Verify that the product of two unitary matrices is unitary. (This may require reviewing the transpose of a product.)
Verify that a unitary matrix is invertible and its inverse is unitary.
Apply the reversible AND gate (as demonstrated in class) to the state
$\frac{1}{2} \ket{000} + \frac{1}{2} \ket{011} + \frac{1}{2} \ket{101} + \frac{1}{2} \ket{111}$.
Make an 8×8 unitary matrix that implements a reversible OR gate.
Determine a $2$-qubit quantum circuit that will, on input $\ket{00}$, produce output
$\frac{1}{2} \ket{00} + \frac{1}{2} \ket{01} + \frac{1}{2} \ket{10} + \frac{1}{2} \ket{11}$. Hint: combine Hadamard gates.