MinimumEigenOptimizer returns a wrong solution

[t-imamichi]

Information

• Qiskit Optimization version: latest
• Python version: 3.8.9
• Operating system: macOS 11.2.3

What is the current behavior?

MinimumEigenOptimizer with qasm_simulator returns a wrong solution.

Steps to reproduce the problem

from docplex.mp.model import Model
mdl = Model("docplex model")
x = mdl.binary_var('x')
y = mdl.binary_var('y')
mdl.minimize(x-2*y)
print(mdl.export_as_lp_string())
result = mdl.solve()
print("result of CPLEX solver")
print(result)

from qiskit_optimization import QuadraticProgram
from qiskit.providers.aer import QasmSimulator
from qiskit.algorithms.optimizers import SPSA
from qiskit.circuit.library import TwoLocal
from qiskit.utils import QuantumInstance
from qiskit.algorithms import VQE
from qiskit_optimization.algorithms import MinimumEigenOptimizer
seed = 1234
qp = QuadraticProgram()
qp.from_docplex(mdl)
backend = QasmSimulator()
optimizer = SPSA(maxiter=100)
ry = TwoLocal(2, 'ry', 'cz', reps=3, entanglement='full')
quantum_instance = QuantumInstance(backend=backend, seed_simulator=seed, seed_transpiler=seed)
vqe_mes = VQE(ry, optimizer=optimizer, quantum_instance=quantum_instance)
vqe = MinimumEigenOptimizer(vqe_mes)
result = vqe.solve(qp)
print("result of VQE solver")
print(result)
print(result.raw_samples)

output:

\ This file has been generated by DOcplex
\ ENCODING=ISO-8859-1
\Problem name: docplex model

Minimize
 obj: x - 2 y
Subject To

Bounds
 0 <= x <= 1
 0 <= y <= 1

Binaries
 x y
End

result of CPLEX solver
solution for: docplex model
objective: -2
y=1

result of VQE solver
optimal function value: 1.0
optimal value: [1. 0.]
status: SUCCESS

What is the expected behavior?

The solution of VQE should be [0. 1.].

Suggested solutions

We may need to reverse the bitstrings as x = np.fromiter(list(bitstr[::-1]), dtype=int). But, it may affect other algorithms and unit tests.
https://github.com/Qiskit/qiskit-optimization/blob/54a6d0750492132aa019975e3a8648c507b7553c/qiskit_optimization/algorithms/optimization_algorithm.py#L511

[Cryoris]

Do we need to reverse the solution bitstring or would it maybe be better to reverse the bits in the Hamiltonian? Then the solution with the MinimumEigenOptimizer would be consistent with both CPLEX and VQE.

If we only flip the solution in MinimumEigenOptimizer, the solution bitstring will be the same as for CPLEX but if I do a manual optimization by using VQE directly, the order will not be the same, right?

[t-imamichi]

Yes, it will be fixed in #97

[a-matsuo]

If we only flip the solution in MinimumEigenOptimizer, the solution bitstring will be the same as for CPLEX but if I do a manual optimization by using VQE directly, the order will not be the same, right?

You're right. I only flipped the solution in MinimumEigenOptimizer in #97.
Hmm, ya, it might be better to reverse the bits in the Hamiltonian for consistency.
We can reverse the bits in the Hamiltonian, easily. Currently, variable x_0 is mapped to qubit q_0, x1 -> q1,..., and x_n -> q_n. If we want reverse the bits in the Hamiltonian, we map x_0 -> q_n, x_1 -> q_n-1, ..., and x_n -> q_0.

[t-imamichi]

Oh, sorry. I missed the point. We need to revisit the ordering of Hamiltonian. How about discussing it in another issue?

[Cryoris]

Why not in this issue (since the bug is described here)? 🙂 If the changes are not too big it would probably be better to do only one fix instead of first re-ordering the solution bits and then undoing this by re-ordering the Hamiltonian.

@a-matsuo do you think you could check if reversing the Hamiltonian order fixes the problem consistently? 🙂

[t-imamichi]

It's just in case. Some users may use the current order.

[t-imamichi]

But, as you say, it's a good opportunity to change the order because this library is new.

[t-imamichi]

Anyways, we need to clarify the order of Hamiltonian in docstrings of to_ising and from_ising.

[a-matsuo]

@Cryoris Sure. Let me check reversing the Hamiltonian order works correctly as I expect. I will work on it next week.
@t-imamichi Ya, we need to clarify the order of Hamiltonian in docstrings if we change it.

[t-imamichi]

If we reverse the Hamiltonian ordering, QuantumInstance.initial_layout might be mapped in the reverse order. We need to verify it. Users expect initial_layout is mapped to the same order of variables. coupling_map may have the same problem.

[t-imamichi]

I'm checking some PRs related to endian and wondering what is the best option.
Qiskit/qiskit#5848
Qiskit/qiskit#4849
@ikkoham Do you have any idea from PauliSumOp point of view?

[ikkoham]

I think all of the qiskit operators (including PauliSumOp) and circuits should be little endian if possible.
Qiskit/qiskit#1148

Second quantized operators in qiskit-nature is only exception since the application users are familiar with BIG endian.

[t-imamichi]

Thanks @ikkoham. The bit ordering is based on the Terra's convention. So, I don't think we need to reverse it in this optimization layer. The same mapping (variable_i to qubit_i) makes sense to me. I would like to merge #97 as is.

[a-matsuo]

From the perspective of operators, when users manually make Ising Hamiltonians for optimization problems, it is natural to think mapping qubit 1 to variable 1. I think the current way (mapping x1 to q1) makes sense.

If we only flip the solution in MinimumEigenOptimizer, the solution bitstring will be the same as for CPLEX but if I do a manual optimization by using VQE directly, the order will not be the same, right?

Then, for the above issue, maybe, writing clear docstrings is the only solution?

[t-imamichi]

Agree. It's good to add a docstring about mapping of variables to qubits.

[Cryoris]

I don't think it's a good long term solution to have different qubit ordering in Qiskit Core and in the application modules. This will require users to exactly know in which part of Qiskit they are operating and swap qubit orders in the right places -- which can even be confusing for us developers! 😄

It's true that many users are used to big endian notation, but Qiskit just doesn't use big endian so I would argue it's better to be clear about this and not have different conventions in on software package. As a compromise, we could add a little_endian argument in some places, which is True by default but can be set to False such that users can use big endian.

[t-imamichi]

Yes. So, let's keep the current qubit order (variable_i -> qubit_i) to align with qiskit core's convention and clarify it in the docstring of to_ising and from_ising.

The endian option sounds interesting. I would like to discuss it as a future work.

[t-imamichi]

I updated the docstrings of to_ising and from_ising. If there is no more comments about #97, I will merge it.

[Cryoris]

Ok 👍🏻 yeah let's revisit the ordering in another issue, I'm not sure I fully understood where which order is assumed 😉 Thanks for the clarifications!