For successful realization of a quantum computer, its building blocks (qubits) should be simultaneously scalable and sufficiently protected from environmental noise. Recently, a novel approach to the protection of superconducting qubits has been proposed. The idea is to prevent errors at the "hardware" level, by building a fault-free (topologically protected) logical qubit from "faulty" physical qubits with properly engineered interactions between them. It has been predicted that the decoupling of a protected logical qubit from local noises would grow exponentially with the number of physical qubits. Here we report on the proof-of-concept experiments with a prototype device which consists of twelve physical qubits made of nanoscale Josephson junctions. We observed that due to properly tuned quantum fluctuations, this qubit is protected against magnetic flux variations well beyond linear order, in agreement with theoretical predictions. These results demonstrate the feasibility of topologically protected superconducting qubits. ; Comment: 25 pages, 5 figures