Related papers: Quantum Computing, Ising Formulation, and the Trav…
Quantum computing offers new heuristics for combinatorial problems. With small- and intermediate-scale quantum devices becoming available, it is possible to implement and test these heuristics on small-size problems. A candidate for such…
Ising machines are hardware solvers which aim to find the absolute or approximate ground states of the Ising model. The Ising model is of fundamental computational interest because it is possible to formulate any problem in the complexity…
For some weighted $NP$-complete problems, checking whether a proposed solution is optimal is a non-trivial task. Such is the case for the celebrated traveling salesman problem, or the spin-glass problem in 3 dimensions. In this letter, we…
In this paper we propose some novel path planning strategies for a double integrator with bounded velocity and bounded control inputs. First, we study the following version of the Traveling Salesperson Problem (TSP): given a set of points…
Grover's search algorithm is one of the basic building block in the world of quantum algorithms. Successfully applying it to combinatorial optimization problems is a subtle challenge. As a quadratic speedup is not enough to naively search…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. Quantum computational algorithms have the potential to be an exciting new way of studying quantum cosmology. In quantum…
In this paper, we explore the potential for quantum annealing to solve realistic routing problems. We focus on two NP-Hard problems, including the Traveling Salesman Problem with Time Windows and the Capacitated Vehicle Routing Problem with…
We introduce a methodology for generating benchmark problem sets for Ising machines---devices designed to solve discrete optimization problems cast as Ising models. In our approach, linear systems of equations are cast as Ising cost…
The Traveling Salesman Problem (TSP) is one of the classic and hard problems in combinatorial optimization. We develop a new heuristic that uses a connection between Minimum Cost Flow Problems and the TSP to improve on a given suboptimal…
Recent advances in quantum computing and their increased availability has led to a growing interest in possible applications. Among those is the solution of partial differential equations (PDEs) for, e.g., material or flow simulation.…
Quantum computing poses a threat to contemporary cryptosystems, with advances to a state in which it will cause problems predicted for the next few decades. Many of the proposed cryptosystems designed to be quantum-secure are based on the…
This paper studies the Hamiltonian Cycle Problem (HCP) and the Traveling Salesman Problem (TSP) on D-Wave's quantum systems. Initially, motivated by the fact that most libraries present their benchmark instances in terms of adjacency…
Quantum annealing is a promising heuristic method to solve combinatorial optimization problems, and efforts to quantify performance on real-world problems provide insights into how this approach may be best used in practice. We investigate…
The Traveling Salesman Problem (TSP) is the most popular and most studied combinatorial problem, starting with von Neumann in 1951. It has driven the discovery of several optimization techniques such as cutting planes, branch-and-bound,…
Digital simulation of quantum dynamics by evaluating the time evolution of a Hamiltonian is the initially proposed application of quantum computing. The large number of quantum gates required for emulating the complete second quantization…
We propose an innovative Parallel Quantum Local Search (PQLS) methodology that leverages the capabilities of small-scale quantum computers to efficiently address complex combinatorial optimization problems. Traditional Quantum Local Search…
This letter concerns optimal power transmission line inspection formulated as a proposed generalization of the traveling salesman problem for a multi-route one-depot scenario. The problem is formulated for an inspection vehicle with a…
We explore the application of the Variational Quantum Eigensolver (VQE) to investigate the ground state properties, particularly the entanglement entropy, of the Transverse Field Ising Model (TFIM) in one, two, and three dimensions,…
A pivotal task for quantum computing is to speed up solving problems that are both classically intractable and practically valuable. Among these, combinatorial optimization problems have attracted tremendous attention due to their broad…
There is great interest in using near-term quantum computers to simulate and study foundational problems in quantum mechanics and quantum information science, such as the scrambling measured by an out-of-time-ordered correlator (OTOC). Here…