For Wednesday, November 6th, 2024

  1. The poster draft is due Friday!
  2. Verify that the product of two unitary matrices is unitary.  (This may require reviewing the transpose of a product.)
  3. Verify that a unitary matrix is invertible and its inverse is unitary.
  4. Apply the reversible AND gate (as demonstrated in class) to the state
    $\frac{1}{2} \ket{000} + \frac{1}{2} \ket{011} + \frac{1}{2} \ket{101} + \frac{1}{2} \ket{111}$.
  5. Make an 8×8 unitary matrix that implements a reversible OR gate.
  6. 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.