Constant-depth circuits for Boolean functions and quantum memory devices using multi-qubit gates

Understand

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.