Related papers: Quantum heuristic algorithm for traveling salesman…
We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably…
In this paper, we study Grover's search algorithm focusing on continuous-time quantum walk on graphs. We propose an alternative optimization approach to Grover's algorithm on graphs that can be summarized as follows: instead of finding…
Quantum robots are described as mobile quantum computers and ancillary systems that move in and interact with arbitrary environments. Their dynamics is given as tasks which consist of sequences of alternating computation and action phases.…
The new model of quantum computation is proposed, for which an effective algorithm of solving any task in NP is described. The work is based and inspired be the Grover's algorithm for solving NP-tasks with quadratic speedup compared to the…
Grover's search algorithm is the cornerstone of many applications of quantum computing, providing a quadratic speed-up over classical methods. One limitation of the algorithm is that it requires knowledge of the number of solutions to…
We operate a superconducting quantum processor consisting of two tunable transmon qubits coupled by a swapping interaction, and equipped with non destructive single-shot readout of the two qubits. With this processor, we run the Grover…
In this work we revisit the Hopfield-Tank algorithm for the traveling salesman problem (TSP) and report encouraging results, with a different dynamics, that makes the algorithm more efficient finding better solutions in much less…
The quadratic traveling salesperson problem (QTSP) is a generalization of the traveling salesperson problem, in which all triples of consecutive customers in a tour determine the travel cost. We propose compact optimization models for QTSP…
We study an oracle operation, along with its circuit design, which combined with the Grover diffusion operator boosts the probability of finding minimum or maximum solutions on a weighted directed graph. We focus on a geometry of…
Constant-factor, polynomial-time approximation algorithms are presented for two variations of the traveling salesman problem with time windows. In the first variation, the traveling repairman problem, the goal is to find a tour that visits…
Quantum multi-programming is a method utilizing contemporary noisy intermediate-scale quantum computers by executing multiple quantum circuits concurrently. Despite early research on it, the research remains on quantum gates or small-size…
Grover's quantum search algorithm provides a quadratic speedup over the classical one. The computational complexity is based on the number of queries to the oracle. However, depth is a more modern metric for noisy intermediate-scale quantum…
Quantum algorithms use the principles of quantum mechanics, as for example quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimisation,…
Combinatorial optimization problems have attracted much interest in the quantum computing community in the recent years as a potential testbed to showcase quantum advantage. In this paper, we show how to exploit multilevel carriers of…
Grover's quantum search algorithm can be formulated as a quantum particle randomly walking on the (highly symmetric) complete graph, with one vertex marked by a nonzero potential. From an initial equal superposition, the state evolves in a…
This thesis introduces stochastic generalized routing problem model and proposes exact and heuristic algorithms to solve it efficiently, in a wide range of problem sizes. At first, the classic routing problem with its common variations in…
The task of finding an entry in an unsorted list of $N$ elements famously takes $O(N)$ queries to an oracle for a classical computer and $O(\sqrt{N})$ queries for a quantum computer using Grover's algorithm. Reformulated as a spatial search…
An algebraic analysis of Grover's quantum search algorithm is presented for the case in which the initial state is an arbitrary pure quantum state of n qubits. This approach reveals the geometrical structure of the quantum search process,…
In this paper, we study the subset-sum problem by using a quantum heuristic approach similar to the verification circuit of quantum Arthur-Merlin games. Under described certain assumptions, we show that the exact solution of the subset sum…
Optimizing high-degree of freedom robotic manipulators requires searching complex, high-dimensional configuration spaces, a task that is computationally challenging for classical methods. This paper introduces a quantum native framework…