A Near-Quadratic Lower Bound for the Size of Quantum Circuits of Constant Treewidth

@article{Oliveira2018ANL,
  title={A Near-Quadratic Lower Bound for the Size of Quantum Circuits of Constant Treewidth},
  author={Mateus de Oliveira Oliveira},
  journal={ArXiv},
  year={2018},
  volume={abs/1609.09643}
}
  • Mateus de Oliveira Oliveira
  • Published 2018
  • Mathematics, Computer Science, Physics
  • ArXiv
  • We show that any quantum circuit of treewidth $t$, built from $r$-qubit gates, requires at least $\Omega(\frac{n^{2}}{2^{O(r\cdot t)}\cdot \log^4 n})$ gates to compute the element distinctness function. Our result generalizes a near-quadratic lower bound for quantum formula size obtained by Roychowdhury and Vatan [SIAM J. on Computing, 2001]. The proof of our lower bound follows by an extension of Ne\v{c}iporuk's method to the context of quantum circuits of constant treewidth. This extension is… CONTINUE READING

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