Kvantu vaicājumu sarežģītība dinamiskās programmēšanas problēmām
Date
2022
Authors
Zvirbulis, Ansis
Journal Title
Journal ISSN
Volume Title
Publisher
Latvijas Universitāte
Abstract
Dinamiskā programmēšana (DP) ir plaši pētīta no klasiskās skaitļošanas puses, un jauni rezultāti tiek atrasti katru gadu. Taču no kvantu skaitļošanas puses tā ir pētīta daudz mazāk. Tāpēc tika izvēlētas un pētītas vairākas plaši pazīstamas 1-dimensiju DP problēmas, izmantojot kvantu vaicājumu modeli. Darbā tika aplūkotas mazākā svara apakš-sekvences (LWS) problēmas, kā, piemēram, kastu komplektēšanas (NestedBoxes) problēma, kā arī dažas saistītās problēmas. Darba mērķis bija atrast aplūkotajām LWS problēmām augšējo novērtējumu, kas labāks par triviālo O ̃(n^1.5 ) vai labu apakšējo novērtējumu. Izdevās atrast vairākus mazākus rezultātus NestedBoxes problēmai – kvantu apakšējo novērtējumu Ω(n√d), klasisku O ̃(n) algoritmu pie konstanta dimensiju skaita, kvantu O ̃(n^1.34 ) algoritmu 4-ķēdes meklēšanai. Kā arī dažus rezultātus saistīto problēmu speciālgadījumiem.
Dynamic programming (DP) is widely researched from the perspective of classical computing, yet new results are found every year. However, it is studied far less from the quantum perspective. Therefore, it was decided to research some well-known 1-dimensional DP problems using quantum query model. In this work we consider several least-weight-sequence (LWS) problems, e.g. nested boxes problem, as well as some related problems. The goal of this work was to find better upper bounds than trivial O ̃(n^1.5 ) or good enough lower bounds. We managed to find several smaller results for nested boxes problem – Ω(n√d) quantum lower bounds, classical O ̃(n) algorithm when dimensions are a constant and O ̃(n^1.34 ) quantum algorithm for 4-chain finding. Also, we found some results for special cases of related problems.
Dynamic programming (DP) is widely researched from the perspective of classical computing, yet new results are found every year. However, it is studied far less from the quantum perspective. Therefore, it was decided to research some well-known 1-dimensional DP problems using quantum query model. In this work we consider several least-weight-sequence (LWS) problems, e.g. nested boxes problem, as well as some related problems. The goal of this work was to find better upper bounds than trivial O ̃(n^1.5 ) or good enough lower bounds. We managed to find several smaller results for nested boxes problem – Ω(n√d) quantum lower bounds, classical O ̃(n) algorithm when dimensions are a constant and O ̃(n^1.34 ) quantum algorithm for 4-chain finding. Also, we found some results for special cases of related problems.
Description
Keywords
Datorzinātne , kvantu vaicājums , kvantu vaicājumu sarežģītība , 1-dimensiju dinamiskā programmēšana , LWS , kvantu minimuma meklēšana