# Solving search problems by strongly simulating quantum circuits

### Reference:

Johnson, T. H., Biamonte, J. D., Clark, S. R. and Jaksch, D., 2013. Solving search problems by strongly simulating quantum circuits. Scientific Reports, 3, 1235.

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### Official URL:

http://dx.doi.org/10.1038/srep01235

### Abstract

Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several efficient strong simulation techniques are known for restricted families of quantum circuits and we develop an additional technique in this article. Further, we show that strong simulation algorithms perform another fundamental task: solving search problems. Efficient strong simulation techniques allow solutions to a class of search problems to be counted and found efficiently. This enhances the utility of strong simulation methods, known or yet to be discovered, and extends the class of search problems known to be efficiently simulable. Relating strong simulation to search problems also bounds the computational power of efficiently strongly simulable circuits; if they could solve all problems in $\mathrm{P}$ this would imply the collapse of the complexity hierarchy $\mathrm{P} \subseteq \mathrm{NP} \subseteq # \mathrm{P}$.

### Details

 Item Type Articles Creators Johnson, T. H., Biamonte, J. D., Clark, S. R. and Jaksch, D. DOI 10.1038/srep01235 Uncontrolled Keywords quant-ph Departments Faculty of Science > Physics Refereed Yes Status Published ID Code 47352 Additional Information 9 pages, 3 figures