Interesting Quantum Circuits

10 Mar 2020

 

In reference [1] it was shown that a set of gates that consists of all one-bit quantum gates and the two-bit exclusive-or gate is universal in the sense that all unitary operations on arbitrary many bits can be expressed as compositions of these gates.

In this Qiskit notebook we are interested in constructing a gate V such that VxV=X (NOT) gate. Thanks to Lemma 4.3 from the reference [1] V gate can be easily expressed in terms of elementary gates. A cool thing about this is, if we have V gate, we can follow Lemma 6.1 from the same reference and construct a Toffoli gate.

 

[1] https://arxiv.org/abs/quant-ph/9503016

 

The quantum circuit for our construction of the Toffoli gate is displayed below.

 

The pdf version of the notebook can be found here