Add initialise simulator instruction to statevector_state

[ShellyGarion]

Summary

#82

Details and comments

Added some printouts for debugging - should be removed later

TODO

• Update Changelog

[ShellyGarion]

Added examples (in comments) to the functions index0 and indexes in QubitVector class, to explain what they are doing

[ShellyGarion]

• Now the code compiles and running - still need to verify that it does the right calculation
• Removed printouts (for debugging)
• Added some comments with explanation & examples

[chriseclectic]

@ShellyGarion great! For verifying can you add some basic unit tests for initializing subsets of qubits. Some simple tests could be something like a 3-qubit state prepared in the |+++⟩ state:

1. Initialize qubit [i] to |1⟩ state (for i =[0], [1], [2])
2. Initialize qubits [i, j] to |01⟩ state for [i,j] = [0,1], [1, 0], [0, 2], [2, 0], [1, 2], [2, 1], where checking i->|1⟩, j->|0⟩.
3. Initialize qubits [i, j, k] to |-01⟩ state for permutations of [i,j,j] = [0, 1, 2], [0, 2, 1], [1, 0, 2], etc.. the permutations are checking qubit i -> |1⟩, j->|0⟩, k->|-⟩.

You could also add tests that it works correctly for an entangled state: Eg 2-qubits prepared in |00⟩+|11⟩ / sqrt(2), and reset qubit [0] to |+⟩, the final state should be |0+⟩ or |1+⟩ with 50% probability each.

[ShellyGarion]

The initialize_component function is not producing the correct output (the norm of the vector is not 1) - I need to debug it

[ShellyGarion]

@chriseclectic - In the function initialize_component - what should N be?
The number of qubits to be initialized ( N = qubits.size() ) or the total number of qubits in the state?
If it's the second option - how do I get this number? (I tried to use the function num_qubits() but got some error when running the code).

[ShellyGarion]

@chriseclectic - I updated the code following your comments and PR #126, and performed the checks that you suggested above, and it looks OK (see details below).
But I still need to update test_statevector_simulator.py accordingly.

In particular, we started from |+++> state:

[0.35355339+0.j 0.35355339+0.j 0.35355339+0.j 0.35355339+0.j
 0.35355339+0.j 0.35355339+0.j 0.35355339+0.j 0.35355339+0.j]

• Initialized qubit i to |1> state for i=0,1,2 - and got that this was the "complement" of reset, e.g.

reset: qubit 0
statevector: [0.5+0.j 0. +0.j 0.5+0.j 0. +0.j 0.5+0.j 0. +0.j 0.5+0.j 0. +0.j] 
initialize: qubit 0
statevector: [0. +0.j 0.5+0.j 0. +0.j 0.5+0.j 0. +0.j 0.5+0.j 0. +0.j 0.5+0.j]

• Initialized qubits i,j (for i,j=0,1,2) in two different ways and got the same results:

(name='initialize', qubits=[qubit_i], params=[[0, 0],[1, 0]]))
(name='initialize', qubits=[qubit_j], params=[[1, 0],[0, 0]]))

and:
(name='initialize', qubits=[qubit_i, qubit_j], params=[[0, 0], [1, 0], [0, 0], [0, 0]]))

• Initialized qubits i,j,k (for i,j,k=0,1,2) in two different ways and got the same results:

(name='initialize', qubits=[qubit_i], params=[[0, 0], [1, 0]]))
(name='initialize', qubits=[qubit_j], params=[[1, 0], [0, 0]]))
(name='initialize', qubits=[qubit_k], params=[[0.70710678, 0], [-0.70710678, 0]]))

and:

(name='initialize', qubits=[qubit_i,qubit_j,qubit_k],
params=[[0, 0], [0.70710678, 0], [0, 0], [0, 0], [0, 0], [-0.70710678, 0], [0, 0], [0, 0]]))

I also started with the Bell state:
[0.70710678+0.j 0. +0.j 0. +0.j 0.70710678+0.j]
and reset qubit [0] to |+⟩, then I got either:
[ 0. +0.j 0. +0.j 0.70710678+0.j -0.70710678+0.j] or:
[ 0.70710678+0.j -0.70710678+0.j 0. +0.j 0. +0.j]

[chriseclectic]

@ShellyGarion can you add a proper unit file for the above tests (and the failing test from your issue comments) and we can look to debugging them.

[ShellyGarion]

@chriseclectic - please see the updated test/terra/test_statevector_simulator.py in the recent commit to this PR.
It calls the following two temporary files:

• test/terra/utils/ref_initialize_temp_1.py:
  in which I Initialized the Qobj directly by adding QasmQobjInstruction, and the calculation of the statevector after the initialize looks correct.
  In particular after initializing qubit 0 directly using
  qobj.experiments[0].instructions.append(QasmQobjInstruction(name='initialize', qubits=[0], params=[[0,0],[1,0]]))
  we get:
  initialize: qubit 0 statevector: [0. +0.j 0.5+0.j 0. +0.j 0.5+0.j 0. +0.j 0.5+0.j 0. +0.j 0.5+0.j]
• test/terra/utils/ref_initialize_temp_2.py:
  in which I used the API of: circ6.initialize(np.array([0.+0.j, 1.+0.j]), [qr[0]]), and the output statevector is wrong...
  statevector of circ6: [-0.35355339+0.j 0.35355339+0.j -0.35355339+0.j 0.35355339+0.j -0.35355339+0.j 0.35355339+0.j -0.35355339+0.j 0.35355339+0.j]

[ShellyGarion]

I think that the problem may be with the type of the params given -
see in the code and output of ref_initialize_temp_2.py the difference between circ4 and circ6.

When I update the Qobj in circ4 directly using:
qobj = assemble_circuits(circ4, run_config=RunConfig(shots=1000)) qobj.experiments[0].instructions.append(QasmQobjInstruction(name='initialize', qubits=[0], params= [[0,0],[1,0]]))
I get the following Qobj:
QasmQobj(config=QasmQobjConfig(memory_slots=0, n_qubits=3, shots=1000), experiments=[QasmQobjExperiment(config=QasmQobjExperimentConfig(memory_slots=0, n_qubits=3), header=QobjExperimentHeader(clbit_labels=[], creg_sizes=[], memory_slots=0, n_qubits=3, name='circuit248', qreg_sizes=[['q65', 3]], qubit_labels=[['q65', 0], ['q65', 1], ['q65', 2]]), instructions=[QasmQobjInstruction(name='h', qubits=[0]), QasmQobjInstruction(name='h', qubits=[1]), QasmQobjInstruction(name='h', qubits=[2]), QasmQobjInstruction(name='initialize', params=[[0, 0], [1, 0]], qubits=[0])])], header=QobjHeader(), qobj_id='2279534b-04fd-4ee4-8802-404d5664558b', schema_version='1.1.0', type='QASM')
and the correct output:
statevector of updated circ4 (after initialize): [0. +0.j 0.5+0.j 0. +0.j 0.5+0.j 0. +0.j 0.5+0.j 0. +0.j 0.5+0.j]

When I update circ6 using circ6.initialize(np.array([0.+0.j, 1.+0.j]), [qr[0]])
then I get the following Qobj:
QasmQobj(config=QasmQobjConfig(memory_slots=0, n_qubits=3), experiments=[QasmQobjExperiment(config=QasmQobjExperimentConfig(memory_slots=0, n_qubits=3), header=QobjExperimentHeader(clbit_labels=[], creg_sizes=[], memory_slots=0, n_qubits=3, name='circuit252', qreg_sizes=[['q65', 3]], qubit_labels=[['q65', 0], ['q65', 1], ['q65', 2]]), instructions=[QasmQobjInstruction(name='h', qubits=[0]), QasmQobjInstruction(name='h', qubits=[1]), QasmQobjInstruction(name='h', qubits=[2]), QasmQobjInstruction(name='initialize', params=[0, 1.00000000000000], qubits=[0])])], header=QobjHeader(), qobj_id='e0f15fcb-9e66-402c-8a25-564100caf24f', schema_version='1.1.0', type='QASM')
and the output is not correct:
statevector of circ6: [-0.35355339+0.j 0.35355339+0.j -0.35355339+0.j 0.35355339+0.j -0.35355339+0.j 0.35355339+0.j -0.35355339+0.j 0.35355339+0.j]

As you can see, in the Qobj of circ4 we have: (name='initialize', params=[[0, 0], [1, 0]], qubits=[0])])
whereas in the Qobj of circ6 we have: (name='initialize', params=[0, 1.00000000000000], qubits=[0])

[chriseclectic]

@ShellyGarion the code looks good to me. I think the failing tests are when you use execute instead of assemble_circuits. Since 'initialize' is not in the simulators basis gates the terra compiler is unrolling the initialize instruction to gates and there is a bug with this unrolling in terra in that it does not insert the required reset operations so it will fail if initialize isn't the first instruction in a circuit.

Can you edit the StatevectorSimulator and QasmSimulator python classes to include 'initalize' in their basis gates and then i think it should work

Note that you can check the correct qobj is being produced by using old compile instead of new assemble_circuits since it will unroll to the simulators basis gates.

From local testing I didn't find any problems with different format of the input state, the following all produced the same result for me:

qr = QuantumRegister(3)

circ0 = QuantumCircuit(qr)
circ0.h(qr)
circ0.reset(qr[0])
circ0.x(qr[0])

circ1 = QuantumCircuit(qr)
circ1.h(qr)
circ1.initialize([0, 1], [qr[0]])

circ2 = QuantumCircuit(qr)
circ2.h(qr)
circ2.initialize([0.0, 1.0], [qr[0]])

circ3 = QuantumCircuit(qr)
circ3.h(qr)
circ3.initialize([0j, 1.0 + 0j], [qr[0]])

circ4 = QuantumCircuit(qr)
circ4.h(qr)
circ4.initialize(np.array([0, 1], dtype=float), [qr[0]])

circ5 = QuantumCircuit(qr)
circ5.h(qr)
circ5.initialize(np.array([0, 1], dtype=complex), [qr[0]])

[ShellyGarion]

@chriseclectic - Indeed, I am now using the new API of assemble_circuits and the deterministic tests are running OK.

However, I am not sure how to combine a nondeterministic test as you suggested above:
"Start with an entangled state: Eg 2-qubits prepared in |00⟩+|11⟩ / sqrt(2), and reset qubit [0] to |+⟩, the final state should be |0+⟩ or |1+⟩ with 50% probability each."

I also added initialize and reset to the StatevectorSimulator and QasmSimulator python classes.

[ShellyGarion]

@chriseclectic - I think that most of the test_statevector_simulator.py (namely, testing reset and other gates) is written with the old API of "execute" that will be deprecated soon.

[chriseclectic]

This is passing so I will merge here, and @yaelbh will continue working on tests in follow up PR #137