Phase transitions in random circuit sampling
Alexis Morvan, Benjamin Villalonga, Xiao Mi, Salvatore Mandrà, Andreas Bengtsson, Paul V. Klimov, Z. Chen, Sabrina Hong, Catherine Erickson, Ilya Drozdov, J. Chau, G. Laun, R. Movassagh, Abraham Asfaw, Luís T. A. N. Brandão, René Peralta, Dmitry A. Abanin, Rajeev Acharya, R. M. Allen, T. I. Andersen, K. R. Anderson, M. Ansmann, Frank Arute, Kunal Arya, Juan Atalaya, Joseph C. Bardin, Alexander Bilmes, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, L. Brill, Michael Broughton, B. B. Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Juan Campero, Hung-Shen Chang, B. Chiaro, D. Chik, C. W. Chou, J. Cogan, Roberto Collins, P. Conner, William Courtney, A. L. Crook, Ben Curtin, Dripto M. Debroy, Alexander Del Toro Barba, Sean Demura, Agustín Di Paolo, A. Dunsworth, Lara Faoro, Edward Farhi, Reza Fatemi, V. S. Ferreira, Leslie Flores Burgos, Ebrahim Forati, A. G. Fowler, Brooks Foxen, G. Garcia, Élie Genois, William Giang, Craig Gidney, D. Gilboa, Marissa Giustina, Raja Gosula, Alejandro Grajales Dau, Jonathan A. Gross, Steve Habegger, Michael C. Hamilton, M. Hansen, Matthew P. Harrigan, Sean D. Harrington, Paula Heu, M. R. Hoffmann, Trent Huang, Ashley Huff, William J. Huggins, L. B. Ioffe, S. V. Isakov, Justin Iveland, E. Jeffrey, Z. Jiang, C. Jones, Pavol Juhás, Dvir Kafri, Tanuj Khattar, Mostafa Khezri, Mária Kieferová, S. Kim, Alexei Kitaev, A. R. Klots, A. N. Korotkov, Fedor Kostritsa, John Mark Kreikebaum, David Landhuis, Pavel Laptev, K-M Lau
Abstract
Undesired coupling to the surrounding environment destroys long-range correlations in quantum processors and hinders coherent evolution in the nominally available computational space. This noise is an outstanding challenge when leveraging the computation power of near-term quantum processors1. It has been shown that benchmarking random circuit sampling with cross-entropy benchmarking can provide an estimate of the effective size of the Hilbert space coherently available2–8. Nevertheless, quantum algorithms’ outputs can be trivialized by noise, making them susceptible to classical computation spoofing. Here, by implementing an algorithm for random circuit sampling, we demonstrate experimentally that two phase transitions are observable with cross-entropy benchmarking, which we explain theoretically with a statistical model. The first is a dynamical transition as a function of the number of cycles and is the continuation of the anti-concentration point in the noiseless case. The second is a quantum phase transition controlled by the error per cycle; to identify it analytically and experimentally, we create a weak-link model, which allows us to vary the strength of the noise versus coherent evolution. Furthermore, by presenting a random circuit sampling experiment in the weak-noise phase with 67 qubits at 32 cycles, we demonstrate that the computational cost of our experiment is beyond the capabilities of existing classical supercomputers. Our experimental and theoretical work establishes the existence of transitions to a stable, computationally complex phase that is reachable with current quantum processors. By implementing random circuit sampling, experimental and theoretical results establish the existence of transitions to a stable, computationally complex phase that is reachable with current quantum processors.