Super controlled gates and controlled gates in two-qubit gate simulations

TL;DR

This paper explores the simulation capabilities of super controlled and controlled gates in two-qubit systems, establishing their power to simulate arbitrary gates with minimal applications and analyzing their relationships.

Contribution

It introduces the concept of mirror gates, demonstrates that three applications of a super controlled gate suffice for universal simulation, and provides constructive methods for gate simulation.

Findings

Arbitrary two-qubit gates can be simulated with three super controlled gates.

A set of gates can be simulated with n controlled gate applications.

Some gates can be simulated with four applications of controlled gates.

Abstract

In two-qubit gate simulations an entangling gate is used several times together with single qubit gates to simulate another two-qubit gate. We show how a two-qubit gate's simulation power is related to the simulation power of its mirror gate. And we show that an arbitrary two-qubit gate can be simulated by three applications of a super controlled gate together with single qubit gates. We also give the gates set that can be simulated by n applications of a controlled gate in a constructive way. In addition we give some gates which can be used four times to simulate an arbitrary two-qubit gate.