quantum algorithms for computational geometry problems andris ambainis faculty of computing university of latvia raina bulvaris 19 riga lv 1586 latvia ambainis lu lv nikita larka faculty of computing university ...
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...Quantum algorithms for computational geometry problems andris ambainis faculty of computing university latvia raina bulvaris riga lv lu nikita larka nikitalarka gmail com abstract westudy in such as point on lines problem this we are given a set and asked to nd that lies at least these many other o known be sum hard is solving them classically requires time n unless there faster algorithm the well which s integers have determine if b c quantumly can solved nlogn using grover search leads question solve answer armatively by constructing solves combines recursive use amplitude amplication with geometrical ideas show same give acm subject classication theory computation query complexity keywords phrases digital object identier lipics tqc funding supported erdf project from experiment introduction follows numbers do exist nearly trivial classical more advanced only logarithmic improvement quadratic it conjectured no example determining whether points contains lie line also seem require gaj...