A nested Grover algorithm for tree search claims cost O(m*2^(m/4)) using partial candidate solutions, but the speedup relies on an unexamined assumption that the candidate set contains the solution.
Mirror modular cloning and fast quantum associative retrieval
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We show that a quantum state can be perfectly cloned up to global mirroring with a unitary transformation that depends on one single parameter. We then show that this is equivalent to "perfect" cloning for quantum associative memories which, as a consequence efficiently hold exponentially more information than their classical counterparts. Finally, we present a quantum associative retrieval algorithm which can correct corrupted inputs and is exponentially faster than the Grover algorithm.
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Nested Grover's Algorithm for Tree Search
A nested Grover algorithm for tree search claims cost O(m*2^(m/4)) using partial candidate solutions, but the speedup relies on an unexamined assumption that the candidate set contains the solution.