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arXiv · 2011.08165

Generating Target Graph Couplings for QAOA from Native Quantum Hardware Couplings

Joel Rajakumar·Jai Moondra·Bryan Gard·Swati Gupta·Creston D. Herold
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Abstract

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 that generate arbitrary unweighted coupling graphs with $n$ nodes in $O(n)$ global entangling operations and weighted graphs with $m$ edges in $O(m)$ operations. 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 $n\le8$ and show that optimal sequences, which use fewer operations, can be found using mixed-integer programs. Noisy simulations of Max-Cut QAOA show that our implementation is less susceptible to noise than the standard gate-based compilation.

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Joel Rajakumar, Jai Moondra, Bryan Gard, Swati Gupta, Creston D. Herold. 2020-11-16. Generating Target Graph Couplings for QAOA from Native Quantum Hardware Couplings. https://doi.org/10.1103/physreva.106.022606

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