This work presents the first evaluation of timing and higher-energy attacks on Quantum Random Access Memory (QRAM) circuits. By leveraging quantum principles, QRAM can efficiently store and manipulate both quantum and classical data, leading to potential significant speedups in a variety of quantum algorithms. However, as demonstrated in this work, when used in remote cloud-based quantum computers QRAM is vulnerable to different security attacks. The work demonstrates side-channel attacks, e.g., the timing attacks, as well as fault-injection-like attacks, e.g., the higher-energy attacks. This work evaluates the attacks on QRAM and different circuits that use QRAM. The work also proposes a set of defenses.