Quantum Approximate Optimization of Non-Planar Graph Problems on a Planar Superconducting Processor
Abstract
We demonstrate the application of the Google Sycamore superconducting qubit quantum processor to combinatorial optimization problems with the quantum approximate optimization algorithm (QAOA). Like past QAOA experiments, we study performance for problems defined on the (planar) connectivity graph of our hardware; however, we also apply the QAOA to the Sherrington-Kirkpatrick model and MaxCut, both high dimensional graph problems for which the QAOA requires significant compilation. Experimental scans of the QAOA energy landscape show good agreement with theory across even the largest instances studied (23 qubits) and we are able to perform variational optimization successfully. For problems defined on our hardware graph we obtain an approximation ratio that is independent of problem size and observe, for the first time, that performance increases with circuit depth. For problems requiring compilation, performance decreases with problem size but still provides an advantage over random guessing for circuits involving several thousand gates. This behavior highlights the challenge of using near-term quantum computers to optimize problems on graphs differing from hardware connectivity. As these graphs are more representative of real world instances, our results advocate for more emphasis on such problems in the developing tradition of using the QAOA as a holistic, device-level benchmark of quantum processors.
Cite
@article{arxiv.2004.04197,
title = {Quantum Approximate Optimization of Non-Planar Graph Problems on a Planar Superconducting Processor},
author = {Matthew P. Harrigan and Kevin J. Sung and Matthew Neeley and Kevin J. Satzinger and Frank Arute and Kunal Arya and Juan Atalaya and Joseph C. Bardin and Rami Barends and Sergio Boixo and Michael Broughton and Bob B. Buckley and David A. Buell and Brian Burkett and Nicholas Bushnell and Yu Chen and Zijun Chen and Ben Chiaro and Roberto Collins and William Courtney and Sean Demura and Andrew Dunsworth and Daniel Eppens and Austin Fowler and Brooks Foxen and Craig Gidney and Marissa Giustina and Rob Graff and Steve Habegger and Alan Ho and Sabrina Hong and Trent Huang and L. B. Ioffe and Sergei V. Isakov and Evan Jeffrey and Zhang Jiang and Cody Jones and Dvir Kafri and Kostyantyn Kechedzhi and Julian Kelly and Seon Kim and Paul V. Klimov and Alexander N. Korotkov and Fedor Kostritsa and David Landhuis and Pavel Laptev and Mike Lindmark and Martin Leib and Orion Martin and John M. Martinis and Jarrod R. McClean and Matt McEwen and Anthony Megrant and Xiao Mi and Masoud Mohseni and Wojciech Mruczkiewicz and Josh Mutus and Ofer Naaman and Charles Neill and Florian Neukart and Murphy Yuezhen Niu and Thomas E. O'Brien and Bryan O'Gorman and Eric Ostby and Andre Petukhov and Harald Putterman and Chris Quintana and Pedram Roushan and Nicholas C. Rubin and Daniel Sank and Andrea Skolik and Vadim Smelyanskiy and Doug Strain and Michael Streif and Marco Szalay and Amit Vainsencher and Theodore White and Z. Jamie Yao and Ping Yeh and Adam Zalcman and Leo Zhou and Hartmut Neven and Dave Bacon and Erik Lucero and Edward Farhi and Ryan Babbush},
journal= {arXiv preprint arXiv:2004.04197},
year = {2021}
}
Comments
19 pages, 15 figures