Quantum Local Search with the Quantum Alternating Operator Ansatz

Abstract

We present a new hybrid, local search algorithm for quantum approximate optimization of constrained combinatorial optimization problems. We focus on the Maximum Independent Set problem and demonstrate the ability of quantum local search to solve large problem instances on quantum devices with few qubits. This hybrid algorithm iteratively finds independent sets over carefully constructed neighborhoods and combines these solutions to obtain a global solution. We study the performance of this algorithm on 3-regular, Community, and Erdős-Rényi graphs with up to 100 nodes.

Investigating the effect of circuit cutting in QAOA for the MaxCut problem on NISQ devices

“…Besides methods on the circuit level, decomposition approaches on the algorithmic level exist [18,[43][44][45][46][47][48]. Examples include divide and conquer approaches for QAOA [18,43] and quantum local search methods that iteratively optimize local subproblems of a problem [44][45][46][47].…”

“…Besides methods on the circuit level, decomposition approaches on the algorithmic level exist [18,[43][44][45][46][47][48]. Examples include divide and conquer approaches for QAOA [18,43] and quantum local search methods that iteratively optimize local subproblems of a problem [44][45][46][47]. In addition, Ayanzadeh et al [48] demonstrate for the MaxCut problem that by removing nodes with high connectivity from the graph and accounting for their possible assignments in the objective function, the circuit size can be reduced, and the fidelity of QAOA on NISQ devices can increase.…”

“…Moreover, as circuit cutting operates at the level of quantum circuits, it is to be expected that the results generalize to other problems and VQAs. Furthermore, other decomposition schemes in VQAs [18,[43][44][45][46] that reduce the size of executed quantum circuits may exhibit similar effects. Both will be evaluated as part of our future work.…”

Investigating the effect of circuit cutting in QAOA for the MaxCut problem on NISQ devices

“…Besides methods on the circuit level, decomposition approaches on the algorithmic level exist [18,[44][45][46][47][48][49]. Examples include divide and conquer approaches for QAOA [18,44] and quantum local search methods that iteratively optimize local subproblems of a problem [45][46][47][48].…”

“…Besides methods on the circuit level, decomposition approaches on the algorithmic level exist [18,[44][45][46][47][48][49]. Examples include divide and conquer approaches for QAOA [18,44] and quantum local search methods that iteratively optimize local subproblems of a problem [45][46][47][48]. In addition, Ayanzadeh et al [49] demonstrate for the MaxCut problem that by removing nodes with high connectivity from the graph and accounting for their possible assignments in the objective function, the circuit size can be reduced, and the fidelity of QAOA on NISQ devices can increase.…”