The reliability of the outcome of a quantum circuit in near-term noisy quantum computers depends on the gate count and depth for a given problem. Circuits with a short depth and lower gate count can yield the correct solution more often than the circuit variant with a higher gate count and depth. To work successfully for Noisy Intermediate Scale Quantum (NISQ) computers, quantum circuits need to be optimized efficiently using a compiler that decomposes high-level gates to native gates of the hardware. Many 3rd party compilers are being developed for lower compilation time, reduced circuit depth, and lower gate count for large quantum circuits. Such compilers, or even a specific release version of a compiler that is otherwise trustworthy, may be unreliable and give rise to security risks. Security breaches could allow an adversary to insert a quantum Trojan during compilation that evades detection due to the lack of a golden/Oracle model in quantum computing. Inherently, quantum circuits have a margin between the probability of correct and incorrect basis states. Trojans may corrupt the functionality to give flipped probabilities of basis states, or result in a lower probability of correct basis states in the output. In this paper, we investigate and discuss the impact of a single qubit Trojan (we have chosen a Hadamard gate and a NOT gate) inserted one at a time at various locations in a benchmark quantum circuits such that the depth of the circuit is not altered. Results indicate an average of 16.18% degradation for the Hadamard Trojan without noise, and 7.78% with noise. For the NOT Trojan (with noise) there is 14.6% degradation over all possible inputs. We then discuss the detection of such Trojans in a quantum circuit using CNN-based classifier achieving an accuracy of 90%.