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Quantum computing is a promising technology to address combinatorial optimization problems, for example via the quantum approximate optimization algorithm (QAOA). Its potential, however, hinges on scaling toy problems to sizes relevant for…
As customer demands become increasingly diverse, the colors and styles of vehicles offered by automotive companies have also grown substantially. It poses great challenges to design and management of automotive manufacturing system, among…
The genetic algorithm includes some parameters that should be adjusted, so as to get reliable results. Choosing a representation of the problem addressed, an initial population, a method of selection, a crossover operator, mutation…
Motivated from the theory of quantum error correcting codes, we investigate a combinatorial problem that involves a symmetric $n$-vertices colourable graph and a group of operations (colouring rules) on the graph: find the minimum sequence…
In the era of noisy intermediate-scale quantum computers, variational quantum algorithms are promising approaches for solving optimization tasks by training parameterized quantum circuits with the aid of classical routines informed by…
We present a quantum algorithm for combinatorial optimization using the cost structure of the search states. Its behavior is illustrated for overconstrained satisfiability and asymmetric traveling salesman problems. Simulations with…
The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly…
Quantum annealing is a method developed to solve combinatorial optimization problems by utilizing quantum bits. Solving such problems corresponds to minimizing a cost function defined over binary variables. However, in many practical cases,…
Vehicle routing problem (VRP) is an NP-hard optimization problem that has been an interest of research for decades in science and industry. The objective is to plan routes of vehicles to deliver a fixed number of customers with optimal…
We propose a new Quadratic Unconstrained Binary Optimization (QUBO) formulation of the Travelling Salesman Problem (TSP), with which we overcame the best formulation of the Vehicle Routing Problem (VRP) in terms of the minimum number of…
We present a numerical method for solving the separability problem of Gaussian quantum states in continuous-variable quantum systems. We show that the separability problem can be cast as an equivalent problem of determining the feasibility…
We introduce the entangled coherent state representation, which provides a powerful technique for efficiently and elegantly describing and analyzing quantum optics sources and detectors while respecting the photon number superselection rule…
Optimization drives advances in quantum science and machine learning, yet most generative models aim to mimic data rather than to discover optimal answers to challenging problems. Here we present a variational generative optimization…
We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a 100-fold improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining…
A seminal task in quantum information theory is to realize a device able to produce copies of a generic input state with the highest possible output fidelity, thus realizing an \textit{optimal} quantum cloning machine. Recently, the concept…
The Traveling salesman problem (TSP) is proved to be NP-complete in most cases. The genetic algorithm (GA) is one of the most useful algorithms for solving this problem. In this paper a conventional GA is compared with an improved hybrid GA…
Reliable preparation of entanglement between distant systems is an outstanding problem in quantum information science and quantum communication. In practice, this has to be accomplished via noisy channels (such as optical fibers) that…
We propose a variational quantum algorithm to study the real time dynamics of quantum systems as a ground-state problem. The method is based on the original proposal of Feynman and Kitaev to encode time into a register of auxiliary qubits.…
Quantum annealing technologies aim to solve computational optimization and sampling problems. QPU (Quantum Processing Unit) machines such as the D-Wave system use the QUBO (Quadratic Unconstrained Binary Optimization) formula to define…
Yatsenko gives a polynomial-time algorithm for solving the traveling salesman problem. We examine the correctness of the algorithm and its construction. We also comment on Yatsenko's evaluation of the algorithm.