Titel
Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality
Autor*in
Daniel Ebler
Huawei Hong Kong Research Center
Abstract
This work analyses the performance of quantum circuits and general processes to transform k uses of an arbitrary unitary operation U into another unitary operation f(U). When the desired function f a homomorphism, i.e., f(UV)=f(U)f(V), it is known that optimal average fidelity is attainable by parallel circuits and indefinite causality does not provide any advantage. Here we show that the situation changes dramatically when considering anti-homomorphisms, i.e., f(UV)=f(V)f(U). In particular, we prove that when f is an anti-homomorphism, sequential circuits could exponentially outperform parallel ones and processes with indefinite causal order could outperform sequential ones. We presented explicit constructions on how to obtain such advantages for the unitary inversion task f(U)=U−1 and the unitary transposition task f(U)=UT. We also stablish a one-to-one connection between the problem of unitary estimation and parallel unitary transposition, allowing one to easily translate results from one field to the other. Finally, we apply our results to several concrete problem instances and present a method based on computer-assisted proofs to show optimality.
Stichwort
Physics and Astronomy (miscellaneous)Atomic and Molecular Physics, and Optics
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
Erschienen in
Titel
Quantum
Band
6
ISSN
2521-327X
Erscheinungsdatum
2022
Publication
Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
Projekt
Kod / Identifikator
F7103
Projekt
Kod / Identifikator
801110
Erscheinungsdatum
2022
Zugänglichkeit
Rechteangabe
Copyright remains with the original copyright holders such as the authors or their institutions

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