Perjalanan Kuantum Tidak Beraturan Atas Aljabar Max-Plus

Firmansyah, Mohamad Ilham Dwi (2022) Perjalanan Kuantum Tidak Beraturan Atas Aljabar Max-Plus. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Perjalanan kuantum (quantum walk) merupakan perumuman dari perjalanan acak sederhana (simple random walk). Perjalanan kuantum dibagi menjadi dua, yaitu perjalanan kuantum waktu disktrit dan perjalanan kuantum waktu kontinu. Dalam perjalanan kuantum mengenal adanya operator koin kuantum berupa matriks uniter, operator koin kuantum ini berguna untuk menentukan arah pergerakan perjalanan kuantum. Pada perjalanan kuantum waktu diskrit secara umum, untuk setiap waktu perjalanan, operator koin yang digunakan bersifat tetap. Jika operator koin kuantum pada setiap waktu perjalanan bersifat acak, maka disebut perjalanan kuantum tidak beraturan (disordered quantum walk). Pada tesis ini, diusulkan tentang perjalanan kuantum waktu diskrit tak beraturan yang baru, yaitu perjalanan kuantum waktu diskrit tak beraturan atas aljabar max-plus. Pada tesis ini dikonstruksi model evolusi waktu total dari perjalanan kuantum waktu diskrit tidak beraturan atas aljabar max plus. Selanjutnya, dikonstruksi bentuk matriks decision dari model evolusi waktu total perjalanan kuantum waktu diskrit tidak beraturan atas aljabar max-plus. Tidak hanya itu, ditentukan kuantitas kekal (conserved quantity) untuk setiap waktu diskrit dari perjalanan kuantum tidak beraturan atas aljabar max-plus, yang analog dengan perjalanan kuantum secara konvensional.
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Quantum walk is a generalization of a simple random walk. The quantum walk can be divided into two, that is discrete-time quantum walk and continuous-time quantum walk. In the quantum walk, we know that there is a quantum coin operator in a unitary matrix. This quantum coin operator is useful for determining the direction of motion of the quantum walk. For discrete-time quantum walks in general, for each time walk, the coin operator used is fixed. If the coin operator quantum at each time of the walk is random, it is called a disordered quantum walk. In the thesis, it is proposed to use the disordered discrete-time quantum walk, which is new, i.e., the disordered-time discrete quantum walk over algebra max-plus. In this thesis, a total time evolution model of a disordered discrete-time quantum walk over the max-plus algebra is constructed. Next, a decision matrix is constructed from the time evolution model’s total disordered discrete-time quantum walk over max-plus algebra. In the end, the conserved quantity is determined for each discrete time of disordered discrete-time quantum walk over max-plus algebra, which is analogous to conventional disordered discrete-time quantum walk.

Item Type:	Thesis (Other)
Additional Information:	RTMa 512 Fir p-1
Uncontrolled Keywords:	perjalanan kuantum, perjalanan kuantum tak beraturan, aljabar max-plus, operator koin uniter
Subjects:	Q Science > QA Mathematics > QA159 Algebra
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44101-(S2) Master Thesis
Depositing User:	Mr. Tondo Indra Nyata
Date Deposited:	18 Jan 2023 03:32
Last Modified:	18 Jan 2023 03:32
URI:	http://repository.its.ac.id/id/eprint/95455

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