We explore the power of the unbounded Fan-Out gate and the Global Tunable gates generated by Ising-type Hamiltonians in constructing constant-depth quantum circuits, with particular attention to quantum memory devices. We propose two types of constant-depth constructions for implementing Uniformly Controlled Gates. These gates include the Fan-In gates defined by (|x\rangle|b\rangle\mapsto |x\rangle|b\oplus f(x)\rangle) for (x\in\{0,1\}^n) and (b\in\{0,1\}), where (f) is a Boolean function. The first of our constructions is based on computing the one-hot encoding of the control register (|x\rangle), while the second is based on Boolean analysis and exploits different representations of (f) such as its Fourier expansion. Via these constructions, we obtain constant-depth circuits for the quantum counterparts of read-only and read-write memory devices – Quantum Random Access Memory (QRAM) and Quantum Random Access Gate (QRAG) – of memory size (n). The implementation based on one-hot encoding requires either (O(nlog^{(d)}{n}log^{(d+1)}{n})) ancillae and (O(nlog^{(d)}{n})) Fan-Out gates or (O(nlog^{(d)}{n})) ancillae and (16d-10) Global Tunable gates, where (d) is any positive integer and (log^{(d)}{n} = log\cdots log{n}) is the (d)-times iterated logarithm. On the other hand, the implementation based on Boolean analysis requires (8d-6) Global Tunable gates at the expense of (O(n^{1/(1-2^{-d})})) ancillae.