Some mathematical results in quantum computation

Masashi Kimura

Yong Wang

By the way of combinatorial computation, sequence of number and series knowledge, and the constructing proof methods, some mathematical results in quantum communication are solved, some equalities in quantum computation are proved. These results will be used in other sciences deeply.

昌史 木村

Гузик Вячеслав Филиппович, Гушанский Сергей Михайлович, Кубраков Евгений Сергеевич

A hardware approach for the quantum computing modeling was considered. A common mathematical model of the quantum computer was described; a methodic of mathematical modeling of the quantum computing was shown. During the mathematical methodic description the most resource-intensive parts of the model are allocated. Considered questions connected with data parallelizing with a hardware accelerator, which is used for quantum computer modeling. A common scheme of the accelerator’s work algorithm was shown. Suggested more compact data format for accelerator implementation, that will reduce time costs spent by elementary arithmetic operations. Proposed the use of the optimization algorithm for data minimization during the calculations in the phase of transforming model of quantum register with quantum gates in quantum computer simulators. Shown results of optimization algorithm execution and compared results with classic mathematical approach.

Hevlie Winda Nazry S, Firahmi Rizky, Ferdy Riza +2 more

his study explores the application of quantum computing in solving complex mathematical problems through the utilization of Grover's Algorithm. Grover's Algorithm, renowned for its efficiency in unstructured search, has been adapted for various mathematical applications requiring rapid solution searches within large solution spaces. In this study, we implement Grover's Algorithm on a quantum computing platform to address a range of complex mathematical problems, including nonlinear equations and combinatorial optimization. Experimental results demonstrate that Grover's Algorithm significantly reduces computational time compared to classical methods, highlighting the immense potential of quantum computing in advanced mathematics. These findings pave the way for the development of more sophisticated quantum algorithms and their applications across science, engineering, and technology domains.

Myo Myo Aung