Has quantum advantage been achieved?
Yes, narrowly: quantum computers have beaten the best known classical methods on contrived benchmark tasks, most credibly Google's verifiable Quantum Echoes result (October 2025) and, pending classical counterattack, IBM's July 2026 material-simulation claims. But the 2019 Sycamore headline collapsed once classical algorithms improved, and as of August 2026 no quantum computer has outperformed classical computing on a problem anyone would pay to solve.
Claimed 2019 — later matched classically Google's original quantum supremacy claim said classical simulation would take 10,000 years. IBM proposed a 2.5-day approach within days, and by 2021 tensor-network methods on the Sunway supercomputer and later on GPUs — eventually a single CPU node — sampled the same circuits in days with comparable fidelity. The experiment was real hardware progress, but the specific classical-runtime gap did not survive.
Yes — October 2024, but unverifiable Willow repeated the random-circuit-sampling benchmark at higher fidelity and depth, far beyond what any published classical method can currently match. Two honest caveats: at this scale the output cannot be directly verified (fidelity is extrapolated from smaller circuits), and every previous astronomical classical estimate has shrunk as algorithms improved. The task itself has no practical use.
Yes — October 2025, first verifiable claim Quantum Echoes measures how information scrambles through a quantum system — a deterministic physical quantity that another quantum computer of similar quality can reproduce and cross-check, unlike random-circuit sampling. Peer reviewers called the result impressive while explicitly warning that earlier advantage claims were later erased by better classical algorithms. 'Best known classical method' is a moving target; this is the strongest standing claim, not a proof.
Claimed July 2026 — awaiting independent replication IBM and Algorithmiq claim an error-mitigated simulation of a heterogeneous quantum material that every deployed classical method — including runs on Fugaku — failed to match, with classical methods also disagreeing among themselves. Because the answer is beyond classical verification, trust rests on noise-injection consistency checks rather than an independent check of the result. The 2019 pattern says wait: classical simulation experts typically need months to years to respond, and that response is still in progress. As of 2026-08-20 no peer-reviewed classical rebuttal has been published; the claim rests on the vendor announcement and should be read as a vendor claim under scrutiny, not a settled result.
No commercial advantage — targets cluster at 2029-2030 Every advantage claim so far is a physics benchmark chosen because it suits quantum hardware. Speedups on optimisation, machine learning or drug discovery remain projections tied to fault-tolerant machines that do not exist yet: Quantinuum targets universal fault tolerance by 2029-2030, IBM targets its Starling system in 2029. Treat these dates as engineering targets published by vendors, not commitments.
What exactly has been demonstrated?
Every quantum advantage claim so far has the same shape: run a task that suits quantum hardware, then argue that the best known classical method would take absurdly long. The word doing the work is known. None of these tasks is proven classically hard — the hardness is conjectured, and classical algorithm designers have repeatedly narrowed or closed the gap after the press release.
The claims fall into three families. Sampling benchmarks (Sycamore 2019, Willow 2024): sample bitstrings from a scrambled random circuit. Useless output, contested classical runtimes. Verifiable physics quantities (Quantum Echoes, October 2025): measure a number describing how information scrambles, which another quantum computer can reproduce and check. Beyond-verification simulations (IBM and partners, July 2026): simulate quantum materials in regimes where classical methods disagree with each other, so nobody can check the quantum answer classically either — trust has to come from consistency checks instead.
What has never been demonstrated, anywhere, is a quantum computer beating classical computing on a task with independent commercial value. See how current devices actually measure up on the hardware comparison.
What does a random-circuit experiment look like?
Why do advantage claims keep collapsing?
Because the benchmark is a moving target. A claim of advantage is really a claim about the entire future of classical algorithms, made on the day of publication. Sycamore's '10,000 years' became days within two years as tensor-network contraction improved, and by 2024 the same circuits ran on a single CPU node. That is not embarrassment — it is how the scientific back-and-forth is supposed to work — but it means any fresh claim should be read with a built-in delay: the classical community's answer takes months to years to arrive.
Verification cuts both ways too. Random-circuit outputs cannot be checked at full scale, so the 2019 and 2024 claims rest on extrapolated fidelity. Quantum Echoes was designed to fix exactly this: it produces a number that can be independently reproduced. That makes it the most defensible claim so far — and it is still a claim about known classical algorithms, not a proof.
What would change the answer to a full yes?
Three things at once: a problem with independent value (someone would pay for the answer even if quantum computers did not exist), a speedup that survives total-cost accounting (including error mitigation overhead, cloud queue time and the classical pre- and post-processing), and a result that stands up to years of classical counterattack rather than months.
IBM's public Quantum Advantage Tracker — inviting classical researchers to refute standing claims — is a genuinely healthy development on the third point. Most researchers expect the first full yes to require fault-tolerant machines, because error-corrected logical qubits are what let algorithms with proven speedups, like Shor's, run at meaningful sizes. Until then, expect the current pattern: real, narrow, contested wins on physics benchmarks.
Classifications follow the QPU137 editorial policy: every applied label carries a date, source, scale, and hardware, or it does not render. Found an error? Report it.