Quantum computational advantage in random-circuit sampling on IBM superconducting quantum computers

We report forward random-circuit sampling (RCS) on the 120-qubit Nighthawk r2 superconducting processor ($\mathit{\text{ibm\_phoenix}}$) with square-lattice connectivity, using 61 qubits, native CZ gates, and the standard cloud execution stack with no benchmark-specific calibration. Two independent fidelity estimators—mirror benchmarking and three- and four-patch cross-entropy benchmarking (XEB)—agree with each other at every measured depth, the mirror from 4 to 40 cycles and the patched estimators from 20 to 40 cycles, across more than two orders of magnitude of fidelity decay, and exceed the first-generation Nighthawk r1 device by more than an order of magnitude at fixed depth. The 36-cycle circuits sit at the depth where tensor-network contraction cost saturates at system size: a contraction-cost estimator validated against the published Sycamore and Zuchongzhi networks places the single-amplitude cost at $\sim$${10}^{22}$ complex operations. At $F_{\mathrm{X}\mathrm{E}\mathrm{B}}(36)=2.3\times {10}^{-3}$ under favorable memory assumptions this implies $1.2\times {10}^{27}$ machine operations within the bounded-fidelity rejection-sampling model — more than a century of runtime on the Frontier supercomputer — to collect a ${10}^6$-sample ensemble, which takes only 19,s on Nighthawk r2. To our knowledge, this is the first demonstration of quantum advantage for a vanilla random-circuit sampling on a commercially and broadly accessible quantum processor that most non-expert quantum computer users can easily replicate.