is the discrimination amongst a set of quantum states of a system. In this paper, we address this problem on an open quantum system described by a graph, whose evolution is defined by…
In this paper, we analyze the dynamics of quantum walks on a graph structure resulting from the integration of a main connected graph $G$ and a secondary connected graph $G'$. This composite graph is formed by a disjoint union of $G$ and…
Quantum walks are powerful kernels in quantum computing protocols that possess strong capabilities in speeding up various simulation and optimisation tasks. One striking example is given by quantum walkers evolving on glued trees for their…
Quantum annealing (QA) has emerged as a powerful technique to solve optimization problems by taking advantages of quantum physics. In QA process, a bottleneck that may prevent QA to scale up is minor embedding step in which we embed…
Quantum walks provide a versatile framework for probing the structural and dynamical properties of complex systems ranging from biological networks to synthetic materials. However, their realization on current noisy pre-fault-tolerant…
Neutral atom arrays provide a versatile platform to implement coherent quantum annealing as an approach to solving hard combinatorial optimization problems. Here we present and experimentally demonstrate an efficient encoding scheme based…
In papers\cite{js,jsa}, the amplitudes of continuous-time quantum walk on graphs possessing quantum decomposition (QD graphs) have been calculated by a new method based on spectral distribution associated to their adjacency matrix. Here in…
We consider to what extent quantum walks can constitute models of thermalization, analogously to how classical random walks can be models for classical thermalization. In a quantum walk over a graph, a walker moves in a superposition of…
Continuous-variable (CV) quantum systems offer a natural framework for continuous optimization through their infinite-dimensional Hilbert spaces. In this paper, we propose the Complex Continuous-Variable Quantum Approximate Optimization…
Graph Neural Networks (GNN) and Transformer-based architectures have achieved remarkable progress in graph learning, yet they still struggle to capture both global structural dependencies and model the dynamic information propagation. In…
In this work, we present a new algorithm for generating quantum circuits that efficiently implement continuous time quantum walks on arbitrary simple sparse graphs. The algorithm, called matching decomposition, works by decomposing a…
We present a quantum variational algorithm based on a novel circuit that generates all permutations that can be spanned by one- and two-qubits permutation gates. The construction of the circuits follows from group-theoretical results, most…
We develop a new framework that extends the quantum walk framework of Magniez, Nayak, Roland, and Santha, by utilizing the idea of quantum data structures to construct an efficient method of nesting quantum walks. Surprisingly, only…
The quantum approximate optimisation ansatz (QAOA) is one of the flagship algorithms used to tackle combinatorial optimisation on graphs problems using a quantum computer, and is considered a strong candidate for early fault-tolerant…
Quantum walks have attracted attention as a promising platform realizing topological phenomena and many physicists have introduced various types of indices to characterize topologically protected bound states that are robust against…