FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3100559158> ?p ?o ?g. }

• W3100559158 abstract "Is a quantum algorithm capable of implementing an if-clause? Given a black-box subroutine, a $d$-dimensional unitary $Uin U(d)$, a quantum if-clause would correspond to applying it to an input qudit if and only if the value of a control qubit is $1$. It was previously shown by Thompson et al. and Araujo et al. that implementations using single access to the oracle $U$ are impossible. Our main result is a strong generalization of this impossibility result: we prove that there is no unitary oracle algorithm implementing $control_phi(U)=left|0right>!!left !!left<1right|otimes U$, for some $U$-dependent phase $phi(U)$, even if allowed any finite number of calls to $U$ and $U^dagger$, and even if required to only approximate the desired operator $control_phi(U)$. Even further, there is no such emph{postselection} oracle algorithm, i.e. a unitary oracle algorithm followed by a binary success/fail measurement, that reports success and implements $control_phi(U)$ with a nonzero probability for each $Uin U(d)$. Our proof relies on topological arguments which can be viewed as a modification of the Borsuk-Ulam theorem. Combining the topological arguments with the algorithm of Dong et al. in fact leads to an interesting dichotomy: implementing $control_phi(U^m)$ in our model is possible if and only if the integer $m$ is a multiple of the oracle's dimension $d$. Our impossibility no longer holds if the model is relaxed, either by dropping the worst-case requirement that the algorithm works for all $Uin U(d)$, or, remarkably, by allowing measurements more general than a binary postselection measurement. We observe that for both relaxations, inefficient algorithms exist, and it remains open whether efficient ones do." @default.
• W3100559158 created "2020-11-23" @default.
• W3100559158 creator A5003292907 @default.
• W3100559158 creator A5012440267 @default.
• W3100559158 creator A5082893358 @default.
• W3100559158 date "2020-11-19" @default.
• W3100559158 modified "2023-09-27" @default.
• W3100559158 title "Topological obstructions to implementing controlled unknown unitaries" @default.
• W3100559158 cites W1492999010 @default.
• W3100559158 cites W1510011366 @default.
• W3100559158 cites W1564862916 @default.
• W3100559158 cites W1965928854 @default.
• W3100559158 cites W2012496360 @default.
• W3100559158 cites W2028406173 @default.
• W3100559158 cites W2046481556 @default.
• W3100559158 cites W2047697440 @default.
• W3100559158 cites W2076084196 @default.
• W3100559158 cites W2102008187 @default.
• W3100559158 cites W2109741106 @default.
• W3100559158 cites W2122780600 @default.
• W3100559158 cites W2126550950 @default.
• W3100559158 cites W2134719239 @default.
• W3100559158 cites W2158764863 @default.
• W3100559158 cites W2168676717 @default.
• W3100559158 cites W2193371463 @default.
• W3100559158 cites W2768206303 @default.
• W3100559158 cites W2962738101 @default.
• W3100559158 cites W2972281442 @default.
• W3100559158 cites W2988181195 @default.
• W3100559158 cites W2989564043 @default.
• W3100559158 cites W3099939913 @default.
• W3100559158 cites W3103310796 @default.
• W3100559158 cites W3106441513 @default.
• W3100559158 cites W934230699 @default.
• W3100559158 hasPublicationYear "2020" @default.
• W3100559158 type Work @default.
• W3100559158 sameAs 3100559158 @default.
• W3100559158 citedByCount "4" @default.
• W3100559158 countsByYear W31005591582019 @default.
• W3100559158 countsByYear W31005591582021 @default.
• W3100559158 crossrefType "posted-content" @default.
• W3100559158 hasAuthorship W3100559158A5003292907 @default.
• W3100559158 hasAuthorship W3100559158A5012440267 @default.
• W3100559158 hasAuthorship W3100559158A5082893358 @default.
• W3100559158 hasConcept C104317684 @default.
• W3100559158 hasConcept C114614502 @default.
• W3100559158 hasConcept C115903868 @default.
• W3100559158 hasConcept C118615104 @default.
• W3100559158 hasConcept C121332964 @default.
• W3100559158 hasConcept C158448853 @default.
• W3100559158 hasConcept C17020691 @default.
• W3100559158 hasConcept C17744445 @default.
• W3100559158 hasConcept C184720557 @default.
• W3100559158 hasConcept C185592680 @default.
• W3100559158 hasConcept C199539241 @default.
• W3100559158 hasConcept C203087015 @default.
• W3100559158 hasConcept C2776261394 @default.
• W3100559158 hasConcept C33676613 @default.
• W3100559158 hasConcept C33923547 @default.
• W3100559158 hasConcept C41008148 @default.
• W3100559158 hasConcept C55166926 @default.
• W3100559158 hasConcept C55493867 @default.
• W3100559158 hasConcept C62520636 @default.
• W3100559158 hasConcept C67820243 @default.
• W3100559158 hasConcept C84114770 @default.
• W3100559158 hasConcept C86339819 @default.
• W3100559158 hasConceptScore W3100559158C104317684 @default.
• W3100559158 hasConceptScore W3100559158C114614502 @default.
• W3100559158 hasConceptScore W3100559158C115903868 @default.
• W3100559158 hasConceptScore W3100559158C118615104 @default.
• W3100559158 hasConceptScore W3100559158C121332964 @default.
• W3100559158 hasConceptScore W3100559158C158448853 @default.
• W3100559158 hasConceptScore W3100559158C17020691 @default.
• W3100559158 hasConceptScore W3100559158C17744445 @default.
• W3100559158 hasConceptScore W3100559158C184720557 @default.
• W3100559158 hasConceptScore W3100559158C185592680 @default.
• W3100559158 hasConceptScore W3100559158C199539241 @default.
• W3100559158 hasConceptScore W3100559158C203087015 @default.
• W3100559158 hasConceptScore W3100559158C2776261394 @default.
• W3100559158 hasConceptScore W3100559158C33676613 @default.
• W3100559158 hasConceptScore W3100559158C33923547 @default.
• W3100559158 hasConceptScore W3100559158C41008148 @default.
• W3100559158 hasConceptScore W3100559158C55166926 @default.
• W3100559158 hasConceptScore W3100559158C55493867 @default.
• W3100559158 hasConceptScore W3100559158C62520636 @default.
• W3100559158 hasConceptScore W3100559158C67820243 @default.
• W3100559158 hasConceptScore W3100559158C84114770 @default.
• W3100559158 hasConceptScore W3100559158C86339819 @default.
• W3100559158 hasLocation W31005591581 @default.
• W3100559158 hasOpenAccess W3100559158 @default.
• W3100559158 hasPrimaryLocation W31005591581 @default.
• W3100559158 hasRelatedWork W1522529429 @default.
• W3100559158 hasRelatedWork W2040088116 @default.
• W3100559158 hasRelatedWork W2097232651 @default.
• W3100559158 hasRelatedWork W2114187680 @default.
• W3100559158 hasRelatedWork W2124364203 @default.
• W3100559158 hasRelatedWork W2126550950 @default.
• W3100559158 hasRelatedWork W2420112823 @default.
• W3100559158 hasRelatedWork W2725596586 @default.
• W3100559158 hasRelatedWork W2767632300 @default.

• next