Generating Target Graph Couplings for QAOA from Native Quantum Hardware Couplings
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We present methods for constructing any target coupling graph using limited global controls in an Ising-like quantum spin system. Our approach is motivated by implementing the quantum approximate optimization algorithm (QAOA) on trapped ion quantum hardware to find approximate solutions to Max-Cut. We present a mathematical description of the problem and provide approximately optimal algorithmic constructions which generate arbitrary unweighted coupling graphs with n nodes in O(n) global control pulses and weighted graphs with m edges in O(m) pulses. These upper bounds are not tight in general, and we formulate a mixed-integer program to solve the graph coupling problem to optimality. We perform numeric experiments on small graphs with n ≤ 8 show that optimal pulse sequences, which use fewer operations, can be found using mixed-integer programs.
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