Quantum computing on the IBM processor

We analyze the basic aspects of the quantum information theory, namely the quantum version of the theory that is behind all the classical implementations like computers and communications. We focus on quantum computation, defining its fundamental unit: the qubit, namely a quantum two-level system that will be described in detail in this thesis. We then concentrate on the possible transformations gates that can be applied to qubits, both unitary and non-unitary ones. The challenges in the construction of qubits are impressive: in particular, it is difficult to isolate the system from the environment. This interaction is modeled by non-unitary transformations. The characteristic times connected to these processes are the relaxation time, the time in which a state decays in another state, and the decoherence time, the time in which quantum coherence is lost. These times are fundamental in quantum computing since they quantify how many operations can be performed on qubits and still obtain reliable results. We measure these characteristic times on the IBM quantum processor ’ibmq_16_melbourne’ performing three different experiments: one for the relaxation time and two for the decoherence time, namely Ramsey and Echo experiments. Finally, we implement a quantum algorithm, an algorithm that uses the resources of quantum mechanics, like entanglement. We focus on finding a protocol to define the quantum version of the elementary cellular automata, the quantum elementary cellular automata, and run it on the IBM processor. They are dynamical systems defined on a lattice in which the evolution is defined using simple local update rules. Comparing the physical results with theoretical expectations and noise-affected simulations we show the performance of the IBM processor.