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arXiv · 1904.09314

$XY$-mixers: analytical and numerical results for QAOA

Zhihui Wang·Nicholas C. Rubin·Jason M. Dominy·Eleanor G. Rieffel
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Abstract

The Quantum Alternating Operator Ansatz (QAOA) is a promising gate-model meta-heuristic for combinatorial optimization. Applying the algorithm to problems with constraints presents an implementation challenge for near-term quantum resources. This work explores strategies for enforcing hard constraints by using $XY$-Hamiltonians as mixing operators (mixers). Despite the complexity of simulating the $XY$ model, we demonstrate that for problems represented through one-hot-encoding, certain classes of the mixer Hamiltonian can be implemented without Trotter error in depth $O(κ)$ where $κ$ is the number of assignable colors. We also specify general strategies for implementing QAOA circuits on all-to-all connected hardware graphs and linearly connected hardware graphs inspired by fermionic simulation techniques. Performance is validated on graph coloring problems that are known to be challenging for a given classical algorithm. The general strategy of using $XY$-mixers is borne out numerically, demonstrating a significant improvement over the general $X$-mixer, and moreover the generalized $W$-state yields better performance than easier-to-generate classical initial states when $XY$ mixers are used.

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Zhihui Wang, Nicholas C. Rubin, Jason M. Dominy, Eleanor G. Rieffel. 2020-05-21. $XY$-mixers: analytical and numerical results for QAOA. https://doi.org/10.1103/physreva.101.012320

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