prepared by Abuzer Yakaryilmaz (QLatvia)


Conventions: When the qubits are enumerated as $ q_0,\ldots,q_n $, we combine them as $ q_n \otimes q_{n-1} \otimes \cdots \otimes q_0 $ and then read in the order $ q_n,q_{n-1},\ldots,q_0 $.

CNOT(controlled_qubit,target_qubit) represents the Controlled-NOT operator.

We have a composite system with two qubits $ q_1 $ and $ q_0 $ and each is in state $ \ket{0} $. Which one of the following operators leads the state of the composite system to $ \sqrttwo \ket{00} + \sqrttwo\ket{11} $?


We have a composite system with two qubits $ q_1 $ and $ q_0 $ that is in state $ \ket{00} $. Which one of the following operators leads the state of the composite system to $ \sqrttwo \ket{01} + \sqrttwo\ket{10} $?


We have a composite system with two qubits $ q_1 $ and $ q_0 $. What is the matrix representation of $ CNOT(q_1,q_0) $ for this system?


We have a composite system with two qubits $ q_1 $ and $ q_0 $. What is the matrix representation of $ CNOT(q_0,q_1) $ for this system?


We have a composite system with two qubits $ q_1 $ and $ q_0 $ that is in state $ \frac{1}{2}\ket{00} - \frac{1}{2}\ket{01} - \frac{1}{2}\ket{10} + \frac{1}{2}\ket{11} $. What are the states of $ q_1 $ and $ q_0 $ separately?


We have a composite system with two qubits $ q_1 $ and $ q_0 $ that is in state $ \ket{00} $. What is the state after applying $ H(q_1) $, $CNOT(q_1,q_0) $, and $ Z(q_0) $ in order?


We have a composite system with two qubits $ q_1 $ and $ q_0 $ that is in state $ \frac{1}{\sqrt{2}}\ket{01} - \frac{1}{\sqrt{2}}\ket{10} $. After applying which one of the following operators, the system will no longer be entangled?


We have a composite system with two qubits $ q_1 $ and $ q_0 $. We apply Hadamard operator to the qubit $ q_0 $ that corresponds to the $ 4 \times 4 $ matrix $ I \otimes H $ applied to the composite sytem. What is this matrix?


We have a composite system with three qubits $ q_2, q_1, q_0 $. What is the final state if $ CNOT(q_0,q_2) $ is applied to state $ \mypar{ \frac{1}{\sqrt{2}} \ket{101} + \frac{1}{\sqrt{3}} \ket{110} + \frac{1}{\sqrt{6}} \ket{011}} $?


We have a composite system with three qubits $ q_2, q_1, q_0 $ that is in state $ \mypar{ \frac{1}{\sqrt{2}} \ket{101} + \frac{1}{\sqrt{3}} \ket{110} + \frac{1}{\sqrt{6}} \ket{011}} $. We measure only the qubit $ q_2 $. What is the probability of observing state $ \ket{1} $?


We have a composite system with three qubits $ q_2, q_1, q_0 $ that is in state $ \mypar{ \frac{1}{\sqrt{2}} \ket{101} + \frac{1}{\sqrt{3}} \ket{110} + \frac{1}{\sqrt{6}} \ket{011}} $. We measure only the qubit $ q_0 $. What is the probability of observing state $ \ket{0} $?


We have a composite system with three qubits $ q_2, q_1, q_0 $ that is in state $ \mypar{ \frac{1}{\sqrt{2}} \ket{101} + \frac{1}{\sqrt{3}} \ket{110} + \frac{1}{\sqrt{6}} \ket{011}} $. If we measure the qubit $ q_1 $ and observe state $ \ket{1} $, what is the new state of the composity system?


We have a composite system with three qubits $ q_2, q_1, q_0 $ that is in state $ \mypar{ \frac{1}{\sqrt{2}} \ket{101} + \frac{1}{\sqrt{3}} \ket{110} + \frac{1}{\sqrt{6}} \ket{011}} $. If we measure the qubit $ q_1 $ and observe state $ \ket{0} $, what is the new state of the composity system?


We have a composite system with three qubits $ q_2, q_1, q_0 $ that is in state $ \mypar{ \frac{1}{\sqrt{2}} \ket{101} + \frac{1}{\sqrt{3}} \ket{110} + \frac{1}{\sqrt{6}} \ket{011}} $. If we measure the qubit $ q_2 $, which one of the following mixtures is obtained?


We have a composite system with three qubits $ q_2, q_1, q_0 $ that is in state $ \mypar{ \frac{1}{\sqrt{2}} \ket{101} + \frac{1}{\sqrt{3}} \ket{110} + \frac{1}{\sqrt{6}} \ket{011}} $. If we apply Hadamard operator to the qubit $ q_0 $, what will be the new state of system?


We have a composite system with two qubits $ q_1 $ and $ q_0 $. In which one of the following states the system is not entangled?


We have a composite system with two qubits $ q_1 $ and $ q_0 $ tensored as $ q_1 \otimes q0 $, which is in state $ \ket{00} $.

After applying which one of the following operators the system will be in state $ \frac{1}{2} \mypar{ \ket{00} - \ket{01} -\ket{10} - \ket{11} } $ ?