Finish refactoring of book

Scinawa · Scinawa · commit 73b426ffdea1 · 2021-06-25T03:38:52.000+08:00
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-# (PART) Part (Quantum Machine Learning) {-} 
 
 # Dimensionality reduction
 
diff --git a/first-quantum-algorithms.Rmd b/first-quantum-algorithms.Rmd
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-# Lower bounds on query complexity of quantum algorithms
+# Lower bounds on query complexity of quantum algorithms {#chap:lowerbounds}
 
 We have discussed about several important quantum algorithms. A large portion of them is query-based, i.e. the input is given as a quantum black box $O: |\mathbf{x}\rangle |y\rangle \mapsto |\mathbf{x}\rangle |y \oplus f(x)\rangle$. In that setting, query complexity plays a key role in determining the advantage and limitation of an algorithm. This chapter will discuss how to obtain a lower bound on query complexity, i.e. the minimal number of queries an algorithm needs to make for a desired output (probably up to some error bound). In particular, we are going to look into __Polynomial method__ and __Adversary method__, along with some simple applications.
 
