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arXiv:quant-ph/0206081 · New Journal of Physics

Comment on `Quantum optimization for combinatorial searches'

Christof Zalka, Todd A. Brun

Published Sep 3, 2002• 1 citation
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Abstract

A recent paper by Trugenberger ( C A Trugenberger 2002 New J. Phys. 4 26 ) is commented on.
DOI
10.1088/1367-2630/4/1/401

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This is a comment on two wrong Phys. Rev. Letters papers by C.A. Trugenberger. Trugenberger claimed that quantum registers could be used as exponentially large "associative" memories. We show that his scheme is no better than one where the quantum register is replaced with a classical one of equal size. We also point out that the Holevo bound and more recent bounds on "quantum random access codes" pretty much rule out powerful memories (for classical information) based on quantum states.
A single machine total weighted tardiness minimization (TWTM) problem in operational planning is considered. The problem is formulated as an NP-hard constrained combinatorial problem, which has no known deterministic polynomial complexity solution using classical computing. Based on efficient Grover's quantum search and Trugenberger's quantum optimization algorithms, a novel efficient quantum optimization algorithm is proposed to solve the NP-hard single machine TWTM problem, which makes the desired solution satisfying the searching constraints and showing the minimal TWT value be measured with the highest probability.