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arXiv:2609.28657

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

Tigran Sedrakyan, Yuxuan Zhang, Hovnatan Karapetyan, Joshua D. Baktay, Hrant Gharibyan, Hayk Tepanyan

quant-phSubmitted Sep 23, 2026• Announced Sep 25, 2026• 0 citations• Revised Oct 15, 2026 (v2)
v1 · Sep 23, 2026v2 · Oct 15, 2026
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Abstract

We report forward random-circuit sampling (RCS) on the 120-qubit Nighthawk r2 superconducting processor (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 $F_{\mathrm{XEB}}(36)=2.3\times10^{-3}$ under favorable memory assumptions this implies $1.2\times10^{27}$ 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.

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In the relentless pursuit of quantum computational advantage, we present a significant advancement with the development of Zuchongzhi 3.0. This superconducting quantum computer prototype, comprising 105 qubits, achieves high operational fidelities, with single-qubit gates, two-qubit gates, and readout fidelity at 99.90%, 99.62%, and 99.13%, respectively. Our experiments with an 83-qubit, 32-cycle random circuit sampling on the Zuchongzhi 3.0 highlight its superior performance, achieving 1×10^{6} samples in just a few hundred seconds. This task is estimated to be infeasible on the most powerful classical supercomputers, Frontier, which would require approximately 5.9×10^{9} yr to replicate the task. This leap in processing power places the classical simulation cost 6 orders of magnitude beyond Google's SYC-67 and SYC-70 experiments [Morvan et al., Nature 634, 328 (2024)10.1038/s41586-024-07998-6], firmly establishing a new benchmark in quantum computational advantage. Our work not only advances the frontiers of quantum computing but also lays the groundwork for a new era where quantum processors play an essential role in tackling sophisticated real-world challenges.
Random circuit sampling has become a popular means for demonstrating the superiority of quantum computers over classical supercomputers. While quantum chips are evolving rapidly, classical sampling algorithms are also getting better and better. The major challenge is to generate bitstrings exhibiting an XEB fidelity above that of the quantum chips. Here we present a classical sampling algorithm for producing the probability distribution of any given random quantum circuit, where the fidelity can be rigorously bounded. Specifically, our algorithm performs rejection sampling after the introduced very recently multi-tensor contraction algorithm. We show that the fidelity can be controlled by partially contracting the dominant paths in the tensor network and by adjusting the number of batches used in the rejection sampling. As a demonstration, we classically produced 1 million samples with the fidelity bounded by 0.2%, based on the 20-cycle circuit of the Sycamore 53-qubit quantum chip. Though this task was initially estimated to take 10,000 years on the Summit supercomputer, it took about 14.5 days using our algorithm on a relatively small cluster with 32 GPUs (Tesla V100 16GB). Furthermore, we estimate that for the Zuchongzhi 56-qubit 20-cycle circuit one can produce 1M samples with fidelity 0.066% using the Selene supercomputer with 4480 GPUs (Tesla A100 80GB) in about 4 days.
We classically simulate the IBM doped Clifford random circuit sampling experiment, comprising 707070 qubits, 707070 entangling layers, and 468468468 inserted TTT gates, as reported in the first version of arXiv:2607.25941. A deterministic temporal-boundary tensor network contraction approach is specifically designed to tackle such open-boundary one-dimensional brickwork circuits with operator-Schmidt-rank-222 entangling gates. For an nnn-qubit circuit of depth ddd, the resulting unsliced path evaluates an exact amplitude with contraction width ⌈d/2⌉\lceil d/2\rceil⌈d/2⌉; Ratcatcher calculations certify that no smaller width is possible for the tested instances. Because one-qubit gates are absorbed without changing the network topology, the width and dense scheduled contraction cost are independent of their values and of the number and placement of TTT gates. For this initial instance, its largest intermediate tensor contains 2352^{35}235 complex64 entries (256 times smaller than IBM's estimation), corresponding to a tensor payload of 256256256 GiB, and is distributed across eight GPUs within a node. Using 32 nodes, with eight NVIDIA H100 GPUs per node, we completed all 2051 amplitude batches corresponding to IBM's published output bitstrings in 37.3 minutes. The resulting probabilities yield a log-XEB estimate of 0.350340.350340.35034 with a 95% interval of [0.29763,0.40305][0.29763,0.40305][0.29763,0.40305]. Under the Porter--Thomas and scrambled-noise assumptions, this is numerically compatible with IBM's fidelity lower bound; separately, fidelity-weighted resource accounting projects a 583-contraction workload with a 10.6-minute makespan on the same 32 nodes. More broadly, the approach provides a practical diagnostic for experimental outputs and a quantitative tool for designing future doped Clifford sampling experiments.
Random circuit sampling, the task to sample bit strings from a random unitary operator, has been performed to demonstrate quantum advantage on the Sycamore quantum processor with 53 qubits and on the Zuchongzhi quantum processor with 56 and 61 qubits. Recently, it has been claimed that classical computers using tensor network simulation could catch on current noisy quantum processors for random circuit sampling. While the linear cross entropy benchmark fidelity is used to certify all these claims, it may not capture in detail statistical properties of outputs. Here, we compare the bit strings sampled from classical computers using tensor network simulation by Pan et al. [Phys. Rev. Lett. 129, 090502 (2022)] and by Kalachev et al. [arXiv:2112.15083 (2021)] and from the Sycamore and Zuchongzhi quantum processors. It is shown that all Kalachev et al.'s samples pass the NIST random number tests. The heat maps of bit strings show that Pan et al.'s and Kalachev et al.'s samples are quite different from the Sycamore or Zuzhongzhi samples. The analysis with the Marchenko-Pastur distribution and the Wasssertein distances demonstrates that Kalachev et al.'s samples are statistically close to the Sycamore samples than Pan et al.'s while the three datasets have similar values of the linear cross entropy fidelity. Our finding implies that further study is needed to certify or beat the claims of quantum advantage for random circuit sampling.
Random circuit sampling, the task of sampling bit strings from a random unitary operator, has been implemented to demonstrate quantum advantage on the Sycamore quantum processor with 53 qubits and on the Zuchongzhi quantum processor with 56 and 61 qubits. Recently, it was claimed that classical computers using tensor network simulation could catch on to current noisy quantum processors for random circuit sampling. While the linear cross-entropy benchmark fidelity was used to certify all these claims, it may not capture statistical properties of outputs in detail. Here, we compare the bit strings sampled from classical computers using tensor network simulation by Pan et al. [F. Pan, K. Chen, and P. Zhang, Phys. Rev. Lett. 129, 090502 (2022)] and by Kalachev et al. [G. Kalachev, P. Panteleev, P. Zhou, and M.-H. Yung, arXiv:2112.15083] with the bit strings from the Sycamore quantum processor. It is shown that all of Kalachev et al.'s samples passed the NIST random number tests. The heat maps of bit strings show that Pan et al.'s and Kalachev et al.'s samples are quite different from the Sycamore or Zuchongzhi samples. The analysis with the Marchenko-Pastur distribution and the Wasssertein distances demonstrates that Kalachev et al.'s samples are statistically closer to the Sycamore samples than Pan et al.'s while the three datasets have similar values for the linear cross-entropy fidelity. Our finding implies that further study is needed to certify or beat the claims of quantum advantage using random circuit sampling.
Scaling up to a large number of qubits with high-precision control is essential in the demonstrations of quantum computational advantage to exponentially outpace the classical hardware and algorithmic improvements. Here, we develop a two-dimensional programmable superconducting quantum processor, Zuchongzhi, which is composed of 66 functional qubits in a tunable coupling architecture. To characterize the performance of the whole system, we perform random quantum circuits sampling for benchmarking, up to a system size of 56 qubits and 20 cycles. The computational cost of the classical simulation of this task is estimated to be 2-3 orders of magnitude higher than the previous work on 53-qubit Sycamore processor [Nature 574, 505 (2019)NATUAS0028-083610.1038/s41586-019-1666-5. We estimate that the sampling task finished by Zuchongzhi in about 1.2 h will take the most powerful supercomputer at least 8 yr. Our work establishes an unambiguous quantum computational advantage that is infeasible for classical computation in a reasonable amount of time. The high-precision and programmable quantum computing platform opens a new door to explore novel many-body phenomena and implement complex quantum algorithms.