Span Programs and Quantum Query Complexity: The General Adversary Bound Is Nearly Tight for Every Boolean Function

@article{Reichardt2009SpanPA,
  title={Span Programs and Quantum Query Complexity: The General Adversary Bound Is Nearly Tight for Every Boolean Function},
  author={Ben Reichardt},
  journal={2009 50th Annual IEEE Symposium on Foundations of Computer Science},
  year={2009},
  pages={544-551}
}
The general adversary bound is a semi-definite program (SDP) that lower-bounds the quantum query complexity of a function. We turn this lower bound into an upper bound, by giving a quantum walk algorithm based on the dual SDP that has query complexity at most the general adversary bound, up to a logarithmic factor. In more detail, the proof has two steps, each based on "span programs," a certain linear-algebraic model of computation. First, we give an SDP that outputs for any boolean function a… CONTINUE READING

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