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• W3131720005 abstract "Research on indefinite causal structures is a rapidly evolving field that has a potential not only to make a radical revision of the classical understanding of space-time but also to achieve enhanced functionalities of quantum information processing. For example, it is known that indefinite causal structures provide exponential advantage in communication complexity when compared to causal protocols. In quantum computation, such structures can decide whether two unitary gates commute or anticommute with a single call to each gate, which is impossible with conventional (causal) quantum algorithms. A generalization of this effect to $n$ unitary gates, originally introduced in M. Araujo et al., Phys. Rev. Lett. 113, 250402 (2014) and often called Fourier promise problem (FPP), can be solved with the quantum-$n$-switch and a single call to each gate, while the best known causal algorithm so far calls $O(n^2)$ gates. In this work, we show that this advantage is smaller than expected. In fact, we present a causal algorithm that solves the only known specific FPP with $O(n log(n))$ queries and a causal algorithm that solves every FPP with $O(nsqrt{n})$ queries. Besides the interest in such algorithms on their own, our results limit the expected advantage of indefinite causal structures for these problems." @default.
• W3131720005 created "2021-03-01" @default.
• W3131720005 creator A5013288134 @default.
• W3131720005 creator A5043278446 @default.
• W3131720005 date "2021-02-22" @default.
• W3131720005 modified "2023-09-27" @default.
• W3131720005 title "Reassessing the computational advantage of quantum-controlled ordering of gates" @default.
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• W3131720005 hasPublicationYear "2021" @default.
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