Please submit your answers as a PDF in PILOT under Assignment 4. For this assignment, you will need to access the IBM Quantum Composer. Exercise 1 ( 3pts) Create a single-qubit circuit using the IBM quantum composer. Apply a Hadamard gate on the qubit. - What possible states, in Dirac Braket notation, exist? (1 pt) - Provide a screenshot containing the circuit, probabilities, and q-sphere. (2 pts) Exercise 2 (3 pts) Create a 2-qubit circuit using the IBM quantum composer. Apply any two single-qubit gates of your choice (one per qubit) such that both qubits are in superposition. - What possible states, in Dirac Braket notation, exist? (1 pt) - Provide a screenshot containing the circuit, probabilities, and q-sphere. (2 pts) Exercise 3 (3 pts) Create a 2-qubit circuit using the IBM quantum composer. Apply exactly two gates on the circuit to maximally entangle both qubits. This should produce the Bell state. - What possible states, in Dirac Braket notation, exist? (1 pt) - Provide a screenshot containing the circuit, probabilities, and q-sphere. (2 pts) Exercise 4 (3 pts) Create a 3-qubit circuit using the IBM quantum composer. Apply a 180-degree (or radians) rotation around the X,Y, and Z axis for qubits 0,1 , and 2 , respectively. You can do this with only one gate per qubit. - What possible states, in Dirac Braket notation, exist? (1 pt) - Provide a screenshot containing the circuit, probabilities, and q-sphere. (2 pts) Exercise 5 (3 pts) Consider the quantum circuit below. q[]+H - What is a Dirac Braket notation for this qubit's state after the gates? (1 pt) - What gate(s) needs to be appended to transform the qubit's state such that its Dirac Braket notation is |1)? (1 pt) - What gate(s) needs to be appended to transform the qubit's state such that its Bloch sphere representation is pointing at the north pole? (1 pt) Exercise 6 (2 pts) Consider this scenario. You're trying to break a lock that uses a case sensitive 16 character alphanumeric passphrase (characters may be a-z, A-Z, and 0-9). How many qubits at a minimum would your quantum computer need to simultaneously represent all possibilities for this passphrase? Show your work. Exercise 7 (2 pts) Consider the quantum circuit below. There are two qubits each with a single-qubit gate applied to them. These two gates can be combined into a single 2-qubit gate using a math operation. State the math expression that yields the matrix for the 2-qubit gate. Show your work. Exercise 8(1pt) Assume a Hadamard gate is applied to a qubit in ground state. Which of these gates when inserted before the Hadamard gate changes final the state vector? Circle all that apply. - X-gate - Y-gate - Z-gate - Identity - Hadamard Please submit your answers as a PDF in PILOT under Assignment 4. For this assignment, you will need to access the IBM Quantum Composer. Exercise 1 ( 3pts) Create a single-qubit circuit using the IBM quantum composer. Apply a Hadamard gate on the qubit. - What possible states, in Dirac Braket notation, exist? (1 pt) - Provide a screenshot containing the circuit, probabilities, and q-sphere. (2 pts) Exercise 2 (3 pts) Create a 2-qubit circuit using the IBM quantum composer. Apply any two single-qubit gates of your choice (one per qubit) such that both qubits are in superposition. - What possible states, in Dirac Braket notation, exist? (1 pt) - Provide a screenshot containing the circuit, probabilities, and q-sphere. (2 pts) Exercise 3 (3 pts) Create a 2-qubit circuit using the IBM quantum composer. Apply exactly two gates on the circuit to maximally entangle both qubits. This should produce the Bell state. - What possible states, in Dirac Braket notation, exist? (1 pt) - Provide a screenshot containing the circuit, probabilities, and q-sphere. (2 pts) Exercise 4 (3 pts) Create a 3-qubit circuit using the IBM quantum composer. Apply a 180-degree (or radians) rotation around the X,Y, and Z axis for qubits 0,1 , and 2 , respectively. You can do this with only one gate per qubit. - What possible states, in Dirac Braket notation, exist? (1 pt) - Provide a screenshot containing the circuit, probabilities, and q-sphere. (2 pts) Exercise 5 (3 pts) Consider the quantum circuit below. q[]+H - What is a Dirac Braket notation for this qubit's state after the gates? (1 pt) - What gate(s) needs to be appended to transform the qubit's state such that its Dirac Braket notation is |1)? (1 pt) - What gate(s) needs to be appended to transform the qubit's state such that its Bloch sphere representation is pointing at the north pole? (1 pt) Exercise 6 (2 pts) Consider this scenario. You're trying to break a lock that uses a case sensitive 16 character alphanumeric passphrase (characters may be a-z, A-Z, and 0-9). How many qubits at a minimum would your quantum computer need to simultaneously represent all possibilities for this passphrase? Show your work. Exercise 7 (2 pts) Consider the quantum circuit below. There are two qubits each with a single-qubit gate applied to them. These two gates can be combined into a single 2-qubit gate using a math operation. State the math expression that yields the matrix for the 2-qubit gate. Show your work. Exercise 8(1pt) Assume a Hadamard gate is applied to a qubit in ground state. Which of these gates when inserted before the Hadamard gate changes final the state vector? Circle all that apply. - X-gate - Y-gate - Z-gate - Identity - Hadamard