What Is Quantum Advantage?

In 2019, Google announced that its quantum computer had done in 200 seconds a calculation that would take the world’s fastest supercomputer 10,000 years. It was a landmark, and within a few years classical computers had quietly closed most of the gap. In 2023 IBM made a similar claim. Within months, ordinary computers caught up again. This is not a story of failure or hype. It is a story about how genuinely hard it is to prove that a quantum computer has beaten every classical one, and about why the proof turns out to be almost as difficult as building the machine in the first place.

A claim about one task, not about quantum computers in general

Quantum advantage means a quantum computer has performed one specific, well-defined task faster than any classical computer or algorithm can. The claim applies to that task, at that problem size, and nothing broader. It does not mean the quantum computer is generally faster or more powerful. Most useful problems run better on an ordinary laptop than on any quantum computer that exists or is likely to exist soon. Sorting a list and adding numbers are two examples.

The tasks chosen to demonstrate advantage are therefore usually not useful in themselves. Researchers pick them because a quantum computer performs them naturally, by simply evolving forward in time. A classical computer, by contrast, must track an exponentially growing amount of information to reproduce the same output. That mismatch is the entire point. It means an advantage demonstration is a statement about computational complexity, not a preview of a practical application.

2019: a claim nobody could check directly

Google’s original 2019 claim rested on random circuit sampling. Their 53-qubit Sycamore processor generated bitstrings from a randomly chosen quantum circuit. Measuring the output is a task the hardware performs by its native physics. Reproducing the same output distribution classically means simulating the full quantum state, which grows exponentially with qubit count. Google estimated the task would take the world’s most powerful supercomputer roughly 10,000 years. Sycamore did it in 200 seconds.

The claim carried a structural weakness from the outset. Nobody, not even Google, could independently compute the correct output distribution to check Sycamore’s answer directly. That computation was the very thing claimed to be classically infeasible. Confidence rested instead on a statistical proxy called cross-entropy benchmarking. It also rested on the argument that no known classical algorithm could do better than brute-force simulation.

The classical side kept catching up

That is exactly what happened. Tensor network methods represent a quantum state as a network of connected mathematical objects, rather than a raw exponential array. They turned out to be far more effective against Sycamore’s specific circuit than Google’s original estimate assumed. Successive papers chipped away at the 10,000-year figure. By 2024, one team generated equivalent samples on a supercomputer in about 304 seconds. By 2025, a 1,432-GPU cluster produced samples seven times faster than Sycamore’s original run, at higher fidelity.

None of this means Sycamore’s 2019 hardware run failed or that Google faked it. It means the classical difficulty of that specific task, at that specific size, was smaller than the 2019 estimate suggested, once better algorithms arrived. The lesson generalised well beyond Google. Any advantage claim resting on “no known classical algorithm beats this” has an expiration date, and nobody can predict it in advance.

2023: the same pattern, on different hardware

IBM’s 2023 Nature paper made a related but distinct claim, calling it quantum “utility” rather than advantage. Their 127-qubit Eagle processor computed expectation values for a kicked Ising model, a physically motivated simulation problem rather than an abstract sampling task. IBM argued the calculation sat beyond the reach of the leading classical methods available at the time.

Within months, several independent groups had classically reproduced, and in some cases exceeded, the accuracy of IBM’s quantum results. They used tensor network techniques tuned to the specific geometry of Eagle’s heavy-hexagon qubit layout. One approach used belief propagation on tensor networks. It proved not just competitive but more accurate than the quantum hardware itself, for the regime IBM had studied. The same method was later shown to scale to IBM’s larger Osprey and Condor processors as well.

In 2026 IBM tried again, this time with a certificate of accuracy attached. A classical team answered within a fortnight, and IBM rebuilt the experiment in response.

2026: an advantage claim with a certificate attached

“We are now firmly in the quantum advantage era,” Jay Gambetta, director of IBM Research, announced on 30 July 2026. This claim arrived with something earlier ones lacked: a certificate. The paper behind it, led by Simon Martiel, Jay-U Chung and Ali Javadi-Abhari at IBM with Bill Fefferman at the University of Chicago, starts from a well-known fact. Circuits made only of Clifford gates are easy to simulate classically, however many qubits they use. Adding T gates is what makes a circuit hard.

So the team ran the same circuit twice. The Clifford-only version could have its fidelity measured directly. The T-doped version could not, because it was classically hard. An error-detecting code wrapped both, and the T gates went only where they left the code’s checks untouched, so both versions caught exactly the same faults. IBM hardware applies a T gate in software, so it adds no noise of its own. Together, those facts turn the easy circuit’s measured fidelity into a lower bound on the hard one’s.

The first version of the paper reported 70 qubits, 70 layers and 468 T gates, encoded on 97 physical qubits. It returned 2,051 samples in 16.1 minutes, with a certified fidelity of at least 0.284 at 95 percent confidence. Early sampling experiments reported fidelities of a few parts in a thousand. The two numbers measure slightly different things, but the gap is enormous.

The certificate still rests on assumptions, and the paper states them. It is device dependent. It treats the noise as random Pauli errors, which the team enforces by randomising the gates, and it assumes the T gates add no error. Those assumptions are weaker than the ones behind earlier benchmarks. They are not nothing.

A 37-minute reply, and a rebuilt experiment

On 13 August Hidetaka Manabe and Feng Pan of the Singapore University of Technology and Design, with Hanfeng Gu of NVIDIA, replied. They had found a geometric shortcut. Every two-qubit gate was the same simple type, and the qubits sat along an open line. As a tensor network, the circuit becomes a flat grid just 35 tensors wide. Contracting that grid costs the same whatever the T gates do, so the ingredient meant to supply the hardness was invisible to this method.

On 256 NVIDIA H100 GPUs they computed the exact probability of all 2,051 outputs IBM had published, in 37.3 minutes. Scoring IBM’s samples against them gave 0.350, consistent with IBM’s certified bound under the usual assumptions. The attack ended up supporting IBM’s accuracy claim.

Scoring known outputs is not sampling, which is harder. The team projects that sampling at IBM’s fidelity would take about 10.6 minutes on the same cluster, less than the quantum computer needed. That figure is an estimate, not a run.

IBM revised the paper on 2 September and added all three as co-authors. The headline is now a new circuit: 64 qubits joined in a closed loop, a layout IBM says frustrates tensor-network methods, citing the Singapore analysis. It carries 314 T gates on 76 physical qubits and produced 1,389 samples in 14.5 minutes, with a fidelity bound of 0.349. The 70-qubit run moved to the supplement. The authors expect the classical cost of the new instance to change as methods improve.

IBM’s 2026 paper is the cleanest example yet: the three researchers who found a shortcut through its first version are co-authors of the second.

Whether Quantum Echoes or IBM’s rebuilt 64-qubit circuit becomes the first to do so is an open question. So is whether a smarter classical algorithm eventually catches up with either, as happened twice before and, in part, a third time in 2026.

Both 2026 papers discussed here are preprints. IBM’s paper was revised after its announcement, and this article follows the current version, posted on 2 September 2026; most press coverage describes the first. The Singapore team’s 10.6-minute sampling figure is a projection rather than a measured run.

Verifiability as the explicit design goal

Google’s October 2025 Quantum Echoes experiment on the Willow processor was built around this history, rather than despite it. Instead of sampling, it measures an out-of-time-order correlator, a quantity describing how a small disturbance to one qubit scrambles outward through an entangled system. The key design choice is this. The same physical quantity can, in principle, be measured again on a separate quantum computer and directly compared. That beats checking only against a classical proxy statistic.

Google reported the measurement ran roughly 13,000 times faster than the best available classical algorithm. At 65 qubits, it estimated a classical simulation on the Frontier supercomputer would take about 3.2 years per circuit, against 2.1 hours on the hardware. The team described stress-testing the result against nine separate classical simulation methods before publication, and the paper passed peer review at Nature. We place it alongside the other recent milestones in the latest in quantum computing.

What has and has not been tested

Tensor networks using belief propagation once spoofed advantage claims most successfully of any classical method. That specific technique has now been tested against Quantum Echoes directly. A 2026 analysis found it cannot feasibly simulate the experiment. The circuits generate too much entanglement for tensor network states to compress efficiently. And Willow’s dense two-dimensional connectivity is precisely the structure belief propagation handles worst.

The same paper found something else. Make the circuits artificially compressible, and the same classical method succeeds easily. That result supports the claim that the hardness is real, rather than an artefact of insufficient classical effort.

There is an important limit to the claim, though, and it is one Google’s own collaborators are careful about. The simplest version of the measurement, the first-order correlator, is not clearly beyond classical reach. The genuinely hard case is the higher-order version, where the interference structure becomes far harder to reproduce. Reading which order a given result refers to is essential to judging how strong the claim actually is.

Why the goalposts keep moving, and why that’s healthy

It is tempting to read this history as quantum computing overselling itself. A more accurate reading is that the field is doing exactly what it should. It makes a falsifiable claim, invites the best available classical attack, and either survives it or updates. Each round has produced genuinely harder classical algorithms as a byproduct, which is valuable progress in its own right. Each round has also pushed advantage demonstrations toward designs that are easier to verify. Quantum Echoes and its emphasis on cross-machine reproducibility over statistical proxies is one example of that shift, and the same processors are already simulating particle physics in real time.

What remains unresolved

No advantage claim to date has cleared both bars at once. Independent hardware would need to reproduce it, and classical methods designed to defeat it specifically would need to fail against it. Whether Quantum Echoes becomes the first to do so is an open question. So is whether a smarter classical algorithm eventually catches up to it, as happened twice before. The field is actively working to answer both, not treating either as already settled.