On July 30, 2026, IBM presented three experiments run on its Heron quantum processors as demonstrations of quantum advantage, each described in a preprint that its authors had posted to arXiv that week. “We are now firmly in the quantum advantage era,” Jay Gambetta, director of IBM Research, said in IBM’s announcement.
Quantum advantage is the point at which a quantum computer solves a problem more accurately, cheaply, or quickly than classical methods can. The three teams, from IBM and the University of Chicago, Qedma, and Algorithmiq, made different claims in their papers.
Only the IBM and University of Chicago team reported a certified lower bound on how accurately the quantum processor ran its target circuit, in a preprint that, like the other two, has not been peer reviewed.
Doped Clifford sampling
In their preprint, Simon Martiel, Bill Fefferman of the University of Chicago, Gambetta, Ali Javadi-Abhari, and five colleagues described what they called “a protocol for quantum advantage based on doped Clifford sampling.” They wrote that they had proved the protocol’s “asymptotic hardness” for classical computers.
Circuits built only from Clifford gates, a restricted set of quantum operations, can be simulated efficiently on classical computers, so researchers add non-Clifford T gates, a step called doping, to make them hard to simulate.
The team ran a circuit with 70 layers of two-qubit gates and 468 T gates on IBM’s Boston processor, using 70 physical qubits for data and 27 as helpers, 97 physical qubits in all. IBM described the 70 data qubits as “logical” in its announcement.
The authors embedded the circuit in spacetime codes, which detect errors across both qubits and time steps. They discarded every run that failed a check, a step called post-selection, and reported an effective 10-fold reduction in gate error rates as a result.
They reported a lower bound of 0.284, at 95% confidence, on the fidelity of the output state. Fidelity is a measure of how closely a state matches the ideal one, on a scale where 1 is a perfect match. The authors wrote that the method they used to certify that bound is “device dependent” but “requires substantially weaker noise assumptions than existing fidelity proxy benchmarks.”
The authors reported 2,051 accepted samples in 16.1 minutes of runtime. IBM said in its announcement that many leading classical simulation approaches required prohibitive runtimes for the same task.
Floquet dynamics with Qedma
In a preprint with 41 authors, a team led by Qedma ran the company’s error-mitigation software on a Heron r3 processor, with co-authors from IBM, Japan’s RIKEN institute, BlueQubit, the Hebrew University of Jerusalem, and the Technion. The researchers tracked how magnetization oscillated in a periodically driven model magnet, known as a Floquet Ising model, on up to 74 physical qubits.
In error mitigation, researchers reduce the effect of noise on measured averages with extra runs and classical processing. Tensor networks and sparse Pauli paths are two families of classical methods that approximate quantum dynamics.
The authors wrote that “leading tensor-network simulations fail to converge” in the regimes the experiments reached. Sparse Pauli-path calculations, run on GPUs and Japan’s Fugaku supercomputer, “remain strongly truncation dependent,” they wrote, meaning that the results vary with how far the calculations are simplified. Error-mitigated quantum computation “extends beyond the reach of the state-of-the-art classical methods considered here,” the authors wrote.
IBM and Qedma said in a joint release that the results “mark the first time quantum advantage has been achieved with commercially available hardware and software.”
For late time steps, where its unbiased method became statistically demanding, the team used an extrapolation method that “can therefore introduce extrapolation bias,” the authors wrote. The team also checked selected time points on Quantinuum’s H2 and Helios trapped-ion computers and reported that the Quantinuum and IBM estimates agreed within statistical uncertainties.
Operator Loschmidt echo with Algorithmiq
In a third preprint, 48 researchers from Algorithmiq, IBM, and academic institutions used 56 of the Boston processor’s 156 physical qubits to estimate an operator Loschmidt echo, a quantity the authors introduced to study how information scrambles in a model physical system.
At least three classical simulation groups produced “inconsistent predictions” for the quantity, IBM wrote in a blog post. The authors wrote that the quantum estimates “provide the most credible result among several considered methods.”
Across five noise settings, on two IBM processors and in two synthetic noise models, the team’s global-rescaling estimates differed by at most 0.03. The authors wrote that this estimate, the one they called most credible, “lacks a quantitative statement of its accuracy.”
Tracker and outside views
IBM said the circuits and results were openly released on the Quantum Advantage Tracker, a community site where researchers test such experiments against classical methods. An entry is marked superseded once researchers using classical methods match or beat its quantum results.
Dominik Hangleiter, a researcher at ETH Zurich, told IEEE Spectrum that the Qedma and Algorithmiq teams claimed only that their results seemed hard to simulate classically, which he considered appropriate. He called the IBM and University of Chicago team’s shift to structured circuits that allow verification particularly promising.
IBM said in November 2025, when it introduced the tracker, that it expected the community to confirm the first verified cases of quantum advantage by the end of 2026. In June, IBM said it expected partners to demonstrate quantum advantage in 2026.
Update, November 12, 2026: On August 13, researchers at the Singapore University of Technology and Design and NVIDIA reported computing the ideal output amplitudes for all 2,051 of the team’s samples in 37.3 minutes on 256 NVIDIA H100 GPUs, with a fidelity estimate they called “numerically compatible with IBM’s fidelity lower bound.” Those researchers then joined the team, which revised its preprint on September 1 and 2 around a new experiment on 76 physical qubits, with a fidelity bound of 0.349.
