For most of the past decade, a claim of quantum advantage came with an escape hatch. The machine had solved something a classical computer could not, and the only way to check the answer was to run the classical simulation the machine had supposedly beaten. Verification was circular by construction.
On Thursday, IBM and two quantum software companies published three papers that try to close that gap. Each describes a computation that outran leading classical methods and a way to judge, from the quantum device’s own data, whether the result can be trusted.
The papers are preprints. None has been peer reviewed, and the claims are being filed alongside competing entries in a public tracker that the field uses to argue about exactly this question.
The first paper, with researchers at the University of Chicago, reworks random circuit sampling, the technique behind Google’s 2019 advantage claim. Random circuits are hard to simulate and therefore hard to check. The authors took a different route.
They built circuits from Clifford gates, which classical computers handle easily, and embedded them in a spacetime code that flags errors across both qubits and time. They could then check a run against a baseline they could still simulate, and add non-Clifford gates one at a time until the circuit became classically intractable.
On IBM’s Heron processor, a 70-qubit encoded computation absorbed 468 of those gates, more than twice what the company says leading classical methods can simulate. Among runs that passed the error checks, at least 28 percent were faithful. The result carries a 95 percent confidence bound, which earlier advantage claims could not offer. The cost is inefficiency: the error detection threw away so many runs that the experiment needed 860 times more shots than a straightforward version would have.
Jay Gambetta, who directs IBM Research, said the demonstrations show two things: that quantum computers can solve problems beyond the reach of classical machines, and that their answers can be validated with confidence.
The other two papers stay closer to the physics that customers actually want to simulate. Both used IBM hardware to model a magnetic material driven by regular pulses, and both leaned on error mitigation, the post-processing math that subtracts known noise from a noisy answer.
Qedma, an Israeli startup, worked with RIKEN and BlueQubit on circuits of up to 74 qubits, tracking how magnetization oscillates over time. They compared results against two leading classical methods running on RIKEN’s Fugaku supercomputer and on an Nvidia H100 server.
Up to 35 qubits the three approaches agreed. At 51 qubits the classical methods held for the first few pulses and then broke down. At 74 they were out of reach. In the hardest regime the two classical methods also disagreed with each other, leaving no benchmark to appeal to.
That is precisely the situation where a wrong quantum answer would be hardest to catch. Netanel Lindner, Qedma’s chief technology officer, framed the question as whether the oscillations are real. The team’s answer was indirect: results matched classical simulations of shorter runs, where those simulations are still reliable, and held steady when the same model was run with slower gates, with noise deliberately injected, and on different IBM processors.
Algorithmiq, a Finnish company, ran a related simulation of a magnetic material model over eight months of accumulated runs on IBM machines. Its chief executive, Sabrina Maniscalco, said the consistency across hardware and noise settings was evidence rather than coincidence.
Not everyone is convinced the word advantage applies. Dominik Hangleiter, a postdoctoral researcher at ETH Zurich, said the Chicago paper’s move toward structured circuits that can be checked is promising, and noted that he argued for the approach himself last year. He was cooler on the other two.
In his reading, the Qedma and Algorithmiq authors say their problems appear hard to simulate, which he called reasonable, and do not go further. They should not, he added.
Jens Eisert, a professor at the Free University of Berlin, made a related point about the category. Verifying a quantum simulation beyond classical reach is not a single procedure, he wrote in an email to IEEE Spectrum, but a process of building confidence through a portfolio of methods that complement one another.
That framing matters commercially. IBM sells quantum access to banks, chemical companies and manufacturers, and the error-mitigation software from partners like Qedma and Algorithmiq is part of what those customers buy. A customer in a regulated industry needs an audit trail, not a benchmark score. The three papers are, in effect, a proposal for what that trail looks like.
They also fit IBM’s road map. The company plans to ship Starling, a fault-tolerant machine with 200 logical qubits running 100 million gates, in 2029, and a larger system called Blue Jay with 2,000 qubits after 2033. Error correction at that scale produces its own verification data, and the methods described this week are the scaffolding for reading it.
The counterargument is that classical algorithms keep improving. Most advantage claims of the past six years have been narrowed, sometimes within months, by better simulation techniques, and the tracker exists because the field has learned to expect it. The Chicago result is designed to survive that test: its hardness argument rests on complexity theory, not on the current speed of a supercomputer. The Floquet and magnetic simulations rest on something softer: the failure of specific classical codes at specific sizes, in a regime where the codes could be tuned against the data.
What happens next is a peer review and, more importantly, a classical rejoinder. If a team reproduces the 74-qubit oscillations on a GPU cluster by spring, the advantage disappears and the verification method survives. If nobody can, IBM will have moved the argument from whether quantum computers work to whether anyone can prove they do not.
