Abstract
In this thesis a theoretical analysis of operators acting on qubits systems is presented. Its purpose is to find a method to decompose an arbitrary operator that operates on any number of qubits as the product of elementary operators.
For this, first we introduce the used mathematical formalism and the graphic representation that was given to the operators.
We begin by studying operators that act on one and two qubits, finding their decomposition as elementary quantum gates. For a greater number of qubits we establish an algorithm that allows to find the decomposition of a transformation as the product reflections of Householder. Then we give a method to obtain the representation of the reflections as a series of quantum gates. The decomposition algorithm and the representation method allow to synthesize the quantum circuit for any transformation of qubits.
We observe that, under a specific criterion of selection of the reflections and their representation, it is possible to find a reduced form of the resulting quantum circuit.
For this, first we introduce the used mathematical formalism and the graphic representation that was given to the operators.
We begin by studying operators that act on one and two qubits, finding their decomposition as elementary quantum gates. For a greater number of qubits we establish an algorithm that allows to find the decomposition of a transformation as the product reflections of Householder. Then we give a method to obtain the representation of the reflections as a series of quantum gates. The decomposition algorithm and the representation method allow to synthesize the quantum circuit for any transformation of qubits.
We observe that, under a specific criterion of selection of the reflections and their representation, it is possible to find a reduced form of the resulting quantum circuit.
Translated title of the contribution  Quantum circuits synthesis 

Original language  Spanish 
Qualification  MPhil 
Awarding Institution 

Supervisors/Advisors 

Publication status  Published  2019 