5
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I have a non-convex QUBO problem that I'd like to solve by warm-starting QAOA with a solution obtained from a continuous relaxation solution obtained by a classical algorithm. The specifics of the problem is shown below in the code.

I have 2 questions:

  • In the code below is CPLEX able to solve the original QUBO. However, when I use CPLEX as input to the WarmStartQAOA optimization in QisKit, it tells me it cannot solve because the problem is non-convex?
  • For non-convex problems, there must be an easy reformulation that QisKit and WarmStartQAOA can do on its own since most problems are non-convex. Can someone help me find that functionality in QisKit?
import random
random.seed(0)

def invert_counts(counts):
    return {k[::-1]:v for k, v in counts.items()}

qp = QuadraticProgram()
p = 1
m = 4
n = 4
for i in range(m):
    for j in range(n):
        qp.binary_var("x_{}_{}".format(i,j))

qp.quadratic_dict={}
for i in range(m):
    for p in range(n):
        for i_2 in range(m):
            for p_2 in range(n):
                qp.quadratic_dict[("x_{}_{}".format(i,p), "x_{}_{}".format(i_2, p_2))] = 0
for i in range(m):
    for p in range(n):
        x_i_p = "x_{}_{}".format(i,p)
        curr_entry = qp.quadratic_dict[(x_i_p, x_i_p)]
        qp.quadratic_dict[(x_i_p, x_i_p)]= curr_entry - 40
        
qp.minimize(quadratic=qp.quadratic_dict)

def relax_problem(problem) -> QuadraticProgram:
    """Change all variables to continuous."""
    relaxed_problem = copy.deepcopy(problem)
    for variable in relaxed_problem.variables:
        variable.vartype = VarType.CONTINUOUS
    return relaxed_problem

sol = CplexOptimizer().solve(qp)
print(sol.prettyprint())

qaoa_mes = QAOA(sampler=Sampler(), optimizer=COBYLA())
ws_qaoa = WarmStartQAOAOptimizer(
    pre_solver=CplexOptimizer(), relax_for_pre_solver=True, qaoa=qaoa_mes, epsilon=0.0)

ws_result = ws_qaoa.solve(qp)
print(ws_result.prettyprint())
```
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1
  • $\begingroup$ Did you figure out what was the issue? I get a similar problem. $\endgroup$
    – Stéphane
    Jun 29, 2023 at 16:10

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