Related papers: Grover Adaptive Search with Problem-Specific State…

Grover's algorithm constitutes the optimal quantum solution to the search problem and provides a quadratic speed-up over all possible classical search algorithms. Quantum interference between computational paths has been posited as a key…

The Travelling Salesman Problem (TSP) is an important combinatorial optimisation problem, and is usually solved on a quantum computer using a Quadratic Unconstrained Binary Optimisation (QUBO) formulation or a Higher Order Binary…

The original Grover's algorithm has a success probability to output a correct solution, while deterministic Grover's algorithms improve the success probability to 100%. However, the success probability of deterministic Grover's algorithm…

Grover's quantum search algorithm is considered as one of the milestone in the field of quantum computing. The algorithm can search for a single match in a database with $N$ records in $O(\sqrt{N})$ assuming that the item must exist in the…

This work presents a tensor-network formulation of the Traveling Salesman Problem (TSP) and several of its variants. The approach represents candidate tours with tensor-network layers, weights them by Boltzmann factors, and enforces…

Numerous conceptually important quantum algorithms rely on a black-box device known as an oracle, which is typically difficult to construct without knowing the answer to the problem that the algorithm is intended to solve. A notable example…

The Traveling Salesman Problem (TSP) is one of the most representative NP-hard problems in route planning and a long-standing benchmark in combinatorial optimization. Traditional heuristic tour constructors, such as Farthest or Nearest…

The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0,…

We present an information geometric characterization of Grover's quantum search algorithm. First, we quantify the notion of quantum distinguishability between parametric density operators by means of the Wigner-Yanase quantum information…

Quantum computation, in particular Grover's algorithm, has aroused a great deal of interest since it allows for a quadratic speedup to be obtained in search procedures. Classical search procedures for an $N$ element database require at most…

For quantum computation, we investigate the conjecture that the superposition of macroscopically distinct states is necessary for a large quantum speedup. Although this conjecture was supported for a circuit-based quantum computer…

We use the mapping between two computation frameworks , Adiabatic Grover Search (AGS) and Adiabatic Quantum Computing (AQC), to translate the Grover search algorithm into the AQC regime. We then apply Trotterization on the…

Grover's search algorithms, including various partial Grover searches, experience scaling problems as the number of iterations rises with increased qubits, making implementation more computationally expensive. This paper combines Partial…

The Travelling Salesman Problem (TSP) is a challenging graph task in combinatorial optimization that requires reasoning about both local node neighborhoods and global graph structure. In this paper, we propose to use the novel Graph…

We review the basic theoretical underpinnings of the Grover algorithm, providing a rigorous and well motivated derivation. We then present a generalization of Grover's algorithm that searches an arbitrary subspace of the multi-dimensional…

We study GCS-TSP, a new variant of the Traveling Salesman Problem (TSP) defined over a Graph of Convex Sets (GCS) -- a powerful representation for trajectory planning that decomposes the configuration space into convex regions connected by…

For the traveling salesman problem (TSP), the existing supervised learning based algorithms suffer seriously from the lack of generalization ability. To overcome this drawback, this paper tries to train (in supervised manner) a small-scale…

Grover's search algorithm can be applied to a wide range of problems; even problems not generally regarded as searching problems, can be reformulated to take advantage of quantum parallelism and entanglement, and lead to algorithms which…

I improve the tight bound on quantum searching by Boyer et al. (quant-ph/9605034) to a matching bound, thus showing that for any probability of success Grovers quantum searching algorithm is optimal. E.g. for near certain success we have to…

End-to-end training of neural network solvers for graph combinatorial optimization problems such as the Travelling Salesperson Problem (TSP) have seen a surge of interest recently, but remain intractable and inefficient beyond graphs with…