Quantum Bits Solutions

Solutions for the exercises in ​Try Your Hand​.

1. 1. Since it’s only the ratio of pentagon qubelets to triangle qubelets that matter, we can halve the qubelets of each type, as shown here:

      

   2. 1. False. This qubit has both pentagon and triangle qubelets. Thus, when it’s measured, any of these types of qubelets can be randomly selected. Hence, it could collapse to either of the or idealized states.

      2. True. Since the ratio of pentagon qubelets to triangle qubelets is , we expect to see the pentagon qubelets 3 times more than the triangle qubelets. Hence, we’ll see the corresponding binary state 0 times as often as the 0 state.

      3. False. Once a qubit is measured by selecting a qubelet from its quantum state, the rest of the qubelets vanish.

      4. False. Once a qubit is measured by selecting a qubelet from its quantum state, the rest of the qubelets vanish. Thus, if it’s measured again, the same qubelet is selected again. Thus, it’ll never collapse to a different idealized quantum state.

2. Not much—all you can say is that the qubit had at least one triangle qubelet in its quantum state.

3. is a qubit and 0 is one of the classical binary states. The qubit can be nudged to other blended states while the 0 bit can only be switched to the 1 bit.

4. The Measure would record the classical state 1. That is,

   

5. No. The Measure gate records only the specific idealized state the qubit collapses to when it was probed. So, conceivably, if the quantum circuit was run again, the qubit that the Measure gate is inspecting can collapse to another idealized state. But in each case, only a single value will be recorded by the Measure gate in the classical register.