Related papers: An R||C_{max} Quantum Scheduling Algorithm
Present-day quantum systems face critical bottlenecks, including limited qubit counts, brief coherence intervals, and high susceptibility to errors-all of which obstruct the execution of large and complex circuits. The advancement of…
This paper proposes a quantum algorithm for the capacitated vehicle routing problem with time windows (CVRPTW) based on Grover Search framework. This problem is often faced by Postal services in the context of package delivery or other…
In this paper we consider the problem of scheduling on parallel machines with a presence of incompatibilities between jobs. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of…
This work is a benchmark study for quantum-classical computing method with a real-world optimization problem from industry. The problem involves scheduling and balancing jobs on different machines, with a non-linear objective function. We…
A framework is presented for the design and analysis of quantum mechanical algorithms, the sqrt(N) step quantum search algorithm is an immediate consequence of this framework. It leads to several other search-type applications - several…
Studies on Quantum Computing have been developed since the 1980s, motivating researches on quantum algorithms better than any classical algorithm possible. An example of such algorithms is Grover's algorithm, capable of finding $k$ (marked)…
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…
Grover search is a well-known quantum algorithm that outperforms any classical search algorithm. It is known that quantum correlations such as entanglement are necessary for the power of quantum computation. But entanglement is not the only…
Grover's algorithm for quantum searching is generalized to deal with arbitrary initial complex amplitude distributions. First order linear difference equations are found for the time evolution of the amplitudes of the marked and unmarked…
This paper describes a quantum algorithm for finding the maximum among N items. The classical method for the same problem takes O(N) steps because we need to compare two numbers in one step. This algorithm takes O(sqrt(N)) steps by…
Grover's algorithm solves the unstructured search problem. Grover's algorithm can find the target state with certainty only if searching one out of four. Designing the deterministic search algorithm can avoid any repetition of the…
Grover's algorithm provides a quadratic speedup over classical algorithms to search for marked elements in an unstructured database. The original algorithm is probabilistic, returning a marked element with bounded error. There are several…
We want to find a marked element out of a black box containing N elements. When the number of marked elements is known this can be done elegantly with Grover's algorithm, a variant of which even gives a correct result with certainty. On the…
Executing quantum circuits on currently available quantum computers requires compiling them to a representation that conforms to all restrictions imposed by the targeted architecture. Due to the limited connectivity of the devices' physical…
This paper presents a novel idea for the general case of the Common Due-Date (CDD) scheduling problem. The problem is about scheduling a certain number of jobs on a single or parallel machines where all the jobs possess different processing…
One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem…
Grover's search algorithm is the optimal quantum algorithm that can search an unstructured database quadratically faster than any known classical algorithm. The role of entanglement and correlations in the search algorithm have been studied…
This PhD thesis summarizes research works on the design of exact algorithms that provide a worst-case (time or space) guarantee for NP-hard scheduling problems. Both theoretical and practical aspects are considered with three main results…
We introduce hybrid classical-quantum algorithms for problems involving a large classical data set X and a space of models Y such that a quantum computer has superposition access to Y but not X. These algorithms use data reduction…
In general, a quantum circuit is constructed with elementary gates, such as one-qubit gates and CNOT gates. It is possible, however, to speed up the execution time of a given circuit by merging those elementary gates together into larger…