Related papers: On Quantum Speedups for Nonconvex Optimization via…
Statistical and stochastic analysis based on thermodynamics has been the main analysis framework for stochastic global optimization. Recently, appearing quantum annealing or quantum tunneling algorithm for global optimization, we require a…
Computational advantages gained by quantum algorithms rely largely on the coherence of quantum devices and are generally compromised by decoherence. As an exception, we present a quantum algorithm for graph isomorphism testing whose…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
The advent of quantum algorithms has initiated a discourse on the potential for quantum speedups for optimization problems. However, several factors still hinder a practical realization of the potential benefits. These include the lack of…
Quantum computing promises to improve the information processing power to levels unreachable by classical computation. Quantum walks are heading the development of quantum algorithms for searching information on graphs more efficiently than…
We compare discrete-time quantum walks on graphs to their natural classical equivalents, which we argue are lifted Markov chains, that is, classical Markov chains with added memory. We show that these can simulate quantum walks, allowing us…
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…
The protocol of quantum annealing is applied to an optimization problem with a one-dimensional continuous degree of freedom, a variant of the problem proposed by Shinomoto and Kabashima. The energy landscape has a number of local minima,…
We propose a novel heuristic quantum algorithm for the Minimum Vertex Cover (MVC) problem based on continuous-time quantum walks (CTQWs). In this framework, the coherent propagation of a quantum walker over a graph encodes its structural…
Fast computational algorithms are in constant demand, and their development has been driven by advances such as quantum speedup and classical acceleration. This paper intends to study search algorithms based on quantum walks in quantum…
Variational quantum algorithms (VQAs) are leading strategies for using near-term quantum devices, with a well-studied bottleneck being their trainability. Standard expectation-value objectives with expressive circuits frequently encounter…
Continuous-time quantum walks (CTQWs) on dynamic graphs, referred to as dynamic CTQWs, are a recently introduced universal model of computation that offers a new paradigm in which to envision quantum algorithms. In this work we develop an…
We construct an oracular (i.e., black box) problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different…
This work is a benchmark study for quantum-classical computing method with a real-world optimization problem from industry. The problem involves scheduling and balancing jobs on different machines, with a non-linear objective function. We…
Major players in the global aerospace industry are shifting their focus toward achieving net carbon-neutral operations by 2050. A considerable portion of the overall carbon emission reduction is expected to come from new aircraft…
We provide and analyze examples that counter the widely made claim that tunneling is needed for a quantum speedup in optimization problems. The examples belong to the class of perturbed Hamming-weight optimization problems. In one case,…
Routing in wireless communication networks is shaped by mobility, interference, congestion, and competing service requirements, making route selection a high-dimensional constrained optimization problem rather than a simple shortest-path…
In this paper, we identify a family of nonconvex continuous optimization instances, each $d$-dimensional instance with $2^d$ local minima, to demonstrate a quantum-classical performance separation. Specifically, we prove that the recently…
We present an efficient quantum algorithm aiming to find the negative curvature direction for escaping the saddle point, which is the critical subroutine for many second-order non-convex optimization algorithms. We prove that our algorithm…
A quantum computer, i.e. utilizing the resources of quantum physics, superposition of states and entanglement, could furnish an exponential gain in computing time. A simulation using such resources is called a quantum simulation. The…