Problem-Size Independent Angles for a Grover-Driven Quantum Approximate Optimization Algorithm

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) requires that circuit parameters are determined that allow one to sample from high-quality solutions to combinatorial optimization problems. Such parameters can be obtained using either costly outer-loop optimization procedures and repeated calls to a quantum computer or, alternatively, via analytical means. In this work we demonstrate that if one knows the probability density function describing how the objective function of a problem is distributed, that the calculation of the expectation of such a problem Hamiltonian under a Grover-driven, QAOA-prepared state can be performed independently of system size. Such calculations can help deliver insights into the performance of and predictability of angles in QAOA in the limit of large problem sizes, in particular, for the number partitioning problem.

13 pages, 7 figures

References in corpus (4)

• Parameter Concentration in Quantum Approximate Optimization
• Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian
• Instance Independence of Single Layer Quantum Approximate Optimization Algorithm on Mixed-Spin Models at Infinite Size
• Progress towards analytically optimal angles in quantum approximate optimisation

Cited by in corpus (3)

• Grover-QAOA for 3-SAT: Quadratic Speedup, Fair-Sampling, and Parameter Clustering
• Analytical results for the Quantum Alternating Operator Ansatz with Grover Mixer
• Lower bounds on the number of rounds of the quantum approximate optimization algorithm required for guaranteed approximation ratios