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arXiv · 2004.04197

Quantum Approximate Optimization of Non-Planar Graph Problems on a Planar Superconducting Processor

Matthew P. Harrigan·Kevin J. Sung·Matthew Neeley·Kevin J. Satzinger·Frank Arute·Kunal Arya·Juan Atalaya·Joseph C. Bardin·Rami Barends·Sergio Boixo·Michael Broughton·Bob B. Buckley·David A. Buell·Brian Burkett·Nicholas Bushnell·Yu Chen·Zijun Chen·Ben Chiaro·Roberto Collins·William Courtney·Sean Demura·Andrew Dunsworth·Daniel Eppens·Austin Fowler·Brooks Foxen·Craig Gidney·Marissa Giustina·Rob Graff·Steve Habegger·Alan Ho·Sabrina Hong·Trent Huang·L. B. Ioffe·Sergei V. Isakov·Evan Jeffrey·Zhang Jiang·Cody Jones·Dvir Kafri·Kostyantyn Kechedzhi·Julian Kelly·Seon Kim·Paul V. Klimov·Alexander N. Korotkov·Fedor Kostritsa·David Landhuis·Pavel Laptev·Mike Lindmark·Martin Leib·Orion Martin·John M. Martinis·Jarrod R. McClean·Matt McEwen·Anthony Megrant·Xiao Mi·Masoud Mohseni·Wojciech Mruczkiewicz·Josh Mutus·Ofer Naaman·Charles Neill·Florian Neukart·Murphy Yuezhen Niu·Thomas E. O'Brien·Bryan O'Gorman·Eric Ostby·Andre Petukhov·Harald Putterman·Chris Quintana·Pedram Roushan·Nicholas C. Rubin·Daniel Sank·Andrea Skolik·Vadim Smelyanskiy·Doug Strain·Michael Streif·Marco Szalay·Amit Vainsencher·Theodore White·Z. Jamie Yao·Ping Yeh·Adam Zalcman·Leo Zhou·Hartmut Neven·Dave Bacon·Erik Lucero·Edward Farhi·Ryan Babbush
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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.

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Matthew P. Harrigan, Kevin J. Sung, Matthew Neeley, Kevin J. Satzinger, Frank Arute, Kunal Arya, Juan Atalaya, Joseph C. Bardin, Rami Barends, Sergio Boixo, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, Yu Chen, Zijun Chen, Ben Chiaro, Roberto Collins, William Courtney, Sean Demura, Andrew Dunsworth, Daniel Eppens, Austin Fowler, Brooks Foxen, Craig Gidney, Marissa Giustina, Rob Graff, Steve Habegger, Alan Ho, Sabrina Hong, Trent Huang, L. B. Ioffe, Sergei V. Isakov, Evan Jeffrey, Zhang Jiang, Cody Jones, Dvir Kafri, Kostyantyn Kechedzhi, Julian Kelly, Seon Kim, Paul V. Klimov, Alexander N. Korotkov, Fedor Kostritsa, David Landhuis, Pavel Laptev, Mike Lindmark, Martin Leib, Orion Martin, John M. Martinis, Jarrod R. McClean, Matt McEwen, Anthony Megrant, Xiao Mi, Masoud Mohseni, Wojciech Mruczkiewicz, Josh Mutus, Ofer Naaman, Charles Neill, Florian Neukart, Murphy Yuezhen Niu, Thomas E. O'Brien, Bryan O'Gorman, Eric Ostby, Andre Petukhov, Harald Putterman, Chris Quintana, Pedram Roushan, Nicholas C. Rubin, Daniel Sank, Andrea Skolik, Vadim Smelyanskiy, Doug Strain, Michael Streif, Marco Szalay, Amit Vainsencher, Theodore White, Z. Jamie Yao, Ping Yeh, Adam Zalcman, Leo Zhou, Hartmut Neven, Dave Bacon, Erik Lucero, Edward Farhi, Ryan Babbush. 2020-04-08. Quantum Approximate Optimization of Non-Planar Graph Problems on a Planar Superconducting Processor. https://doi.org/10.1038/s41567-020-01105-y

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