Quantum Algorithms and Methods

Melinda Andrews, Joseph Stephen Dulny, Andrew N. Glaudell +6 more

Anastasia Monika Oktorianti, Achmad Benny Mutiara, Rina Refianti

Developing new computing methods and signal processing algorithms by borrowing from the principle of quantum mechanics is a very interesting and new research topic. By utilizing quantum algorithm in the process of computing, it is expected that this algorithm can solved the problems of image processing faster than using a classical algorithm. In this paper, a quantum digital image halftoning algorithm will be presented.The image would be processed using bitmap image (.bmp) and the applications would be created using Matlab R2009a. Test phase of the applications is using an image, lena.bmp. This application will show three new images as results of three halftoning methods: binary threshold method, ordered dithering method, and method with quantum algorithm. The method with quantum algorithm shows better than two others methods. Kata Kunci: image Processing, quantum Algoritm, halftoning method.

Shilu Yan, Tong Dou, Runqiu Shu +1 more

To assess whether a gate-based quantum algorithm can be executed successfully on a noisy intermediate-scale quantum (NISQ) device, both complexity and actual value of quantum resources should be considered carefully. Based on quantum phase estimation, we implemente arbitrary controlled rotation of quantum algorithms with a proposed modular method. The proposed method is not limited to be used as a submodule of the HHL algorithm and can be applied to more general quantum machine learning algorithms. Compared with the polynomial-fitting function method, our method only requires the least ancillas and the least quantum gates to maintain the high fidelity of quantum algorithms. The method theoretically will not influence the acceleration of original algorithms. Numerical simulations illustrate the effectiveness of the proposed method. Furthermore, if the corresponding diagonal unitary matrix can be effectively decomposed, the method is also polynomial in time cost.

Peter P. Rohde

Yoshifumi Moriyama, Ichiro Iimura, Tomotsugu Ohno +1 more

The quantum-inspired evolutionary algorithm (QEA) is one of the evolutionary algorithms incorporating principles of quantum computation. In QEA, each gene is represented by a quantum bit (qubit), and the quantum superposition state is imitated. QEA can effectively shift from a global search to a local search. Han, et al. showed that QEA has superior search performance to a genetic algorithm (GA) in the 0-1 knapsack problem (0-1KP). Nakayama, et al. proposed a simpler algorithm that is referred to as QEA based on pair swap (QEAPS). QEAPS requires fewer parameters to be adjusted than QEA. Nakayama, et al. showed that QEAPS can find similar or even better quality solutions than QEA in 0-1KP. However, in QEA and QEAPS, each gene is represented by a qubit and both algorithms can only use a binary value as an observation result for a qubit. Therefore, Iimura, et al. proposed a novel integer-type gene-coding method that can obtain an integer value as an observation result by assigning multiple qubits in a gene locus. Moreover, they implemented the gene-coding method in both QEA and QEAPS and showed that it can search for similar or even better quality solutions in a shorter time than a conventional binary-type gene-coding method in the integer knapsack problem (IKP). However, the integer-type gene-coding method cannot deal with permutations simply.In order to expand the gene-coding method based on the qubit representation, Moriyama, et al. proposed two interpretation methods based on the integer-type gene-coding method that can deal with permutations. Also, they clarified that the two proposed interpretation methods can search for the optimal solution, even with the genecoding method based on the qubit representation. This paper proposes a new gene-coding method that can deal with permutations. The proposed method promises effect of improving a solution in permutation space, like the k-Opt method, and can search for the optimal solution of the traveling salesman problem (TSP) effectively. From experimental results for TSP, the discovery rate of the optimal solution using the proposed method is higher than using conventional method in many cases of QEA and QEAPS.

Venkateswaran Kasirajan