Related papers: On Quantum Speedups for Nonconvex Optimization via…
We present a new method that efficiently solves TO problems and provides a practical pathway to leverage quantum computing to exploit potential quantum advantages. This work targets on large-scale, multi-material TO challenges for…
The Quantum Approximate Optimization Algorithm (QAOA) constitutes one of the often mentioned candidates expected to yield a quantum boost in the era of near-term quantum computing. In practice, quantum optimization will have to compete with…
Quantum walks have been shown to have a wide range of applications, from artificial intelligence, to photosynthesis, and quantum transport. Quantum stochastic walks (QSWs) generalize this concept to additional non-unitary evolution. In this…
We investigate a novel quantum random walk (QRW) model, possibly useful in quantum algorithm implementation, that achieves a quadratically faster diffusion rate compared to its classical counterpart. We evaluate its asymptotic behavior…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
We introduce a new tool for quantum algorithms called quantum fast-forwarding (QFF). The tool uses quantum walks as a means to quadratically fast-forward a reversible Markov chain. More specifically, with $P$ the Markov chain transition…
Hybrid classical quantum optimization methods have become an important tool for efficiently solving problems in the current generation of NISQ computers. These methods use an optimization algorithm executed in a classical computer, fed with…
Quantum walk serves as a versatile tool for universal quantum computing and algorithmic research. However, the implementation of discrete-time quantum walks (DTQWs) with superconducting circuits is still constrained by some limitations such…
Quantum mechanics is well known to accelerate statistical sampling processes over classical techniques. In quantitative finance, statistical samplings arise broadly in many use cases. Here we focus on a particular one of such use cases,…
This paper demonstrates the applicability of the Quantum Walk-based Optimisation Algorithm(QWOA) to the Capacitated Vehicle Routing Problem (CVRP). Efficient algorithms are developedfor the indexing and unindexing of the solution space and…
We assess the prospects for algorithms within the general framework of quantum annealing (QA) to achieve a quantum speedup relative to classical state of the art methods in combinatorial optimization and related sampling tasks. We argue for…
Here we explore which heuristic quantum algorithms for combinatorial optimization might be most practical to try out on a small fault-tolerant quantum computer. We compile circuits for several variants of quantum accelerated simulated…
Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization…
In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process…
Partial differential equations frequently appear in the natural sciences and related disciplines. Solving them is often challenging, particularly in high dimensions, due to the "curse of dimensionality". In this work, we explore the…
We present a quantum algorithm for sampling random spanning trees from a weighted graph in $\widetilde{O}(\sqrt{mn})$ time, where $n$ and $m$ denote the number of vertices and edges, respectively. Our algorithm has sublinear runtime for…
In this perspective, we discuss conditions under which it would be possible for a modest fault-tolerant quantum computer to realize a runtime advantage by executing a quantum algorithm with only a small polynomial speedup over the best…
A new model of nonlinear charged quantum relativistic fluids is presented. This model can be discretized into Discrete Time Quantum Walks (DTQWs), and a new hybrid (quantum-classical) algorithm for implementing these walks on NISQ devices…
How can we efficiently mitigate the overhead of gradient communications in distributed optimization? This problem is at the heart of training scalable machine learning models and has been mainly studied in the unconstrained setting. In this…
Recently, the idea of classical Metropolis sampling through Markov chains has been generalized for quantum Hamiltonians. However, the underlying Markov chain of this algorithm is still classical in nature. Due to Szegedy's method, the…