Experimental realization of the simulation of Deutsch's algorithm using Mach-Zehnder interferometer
In this work I present the experimental realization of the simulation of Deutsch's algorithm using a Mach-Zehnder interferometer setup.
It is already known that information processing through quantum systems proves to be more powerful compared to classical systems. Considering the advantages of quantum computing in relation to classical computing, the main motivation in the search for the construction of an efficient quantum computer is due to the ability of this system to solve some problems that are impossible to solve in a classical way. In other cases, it is also possible for the quantum computer to more efficiently solve a problem that already has a classical solution. A simple example of this admirable property is the subject of this work.
The ingredients needed to perform quantum computations, such as superposition of states, interference and entanglement can be emulated in classical optics. The similarities between paraxial optics and non-relativistic quantum mechanics are taken into account to describe optics in terms of the Dirac formalism and to use operator algebra to solve problems in an elegant way. In fact, a laser beam can be described either as a classical electromagnetic field or as a coherent state containing a macroscopic number of photons. Therefore, linear optics experiments performed with intense beams exhibit behaviours that reproduce many results performed with single photos. Optical coherence is the main factor that allows this analogy that has been used in many research works.
From a didactic point of view, the study of quantum information protocols has the potential to apply quantum concepts, providing an opportunity to understand this important theory.
In 1985 Deutsch proposed a sequence of quantum operations capable of solving a mathematical problem impossible to be solved using classical operations or methods: whether a given Boolean function is constant or balanced, executing it only once. We know that classically this test needs at least two executions.
In case you want more details about how we realized Deutsch's algorithm experimentally, click the link below to see the full manuscript (text in Portuguese).