Homework

Here is the homework from the previous sessions. Feel free to ask any questions in the comments section. Keep in mind, this is a training that will help us prepare for the final quiz!

Session 1

Quantum Circuit Ansatz

Given the following ansatz:
In[]:=
QuantumCircuitOperator[{"RX"[θ],"CNOT"}]["Diagram",ImageSize->Small]​​
Out[]=
In[]:=
QuantumCircuitOperator[{"RX"[θ1],"RX"[θ2]->{2},"CNOT"}]["Diagram",ImageSize->Small]​​
Out[]=
◼
  • Prove that the first ansatz cannot generate the state
    |10〉
    .
    • ◼
  • Prove that the second ansatz can generate the state
    |10〉
    .

    • Session 2

    Variational Quantum Eigensolver

    The following code in Python calculates the Hamiltonian for the
    H
    2
    molecule:
    〉
    In[]:=
    import pennylane as qml
    from pennylane import numpy as np
    ​
    symbols = ["H", "H"]
    coordinates = np.array([[0.0, 0.0, -0.6614], [0.0, 0.0, 0.6614]])
    ​
    # Building the molecular hamiltonian
    hamiltonian, qubits = qml.qchem.molecular_hamiltonian(symbols, coordinates)
    ​
    qml.matrix(hamiltonian)
    ◼
  • Calculate the minimal energy
    • You can import the Hamiltonian from the following link:
    In[]:=
    CloudImport["https://wolfr.am/1tP2IKEfw"]
    Out[]=
    NumericArray
    Type: ComplexReal64
    Dimensions: {16,16}
    

    Beyond VQE: Quantum Approximate Optimization Algorithm (QAOA)

    Given the classical cost function for the Max-Cut problem:
    C=
    1
    2
    ∑
    ,∈V
    1-
    s
    
    s
    
    ,s∈{-1,+1}
    And the quantum analogue:
    H
    C
    =
    1
    2
    ∑
    ,∈V
    -
    Z
    
    Z
    
    
    ◼
  • Show that
    H
    C
    |x〉=C(x)|x〉
    • Following the same steps from class:
    Out[]=
    ◼
  • Find the solution for the 5-nodes graph

    • Session 3

    No homework!

    Session 4

    In[]:=
    RandomComplex[{-1-1*I,+1+1*I},2]
    Out[]=
    {0.702043-0.804257,0.411178+0.89022}
    In[]:=
    RandomComplex[{-1-I,1+I},{2,2}]//MatrixForm
    Out[]//MatrixForm=
    0.60789-0.0846206
    -0.0385657+0.121639
    0.206188+0.872187
    0.418208+0.592383
    ◼
  • Solve the linear system for a random complex matrix and complex vector using the Multiplexer-Based Quantum Linear Solver algorithm