The Quantum Circuit Compilation Problem (QCCP) is challenging to the Artificial Intelligence community. It was already tackled with temporal planning, constraint programming, greedy heuristics and other techniques. In this paper, QCCP is formulated as a scheduling problem and solved by a genetic algorithm. We focus on QCCP for Quantum Approximation Optimization Algorithms (QAOA) applied to the MaxCut problem and consider Noisy Intermediate Scale Quantum (NISQ) hardware architectures. Based on the fact that these algorithms apply a set of basic quantum operations repeatedly over a number of rounds, we propose a genetic algorithm approach, termed Decomposition Based Genetic Algorithm (DBGA), that in each round extends the partial solutions obtained for the previous ones. DBGA is compared to the state of the art across a set of conventional instances. The results of the experimental study provided interesting insight in the problem structure and showed that DBGA is quite competitive with the state of the art. In particular, DBGA outperformed the best current method on the largest instances and provided new best solutions to most of them.
The quantum approximate optimization algorithm (QAOA) transforms a simple many-qubit wave function into one that encodes a solution to a difficult classical optimization problem. It does this by optimizing the schedule according to which two unitary operators are alternately applied to the qubits. In this paper, the QAOA is modified by updating the operators themselves to include local fields, using information from the measured wave function at the end of one iteration step to improve the operators at later steps. It is shown by numerical simulation on MaxCut problems that, for a fixed accuracy, this procedure decreases the runtime of QAOA very substantially. This improvement appears to increase with the problem size. Our method requires essentially the same number of quantum gates per optimization step as the standard QAOA, and no additional measurements. This modified algorithm enhances the prospects for quantum advantage for certain optimization problems.
In the search for quantum advantage in real--world problems, one promising avenue is to use a quantum algorithm to improve on the solution found using an efficient classical algorithm. The quantum approximate optimization algorithm (QAOA) is particularly well adapted for such a "warm start" approach, and can be combined with the powerful classical Goemans-Williamson (GW) algorithms based on semi-definite programming. Nonetheless, the best way to leverage the power of the QAOA remains an open question. Here we propose a general model that describes a class of QAOA variants, and use it to explore routes to quantum advantages in a canonical optimization problem, MaxCut. For these algorithms we derive analytic expectation values of the cost Hamiltonian for the MaxCut problem in the level-1 case. Using these analytic results we obtain reliable averages over many instances for fairly large numbers of qubits. We find that the warm start adaptive-bias QAOA (WS-ab-QAOA) initialized by the GW algorithm outperforms previously proposed warm start variants on problems with
40 to
180 qubits. To assess whether a quantum advantage exists with this algorithm, we did numerical simulations with up to
1000 qubits to see whether the level-1 WS-ab-QAOA can improve the GW solution for 3-regular graphs. In fact the improvement in the
1000-qubit case even in level 1 can only be matched by the GW algorithm after about
105.5 random projections performed after the semi-definite program stage. This work gives evidence that the final stage of optimization after an efficient classical algorithm has produced an approximate solution may be a place where quantum advantages can be realized.