Characterization of exact one-query quantum algorithms
Weijiang Chen, Zekun Ye, Lvzhou Li · Physical Review A · 2020
The quantum query model is one of the most important models in quantum computing. Several well-known quantum algorithms are captured by this model, including the Deutsch-Jozsa algorithm, the Simon algorithm, the Grover algorithm, and others. In this paper, we characterize the computational power of exact one-query quantum algorithms. It is proved that a total Boolean function $f:{{0,1}}^{n}\ensuremath{\rightarrow}{0,1}$ can be exactly computed by a one-query quantum algorithm if and only if $f(x)={x}_{{i}_{1}}$ or ${x}_{{i}_{1}}\ensuremath{\bigoplus}{x}_{{i}_{2}}$ (up to isomorphism). Note that, unlike most work in the literature based on the polynomial method, our proof does not resort to any knowledge about the polynomial degree of $f$.