Quantum Formulas: a Lower Bound and Simulation

Vwani P. Roychowdhury; Farrokh Vatan

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Quantum Formulas: a Lower Bound and Simulation

Vwani P. Roychowdhury·Farrokh Vatan

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Abstract

We show that Nechiporuk's method for proving lower bounds for Boolean formulas can be extended to the quantum case. This leads to an $Ω(n^2 / \log^2 n)$ 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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Vwani P. Roychowdhury, Farrokh Vatan. 2001-04-10. Quantum Formulas: a Lower Bound and Simulation. https://arxiv.org/abs/quant-ph/0104053

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