近日，谷歌研究中心的K. Kechedzhi及其研究团队取得一项新进展。经过不懈努力，他们对随机电路采样中的相变进行研究。相关研究成果已于2024年10月9日在国际权威学术期刊《自然》上发表。

该研究团队通过实现一种随机电路采样算法，并借助交叉熵基准测试，在实验上展示了可观察到两个相变过程，这两个过程研究人员通过统计模型进行了理论解释。第一个是随周期数变化的动态相变，它是无噪声情况下反集中点的延续。第二个是由每周期错误率控制的量子相变；为了从分析和实验上识别它，研究人员构建了一个弱链接模型，该模型使他们能够调整噪声强度与相干演化的相对比例。

此外，通过在弱噪声相下展示一个包含67个量子比特、执行32个周期的随机电路采样实验，研究人员证明了该实验的计算成本已超出当前现有经典超级计算机的能力范围。这项实验和理论工作证实了存在向稳定且计算复杂度高的相的转变，而这种相是当前量子处理器可以达到的。

据悉，周围环境中的不良耦合会破坏量子处理器中的长程相关性，并阻碍在名义上可用的计算空间中的相干演化。这种噪声是利用近期量子处理器计算能力时面临的一个重大挑战。研究表明，通过交叉熵基准测试对随机电路采样进行基准评估，可以估算出相干可用的希尔伯特空间的有效大小。然而，量子算法的输出可能会因噪声而变得无关紧要，从而使它们容易受到经典计算欺骗的影响。

附：英文原文

Title: Phase transitions in random circuit sampling

Author: Morvan, A., Villalonga, B., Mi, X., Mandr, S., Bengtsson, A., Klimov, P. V., Chen, Z., Hong, S., Erickson, C., Drozdov, I. K., Chau, J., Laun, G., Movassagh, R., Asfaw, A., Brando, L. T. A. N., Peralta, R., Abanin, D., Acharya, R., Allen, R., Andersen, T. I., Anderson, K., Ansmann, M., Arute, F., Arya, K., Atalaya, J., Bardin, J. C., Bilmes, A., Bortoli, G., Bourassa, A., Bovaird, J., Brill, L., Broughton, M., Buckley, B. B., Buell, D. A., Burger, T., Burkett, B., Bushnell, N., Campero, J., Chang, H.-S., Chiaro, B., Chik, D., Chou, C., Cogan, J., Collins, R., Conner, P., Courtney, W., Crook, A. L., Curtin, B., Debroy, D. M., Barba, A. Del Toro, Demura, S., Paolo, A. Di, Dunsworth, A., Faoro, L., Farhi, E., Fatemi, R., Ferreira, V. S., Burgos, L. Flores, Forati, E., Fowler, A. G., Foxen, B., Garcia, G., Genois, ., Giang, W., Gidney, C., Gilboa, D., Giustina, M., Gosula, R., Dau, A. Grajales, Gross, J. A., Habegger, S., Hamilton, M. C., Hansen, M.

Issue&Volume: 2024-10-09

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 processors. 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 available. 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.

DOI: 10.1038/s41586-024-07998-6

Source: https://www.nature.com/articles/s41586-024-07998-6