Phase transition in Random Circuit Sampling
Abstract
Undesired coupling to the surrounding environment destroys long-range correlations on quantum processors and hinders the coherent evolution in the nominally available computational space. This incoherent noise is an outstanding challenge to fully leverage the computation power of near-term quantum processors. It has been shown that benchmarking Random Circuit Sampling (RCS) with Cross-Entropy Benchmarking (XEB) can provide a reliable estimate of the effective size of the Hilbert space coherently available. The extent to which the presence of noise can trivialize the outputs of a given quantum algorithm, i.e. making it spoofable by a classical computation, is an unanswered question. Here, by implementing an RCS algorithm we demonstrate experimentally that there are two phase transitions observable with XEB, 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 varying the strength of noise versus coherent evolution. Furthermore, by presenting an RCS experiment with 67 qubits at 32 cycles, we demonstrate that the computational cost of our experiment is beyond the capabilities of existing classical supercomputers, even when accounting for the inevitable presence of noise. Our experimental and theoretical work establishes the existence of transitions to a stable computationally complex phase that is reachable with current quantum processors.
Cite
@article{arxiv.2304.11119,
title = {Phase transition in Random Circuit Sampling},
author = {A. Morvan and B. Villalonga and X. Mi and S. Mandrà and A. Bengtsson and P. V. Klimov and Z. Chen and S. Hong and C. Erickson and I. K. Drozdov and J. Chau and G. Laun and R. Movassagh and A. Asfaw and L. T. A. N. Brandão and R. Peralta and D. Abanin and R. Acharya and R. Allen and T. I. Andersen and K. Anderson and M. Ansmann and F. Arute and K. Arya and J. Atalaya and J. C. Bardin and A. Bilmes and G. Bortoli and A. Bourassa and J. Bovaird and L. Brill and M. Broughton and B. B. Buckley and D. A. Buell and T. Burger and B. Burkett and N. Bushnell and J. Campero and H. S. Chang and B. Chiaro and D. Chik and C. Chou and J. Cogan and R. Collins and P. Conner and W. Courtney and A. L. Crook and B. Curtin and D. M. Debroy and A. Del Toro Barba and S. Demura and A. Di Paolo and A. Dunsworth and L. Faoro and E. Farhi and R. Fatemi and V. S. Ferreira and L. Flores Burgos and E. Forati and A. G. Fowler and B. Foxen and G. Garcia and E. Genois and W. Giang and C. Gidney and D. Gilboa and M. Giustina and R. Gosula and A. Grajales Dau and J. A. Gross and S. Habegger and M. C. Hamilton and M. Hansen and M. P. Harrigan and S. D. Harrington and P. Heu and M. R. Hoffmann and T. Huang and A. Huff and W. J. Huggins and L. B. Ioffe and S. V. Isakov and J. Iveland and E. Jeffrey and Z. Jiang and C. Jones and P. Juhas and D. Kafri and T. Khattar and M. Khezri and M. Kieferová and S. Kim and A. Kitaev and A. R. Klots and A. N. Korotkov and F. Kostritsa and J. M. Kreikebaum and D. Landhuis and P. Laptev and K. -M. Lau and L. Laws and J. Lee and K. W. Lee and Y. D. Lensky and B. J. Lester and A. T. Lill and W. Liu and W. P. Livingston and A. Locharla and F. D. Malone and O. Martin and S. Martin and J. R. McClean and M. McEwen and K. C. Miao and A. Mieszala and S. Montazeri and W. Mruczkiewicz and O. Naaman and M. Neeley and C. Neill and A. Nersisyan and M. Newman and J. H. Ng and A. Nguyen and M. Nguyen and M. Yuezhen Niu and T. E. O'Brien and S. Omonije and A. Opremcak and A. Petukhov and R. Potter and L. P. Pryadko and C. Quintana and D. M. Rhodes and E. Rosenberg and C. Rocque and P. Roushan and N. C. Rubin and N. Saei and D. Sank and K. Sankaragomathi and K. J. Satzinger and H. F. Schurkus and C. Schuster and M. J. Shearn and A. Shorter and N. Shutty and V. Shvarts and V. Sivak and J. Skruzny and W. C. Smith and R. D. Somma and G. Sterling and D. Strain and M. Szalay and D. Thor and A. Torres and G. Vidal and C. Vollgraff Heidweiller and T. White and B. W. K. Woo and C. Xing and Z. J. Yao and P. Yeh and J. Yoo and G. Young and A. Zalcman and Y. Zhang and N. Zhu and N. Zobrist and E. G. Rieffel and R. Biswas and R. Babbush and D. Bacon and J. Hilton and E. Lucero and H. Neven and A. Megrant and J. Kelly and I. Aleiner and V. Smelyanskiy and K. Kechedzhi and Y. Chen and S. Boixo},
journal= {arXiv preprint arXiv:2304.11119},
year = {2024}
}