Related papers: Quantum walk informed variational algorithm design
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In…
The quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. A near-optimal solution to the combinatorial optimization…
Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from…
This article presents a novel and succinct algorithmic framework via alternating quantum walks, unifying quantum spatial search, state transfer and uniform sampling on a large class of graphs. Using the framework, we can achieve exact…
Financial markets are noisy yet contain a latent graph-theoretic structure that can be exploited for superior risk-adjusted returns. We propose a quantum stochastic walk (QSW) optimizer that embeds assets in a weighted graph: nodes…
While variational quantum algorithms (VQAs) have demonstrated considerable success in unconstrained optimization, their application to constrained combinatorial problems face a trade-off. Penalty-based methods, despite their circuit…
The theory of random walks on finite graphs is well developed with numerous applications. In quantum walks, the propagation is governed by quantum mechanical rules; generalizing random walks to the quantum setting. They have been…
This paper gives the quantum walks determined by graph zeta functions. The result enables us to obtain the characteristic polynomial of the transition matrix of the quantum walk, and it determines the behavior of the quantum walk. We treat…
Mixing properties of discrete-time quantum walks on two-dimensional grids with torus-like boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an…
We present an approach to simulate the Schr\"odinger equation through continuous time quantum walks. The CTQW-based simulation applies unitary evolution driven by a quantum walk to generate probability amplitude distributions at various…
A continuous-time quantum walk on a dynamic graph evolves by Schr\"odinger's equation with a sequence of Hamiltonians encoding the edges of the graph. This process is universal for quantum computing, but in general, the dynamic graph that…
Quantum variational circuits have gained significant attention due to their applications in the quantum approximate optimization algorithm and quantum machine learning research. This work introduces a novel class of classical probabilistic…
The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work,…
In this paper we analyze the performance of the Quantum Adiabatic Evolution algorithm on a variant of Satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, $\gamma=M/N$. We introduce a…
Variational Quantum Algorithms, including the Quantum Approximate Optimization Algorithm (QAOA), have shown promise in solving optimization problems but rely on costly variational loops that can themselves be hard optimization problems.…
The Quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. In a typical QAOA setup, a set of quantum circuit parameters…
This work describes a new algorithm for creating a superposition over the edge set of a graph, encoding a quantum sample of the random walk stationary distribution. The algorithm requires a number of quantum walk steps scaling as…
Open Quantum Walks (OQW) are a type of quantum walk governed by the system's interaction with its environment. We explore the time evolution and the limit behavior of the OQW framework for Quantum Computation and show how we can represent…
The characterization of the Hamiltonian parameters defining a quantum walk is of paramount importance when performing a variety of tasks, from quantum communication to computation. When dealing with physical implementations of quantum…
This paper proposes a highly efficient quantum algorithm for portfolio optimisation targeted at near-term noisy intermediate-scale quantum computers. Recent work by Hodson et al. (2019) explored potential application of hybrid…