Matches in SemOpenAlex for { <https://semopenalex.org/work/W4366328431> ?p ?o ?g. }
Showing items 1 to 77 of
77
with 100 items per page.
- W4366328431 abstract "TThe welded tree problem is a black-box problem to find the exit of the welded tree with $Theta(2^n)$ vertices starting from the given entrance, for which there are quantum algorithms with exponential speedups over the best classical algorithm. The original quantum algorithm is based on continuous time quantum walks (CTQW), and it has never been clear whether there are efficient algorithms based on discrete time quantum walks (DTQW) until recently the multidimensional quantum walk framework was proposed (Jeffery and Zur, STOC'2023). In this paper, we propose a rather concise algorithm based purely on the simplest coined quantum walks, which is simply to iterate the naturally defined coined quantum walk operator for a predetermined time $T in O(n log n)$ and then measure to obtain the exit name with $Omega(frac{1}{n})$ probability. The algorithm can be further promoted to be error-free and with $O(n^{1.5} log n)$ query complexity. The numerical simulation strongly implies that the actual complexity of our algorithm is $O(n^{4/3})$. The significance of our results may be seen as follows. (i) Our algorithm is rather concise compared with the one in (Jeffery and Zur, STOC'2023), which not only changes the stereotype that the exiting DTQW frameworks before the multidimensional one can achieve at most a quadratic speedup over the best classical algorithm, but also re-displays the power of the simplest framework of quantum walks. (ii) Our algorithm can be made error-free theoretically, whereas all the existing methods cannot. Thus, it is one of the few examples of an exponential separation between the error-free (exact) quantum and the randomized query complexities, which perhaps also change people's idea that quantum mechanics is inherently probabilistic and thus deterministic quantum algorithms with exponential speedups for the problem are out of the question." @default.
- W4366328431 created "2023-04-20" @default.
- W4366328431 creator A5050439589 @default.
- W4366328431 creator A5057070599 @default.
- W4366328431 creator A5068977066 @default.
- W4366328431 date "2023-04-17" @default.
- W4366328431 modified "2023-10-17" @default.
- W4366328431 title "Recover the original simplicity: concise and deterministic quantum algorithm for the welded tree problem" @default.
- W4366328431 doi "https://doi.org/10.48550/arxiv.2304.08395" @default.
- W4366328431 hasPublicationYear "2023" @default.
- W4366328431 type Work @default.
- W4366328431 citedByCount "0" @default.
- W4366328431 crossrefType "posted-content" @default.
- W4366328431 hasAuthorship W4366328431A5050439589 @default.
- W4366328431 hasAuthorship W4366328431A5057070599 @default.
- W4366328431 hasAuthorship W4366328431A5068977066 @default.
- W4366328431 hasBestOaLocation W43663284311 @default.
- W4366328431 hasConcept C104317684 @default.
- W4366328431 hasConcept C111919701 @default.
- W4366328431 hasConcept C113174947 @default.
- W4366328431 hasConcept C11413529 @default.
- W4366328431 hasConcept C114614502 @default.
- W4366328431 hasConcept C118615104 @default.
- W4366328431 hasConcept C121332964 @default.
- W4366328431 hasConcept C137019171 @default.
- W4366328431 hasConcept C140058369 @default.
- W4366328431 hasConcept C158448853 @default.
- W4366328431 hasConcept C17020691 @default.
- W4366328431 hasConcept C185592680 @default.
- W4366328431 hasConcept C2780009758 @default.
- W4366328431 hasConcept C33923547 @default.
- W4366328431 hasConcept C41008148 @default.
- W4366328431 hasConcept C55493867 @default.
- W4366328431 hasConcept C58053490 @default.
- W4366328431 hasConcept C62520636 @default.
- W4366328431 hasConcept C68339613 @default.
- W4366328431 hasConcept C77088390 @default.
- W4366328431 hasConcept C84114770 @default.
- W4366328431 hasConcept C86339819 @default.
- W4366328431 hasConceptScore W4366328431C104317684 @default.
- W4366328431 hasConceptScore W4366328431C111919701 @default.
- W4366328431 hasConceptScore W4366328431C113174947 @default.
- W4366328431 hasConceptScore W4366328431C11413529 @default.
- W4366328431 hasConceptScore W4366328431C114614502 @default.
- W4366328431 hasConceptScore W4366328431C118615104 @default.
- W4366328431 hasConceptScore W4366328431C121332964 @default.
- W4366328431 hasConceptScore W4366328431C137019171 @default.
- W4366328431 hasConceptScore W4366328431C140058369 @default.
- W4366328431 hasConceptScore W4366328431C158448853 @default.
- W4366328431 hasConceptScore W4366328431C17020691 @default.
- W4366328431 hasConceptScore W4366328431C185592680 @default.
- W4366328431 hasConceptScore W4366328431C2780009758 @default.
- W4366328431 hasConceptScore W4366328431C33923547 @default.
- W4366328431 hasConceptScore W4366328431C41008148 @default.
- W4366328431 hasConceptScore W4366328431C55493867 @default.
- W4366328431 hasConceptScore W4366328431C58053490 @default.
- W4366328431 hasConceptScore W4366328431C62520636 @default.
- W4366328431 hasConceptScore W4366328431C68339613 @default.
- W4366328431 hasConceptScore W4366328431C77088390 @default.
- W4366328431 hasConceptScore W4366328431C84114770 @default.
- W4366328431 hasConceptScore W4366328431C86339819 @default.
- W4366328431 hasLocation W43663284311 @default.
- W4366328431 hasOpenAccess W4366328431 @default.
- W4366328431 hasPrimaryLocation W43663284311 @default.
- W4366328431 hasRelatedWork W1493399357 @default.
- W4366328431 hasRelatedWork W2009948449 @default.
- W4366328431 hasRelatedWork W2313088398 @default.
- W4366328431 hasRelatedWork W2800432156 @default.
- W4366328431 hasRelatedWork W2883913628 @default.
- W4366328431 hasRelatedWork W2949694831 @default.
- W4366328431 hasRelatedWork W3189824049 @default.
- W4366328431 hasRelatedWork W4210665696 @default.
- W4366328431 hasRelatedWork W4226352648 @default.
- W4366328431 hasRelatedWork W4297726034 @default.
- W4366328431 isParatext "false" @default.
- W4366328431 isRetracted "false" @default.
- W4366328431 workType "article" @default.