Multi-angle quantum approximate optimization algorithm

Herrman, Rebekah; Lotshaw, Phillip C.; Ostrowski, James; Humble, Travis S.; Siopsis, George

doi:10.1038/s41598-022-10555-8

Multi-angle quantum approximate optimization algorithm

Journal Article · Tue Apr 26 00:00:00 EDT 2022 · Scientific Reports

DOI:https://doi.org/10.1038/s41598-022-10555-8· OSTI ID:1869104

Herrman, Rebekah ^[1]; ^[2]; Ostrowski, James ^[1]; Humble, Travis S. ^[2]; Siopsis, George ^[1]

Univ. of Tennessee, Knoxville, TN (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Quantum Computing Inst.

The quantum approximate optimization algorithm (QAOA) generates an approximate solution to combinatorial optimization problems using a variational ansatz circuit defined by parameterized layers of quantum evolution. In theory, the approximation improves with increasing ansatz depth but gate noise and circuit complexity undermine performance in practice. Here, we investigate a multi-angle ansatz for QAOA that reduces circuit depth and improves the approximation ratio by increasing the number of classical parameters. Even though the number of parameters increases, our results indicate that good parameters can be found in polynomial time for a test dataset we consider. This new ansatz gives a 33% increase in the approximation ratio for an infinite family of MaxCut instances over QAOA. The optimal performance is lower bounded by the conventional ansatz, and we present empirical results for graphs on eight vertices that one layer of the multi-angle anstaz is comparable to three layers of the traditional ansatz on MaxCut problems. Similarly, multi-angle QAOA yields a higher approximation ratio than QAOA at the same depth on a collection of MaxCut instances on fifty and one-hundred vertex graphs. Many of the optimized parameters are found to be zero, so their associated gates can be removed from the circuit, further decreasing the circuit depth. These results indicate that multi-angle QAOA requires shallower circuits to solve problems than QAOA, making it more viable for near-term intermediate-scale quantum devices.

View Accepted Manuscript (DOE)

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: National Science Foundation (NSF); US Air Force Office of Scientific Research (AFOSR); US Army Research Office (ARO); USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1869104

Journal Information:: Scientific Reports, Journal Name: Scientific Reports Journal Issue: 1 Vol. 12; ISSN 2045-2322

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

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Scaling quantum approximate optimization on near-term hardware Lotshaw, Phillip C.; Nguyen, Thien; Santana, Anthony Scientific Reports, Vol. 12, Issue 1 https://doi.org/10.1038/s41598-022-14767-w	journal	July 2022
Simulations of Frustrated Ising Hamiltonians with Quantum Approximate Optimization Lotshaw, Phillip C.; Xu, Hanjing; Khalid, Bilal arXiv https://doi.org/10.48550/arxiv.2206.05343	text	January 2022

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