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I would like to play with a quantum circuit local_qasm_simulator in QISKit, but I do not want to implement a separate quantum circuit that would prepare an initial state.

The way I do it now is by falling back to NumPy. Specifically, first, I extract matrix u from a quantum program qp:

cname = 'circuit name'
results = qp.execute(cname, backend='local_unitary_simulator', shots=1)
data = results.get_data(cname)
u = data['unitary']

Then, I explicitly create the state I need (e.g., $|\psi\rangle = \frac{1}{2}(|00\rangle + |01\rangle + |10\rangle - |11\rangle)$):

num_qubits = 2
psi = np.ones(2**num_qubits) / 2.0
psi[3] = -psi[3]

Finally, I apply u to psi with NumPy:

u @ psi

The advantage of this approach is that I can explicitly obtain the state $U |\psi\rangle$. However, I cannot use local_qasm_simulator and the measure() function.

So, how could I prepare an arbitrary state, and supply it to a circuit, and run a local_qasm_simulator?

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I think you can use the initialize function as detailed at the section "Arbitrary Initialization" at this tutorial.

As an example, this tutorial explicitly shows how to initialize the three qubit state

$$ \frac{i}{\sqrt{16}} | 000 \rangle + \frac{1}{\sqrt{8}} | 001 \rangle + \frac{1+i}{\sqrt{16}} | 010 \rangle + \frac{1+2i}{\sqrt{8}} | 101 \rangle + \frac{1}{\sqrt{16}} | 110 \rangle .$$

Which is done using the following lines of QISKit code.

import math
desired_vector = [
    1 / math.sqrt(16) * complex(0, 1),
    1 / math.sqrt(8) * complex(1, 0),
    1 / math.sqrt(16) * complex(1, 1),
    0,
    0,
    1 / math.sqrt(8) * complex(1, 2),
    1 / math.sqrt(16) * complex(1, 0),
    0]
initialize_circuit_3q = Q_program.create_circuit('initialize_circuit_3q', [qr], [cr])
initialize_circuit_3q.initialize("init", desired_vector, [qr[0],qr[1],qr[2]])
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