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      from qiskit import QuantumRegister, QuantumCircuit
      import numpy as np

      t = 2  # This is not optimal; As an exercise, set this to the
      # value that will get the best results. See section 8 for solution.

      nqubits = 4  # Total number of qubits
      nb = 1  # Number of qubits representing the solution
      nl = 2  # Number of qubits representing the eigenvalues

      theta = 0  # Angle defining |b>

      a = 1  # Matrix diagonal
      b = -1/3  # Matrix off-diagonal

     # Initialise the quantum and classical registers
     qr = QuantumRegister(nqubits)

     # Create a Quantum Circuit
     qc = QuantumCircuit(qr)

     qrb = qr[0:nb]
     qrl = qr[nb:nb+nl]
     qra = qr[nb+nl:nb+nl+1]

    # State preparation. 
    qc.ry(2*theta, qrb[0])

    # QPE with e^{iAt}
    for qu in qrl:
    qc.h(qu)

    qc.u1(a*t, qrl[0])
    qc.u1(a*t*2, qrl[1])

    qc.u3(b*t, -np.pi/2, np.pi/2, qrb[0])


   # Controlled e^{iAt} on \lambda_{1}:
   params=b*t

   qc.u1(np.pi/2,qrb[0])
   qc.cx(qrl[0],qrb[0])
   qc.ry(params,qrb[0])
   qc.cx(qrl[0],qrb[0])
   qc.ry(-params,qrb[0])
   qc.u1(3*np.pi/2,qrb[0])

My question regarding this part of the code is

What is $e^{iAt}$ and controlled-$e^{iAt}$, and why is controlled U gates based on different angles $at,2at$. There are many questions regarding this.

Can somebody explain this code to me, on this site or can somebody share his/her mail. I really am have trouble regarding this HHL algorithm and its implementation.

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