Quantum Formulas: a Lower Bound and Simulation

Details Quantum Formulas: a Lower Bound and Simulation Quantum Formulas: a Lower Bound and Simulation

2001-04-10

arxiv.org/abs/quant-ph/0104053v1

Physics

Quantum Physics

22 pages, LaTeX, 6 figures. Final and extended version of quant-ph/9903042. To appear in SIAM Journal on Computing

Scientific paper

We show that Nechiporuk's method for proving lower bounds for Boolean formulas can be extended to the quantum case. This leads to an $\Omega(n^2 / \log^2 n)$ lower bound for quantum formulas computing an explicit function. The only known previous explicit lower bound for quantum formulas states that the majority function does not have a linear-size quantum formula. We also show that quantum formulas can be simulated by Boolean circuits of almost the same size.

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