Quickstart

Once installed, qiboopt allows the general user to solve QUBO problems with the built-in QUBO class. Along with the QUBO class, there are some combinatorial classes found in qiboopt.combinatorial.

Formulating a QUBO problem:

• Maximal Independent Set:

import networkx as nx
from qiboopt.combinatorial.combinatorial import MIS

g = nx.Graph()
g.add_edges_from([(0, 1), (1, 2), (2, 0)])
mis = MIS(g)
penalty = 10
qp = mis.penalty_method(penalty)

• Shortest Vector Problem:

Qdict = {(0, 0): 1.0, (0, 1): 0.5, (1, 1): -1.0}
qp = QUBO(0, Qdict)

# Brute force search by evaluating all possible binary vectors.
opt_vector, min_value = qp.brute_force()

QUBO problems can be solved using the QAOA method:

from qiboopt.opt_class.opt_class import QUBO
# Train 2 layers of regular QAOA
gammas = [0.1, 0.2]
betas = [0.3, 0.4]
output = qp.train_QAOA(gammas=gammas, betas=betas)

or the more modern XQAOA approach:

from qiboopt.opt_class.opt_class import QUBO
# Train 2 layers of XQAOA
gammas = [0.1, 0.2]
betas = [0.3, 0.4]
alphas = [0.5, 0.6]
output = qp.train_QAOA(gammas=gammas, betas=betas, alphas=alphas)

The Conditional Variance at Risk (CVaR) can also be used as an alternative loss function in solving the QUBO problem:

from qiboopt.opt_class.opt_class import QUBO
# Train 2 layers of regular QAOA with CVaR
gammas = [0.1, 0.2]
betas = [0.3, 0.4]
output = qp.train_QAOA(gammas=gammas, betas=betas, regular_loss=False, cvar_delta=0.1)

To use qiboml’s pytorch training loop instead of the legacy optimizer, set engine="qiboml":

from qiboopt.opt_class.opt_class import QUBO
qp = QUBO(0, {(0, 0): 1.0, (1, 1): 1.0})
gammas = [0.1, 0.2]
betas = [0.3, 0.4]
output = qp.train_QAOA(
   gammas=gammas,
   betas=betas,
   engine="qiboml",
   optimizer="adam",
   lr=0.05,
   epochs=100,
)

You can also run in exact (no-shot) mode by setting nshots=None (or nshots=0):

from qiboopt.opt_class.opt_class import QUBO
gammas = [0.1, 0.2]
betas = [0.3, 0.4]
output = qp.train_QAOA(gammas=gammas, betas=betas, nshots=None)

In sampled mode (nshots > 0), the returned dictionary contains bitstring counts. In exact mode (nshots is None or nshots == 0), it contains exact bitstring probabilities.