In 2019, Google made a sensational announcement claiming that its quantum computer had performed a calculation in just 200 seconds that would take a classical supercomputer 10,000 years. IBM countered almost immediately, arguing that with optimized algorithms and storage, an existing classical machine could solve the exact same problem in 2.5 days. This dramatic exchange exposed to the world the ambiguity inherent in the very concept of "quantum advantage." Even if a quantum computer calculates something at overwhelming speed, there has been no way to verify whether the answer it produces is actually correct. That unresolved dilemma has remained a heavy, unaddressed problem lurking beneath the surface of the quantum computing field.
The problem of verifying quantum computation has an extremely simple yet troublesome structure. When a quantum computer runs in uncharted territory beyond the reach of classical computers, checking whether its computational result is correct using a classical machine becomes, by definition, impossible. If there's no way to check the answer, then in the extreme case, a machine could output a jumble of noise and errors and still claim "this is the correct answer." None of the quantum advantage demonstrations reported so far have squarely solved this fundamental problem; instead, they have sidestepped the burden of proof by relying on the strong assumption that "since the circuit worked correctly at a small, easily computable size, it should work correctly the same way at a larger size beyond the reach of classical machines."
On July 30, 2026, a team from IBM and the University of Chicago announced an experiment that ran through without taking this detour. The paper is titled "Sampling hard circuits with verifiably high fidelity." How did they manage to satisfy both requirements at once—surpassing the limits of classical computation while mathematically guaranteeing the correctness of the answer?
The Asymmetry Between Clifford Gates and T Gates Was the Starting Point of the Solution
The gates that make up a quantum circuit have a fundamental asymmetry in their affinity with classical computers. A group of gates called "Clifford gates" (the Hadamard gate, phase gate, CNOT, and others) can be efficiently simulated on a classical computer no matter how many qubits are combined. This is formalized as the Gottesman-Knill theorem, and a circuit made up only of Clifford gates is equivalent to a state where "the quantum computer isn't doing anything it's good at."
In contrast, the "T gate" (a non-Clifford gate) exponentially increases the cost of classical simulation with each addition. T gates are the essential "fuel" of quantum computation. However, using T gates makes error detection difficult. A circuit composed only of Clifford gates can detect errors, but mixing in T gates disrupts that structure—or so the conventional wisdom held.
The research team from IBM and the University of Chicago found a breakthrough here. What they built is an error-detection framework called a "spacetime code." First, they construct the entire circuit using only Clifford gates, which are easy to simulate classically. In this state, any errors that occur during the computation can be reliably caught. On top of this, they carefully "grafted" the T gates—the "fuel" of the computation—into specific positions that could slip through the mesh of the error-detection net. Add too many T gates recklessly and errors become invisible; use too few and a classical computer catches up. The team mathematically derived a structure that achieves this delicate balance.
As a result, even with 468 T gates embedded in a 70-qubit circuit, the error-detection mechanism continued to function without breaking down. According to the paper's authors, 468 is more than twice the threshold at which classical simulation becomes possible. The team executed 2,415 logical two-qubit operations on a Heron processor, and among the execution results that were not rejected as errors, they confirmed that more than 28% had faithfully completed the computation. The lower bound of fidelity was calculated to be 0.284, a statistical guarantee with a 95% confidence level. No past quantum advantage experiment has been able to produce numbers backed by such rigorous proof.
15 Minutes and an 860-Fold Cost
It took the quantum computer about 15 minutes to complete this calculation. The team attempted the same problem using classical simulation methods but stated only that it would require "an impractical amount of computation time." No estimated figure for how long it would take has been disclosed. This stands in contrast to Google's 2019 announcement, which put forward the concrete figure of "10,000 years."
However, this method from IBM and the University of Chicago comes with a clear price. In order to complete the computation while keeping the error-detection scheme functioning, the total number of runs—including those rejected mid-way due to detected errors—ballooned to a full 860 times what it would be under normal circumstances. This is why the figure of "28% completed the computation faithfully" appears low at first glance. The vast majority of the runs are destined to be rejected due to errors. While the error-detection mechanism keeps generating a large volume of "failed" judgments, mathematical certainty is granted only to the small number of "passing" answers that make it through this stringent filter. This is, in a sense, like an extremely strict quality-control factory line that tolerates a poor yield rate in exchange for absolutely never shipping a defective product. How to reduce this high overhead of 860-fold stands as the next massive engineering challenge on the path toward practical quantum computation.
The fact that the logical error rate was suppressed to one-tenth of the physical error rate is a significant figure as a demonstration of quantum error correction. This number marks a step along the path from the "NISQ" (Noisy Intermediate-Scale Quantum) era, which uses raw physical noise as-is, toward computation protected by logical qubits.
Two Other Experiments Sketched the "Contours of Trust"
On the same day, IBM's partner companies also announced independent quantum advantage demonstrations. Both involve problem settings close to physical applications—simulating the behavior of magnetic materials.
Qedma's experimental team tracked "subharmonic prethermal oscillations" of a two-dimensional Floquet Ising magnet using up to 74 qubits on an IBM Heron R3 processor. The paper is titled "Resolving Structure in Prethermal Floquet Dynamics with Precision Quantum Computation." For comparison, they used the Fugaku supercomputer (deploying over 500,000 CPU hours) and an Nvidia H100 GPU server.
The contrast in results is stark. Up to 35 qubits, the quantum computer, Fugaku, and the H100 all showed the same oscillation pattern. At 51 qubits, both Fugaku and the H100 broke down, only able to track the first few pulses. At 74 qubits, the problem was simply beyond the reach of classical methods altogether.
Qedma's CTO Netanel Lindner emphasized the fundamental question of whether this oscillation truly exists in the physical system. To confirm this, the team deliberately verified that turning off error mitigation caused the results to break down, and showed that results using a theoretically guaranteed mitigation method matched classical computation exactly at small scales.
As an even more decisive verification, they confirmed that the same behavior was reproduced on trapped-ion devices—Quantinuum's H2 and Helios. Superconducting chips and trapped ions have entirely different sources of noise and different error characteristics. The fact that identical results emerged from architecturally distinct quantum computers with different physical properties strongly supports the conclusion that the result is not a phantom caused by hardware noise, but a computational truth. "The results we got from Quantinuum match perfectly with the IBM results. That gives us strong confidence," Lindner said.
Algorithmiq (CEO Sabrina Maniscalco) ran a 56-qubit circuit on IBM Heron and showed that in the complex regime where classical methods struggle the most, different classical methods produced mutually contradictory answers. Against the backdrop of this breakdown on the classical side, the correctness of the quantum computer's output was corroborated through careful cross-validation. They confirmed agreement with classical simulation using a shortened version of the circuit, and further showed that the trend of the results obtained did not change even when they slowed down the operation of the gates, deliberately injected noise, or switched to a different quantum processor. "This agreement is not a coincidence. It's evidence," Maniscalco said.
"Not a Single Test, But a Process of Accumulating Trust"
Dominik Hangleiter, a postdoc at ETH Zurich who evaluated all three experiments, endorsed the University of Chicago collaboration's paper as an approach that "shifts from random circuits to structured circuits to make verification possible." However, regarding the Qedma and Algorithmiq studies, he pointed out that "neither paper's authors explicitly claim quantum advantage themselves." They state their results at the level of having shown that classical simulation is difficult, and Hangleiter himself evaluates this restraint as "appropriate."
Professor Jens Eisert of Freie Universität Berlin offers a structural perspective. Quantum advantage, he argues, is not a "finish line" that, once crossed, is settled for good, but a process of continuously building trust by stacking up various verification methods. "Verification of quantum simulation in regimes beyond the reach of classical simulation is not a single procedure, but a process of accumulating trust through a portfolio of multiple complementary verification methods," he wrote in an email to IEEE Spectrum.
All three papers were published on July 30, 2026, but have not yet undergone peer review. Just as IBM's improvements to classical algorithms partially rebutted Google's claim in 2019, a similar possibility exists for these new claims as well. IBM has published its circuits and results on the Quantum Advantage Tracker, explicitly welcoming refutation from the community. If this openness reflects a stance of "we invite you to challenge this," then the fact that this claim will likely continue to be tested by advances in classical algorithms over the coming years is, if anything, evidence that the science of quantum computing is functioning in a healthy way.