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A one-query lower bound for unitary synthesis and breaking quantum cryptography. (arXiv:2310.08870v1 [quant-ph])
cs.CR updates on arXiv.org arxiv.org
The Unitary Synthesis Problem (Aaronson-Kuperberg 2007) asks whether any
$n$-qubit unitary $U$ can be implemented by an efficient quantum algorithm $A$
augmented with an oracle that computes an arbitrary Boolean function $f$. In
other words, can the task of implementing any unitary be efficiently reduced to
the task of implementing any Boolean function?
In this work, we prove a one-query lower bound for unitary synthesis. We show
that there exist unitaries $U$ such that no quantum polynomial-time oracle
algorithm $A^f$ …
algorithm breaking cryptography function oracle problem quantum quantum cryptography qubit query task