Added some recap examples for session 2

from qcor import *

@qjit 

def ansatz(q: qreg, theta: float):

    X(q[0])

    Ry(q[1], theta)

    CX(q[1], q[0])

# Define the hamiltonian

H = 5.907 - 2.1433 * X(0) * X(1) - 2.1433 * Y(0) * Y(1) + .21829 * Z(0) - 6.125 * Z(1)

# Define the optimization objective

def obj(x : List[float]):

    e_at_x = ansatz.observe(H, qalloc(2), x[0])

    print('E({}) = {}'.format(x[0], e_at_x))

    return e_at_x

# create the cobyla optimizer

optimizer = createOptimizer('nlopt', {'maxeval':25})

# Run VQE...

results = optimizer.optimize(obj, 1)

print(results)

# Honeywell job submission summary:

# - Set up credentials: qcor -set-credentials honeywell 

from qcor import *

@qjit

def ghz(q : qreg):

    H(q[0])

    for i in range(q.size()-1):

        X.ctrl([q[i]], q[i+1])

    Measure(q)

set_qpu('honeywell:HQS-LT-S1-SIM')

set_shots(1024)

q = qalloc(6)

ghz(q)

q.print()

# Interop with Qiskit

from qcor import *

import qiskit

# Generate 3-qubit GHZ state with Qiskit

qiskit_circ = qiskit.QuantumCircuit(3)

qiskit_circ.h(0)

qiskit_circ.cx(0, 1)

qiskit_circ.cx(1, 2)

qiskit_circ.measure_all()

# Convert Qiskit circuit to QCOR IR

qcor_kernel = qjit(qiskit_circ)

# Allocate the qreg

q = qalloc(3)

# Examine the QCOR IR:

print('QCOR IR:')

qcor_kernel.print_kernel(q)

set_qpu('ionq')

set_shots(1024)

qcor_kernel(q)

q.print()

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