QuOne Lab, Phanous Research and Innovation Centre, Tehran, Iran
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Absztrakt
Evolutions of local Hamiltonians in short times are expected to remain local and thus limited. In this paper, we validate this intuition by proving some limitations on short-time evolutions of local time-dependent Hamiltonians. We show that the distribution of the measurement output of short-time (at most logarithmic) evolutions of local Hamiltonians are $concentrated$ and satisfy an $textit{isoperimetric inequality}$. To showcase explicit applications of our results, we study the $M$$small{AX}$$C$$small{UT}$ problem and conclude that quantum annealing needs at least a run-time that scales logarithmically in the problem size to beat classical algorithms on $M$$small{AX}$$C$$small{UT}$. To establish our results, we also prove a Lieb-Robinson bound that works for time-dependent Hamiltonians which might be of independent interest.
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► Referenciák
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Idézi
[1] Giacomo De Palma, Milad Marvian, Cambyse Rouzé és Daniel Stilck França, „Limitations of variational quantum algorithms: a quantum optimal transport approach”, arXiv: 2204.03455.
A fenti idézetek innen származnak SAO/NASA HIRDETÉSEK (utolsó sikeres frissítés: 2022-07-19 03:10:09). Előfordulhat, hogy a lista hiányos, mivel nem minden kiadó ad megfelelő és teljes hivatkozási adatokat.
On Crossref által idézett szolgáltatás művekre hivatkozó adat nem található (utolsó próbálkozás 2022-07-19 03:10:07).
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