Has quantum advantage been achieved?
Yes, but only in a narrow sense. Quantum advantage means a quantum computer beating the best ordinary computers at some task, and so far that has happened only on specially chosen test tasks. The most solid case is Google's checkable Quantum Echoes result (October 2025). IBM's July 2026 materials-simulation claims may count too, if they survive challenges from ordinary computers. But the famous 2019 Sycamore result fell once ordinary algorithms improved, and as of August 2026 no quantum computer has beaten ordinary computing on a problem anyone would pay to solve.
Claimed 2019 — later matched classically Google's original quantum supremacy claim said a classical simulation would take 10,000 years. Within days, IBM proposed a method that would take 2.5 days. By 2021, tensor-network methods on the Sunway supercomputer, and later on GPUs, sampled the same circuits in days with similar fidelity. Eventually a single CPU node could do it. The experiment was real hardware progress, but the specific classical run-time gap did not survive.
Yes — October 2024, but unverifiable Willow repeated the random-circuit-sampling test at higher fidelity (accuracy) and depth (more steps). That is far beyond what any published classical method can match today. Two honest caveats. At this size the output cannot be checked directly; its fidelity is estimated from smaller circuits. And every earlier huge 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. That is a fixed physical number. Unlike random-circuit sampling, another quantum computer of similar quality can reproduce and cross-check it. Peer reviewers called the result impressive. They also warned 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 mixed quantum material. Every deployed classical method, including runs on the Fugaku supercomputer, failed to match it, and the classical methods also disagreed with each other. The answer is beyond classical checking. So trust rests on consistency checks that add noise on purpose, rather than an independent check of the result. The 2019 pattern says wait. Classical simulation experts usually need months to years to respond, and that response is still under way. As of 2026-08-20 no peer-reviewed classical rebuttal has been published. The claim rests on the vendor announcement. Read it 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 test chosen because it suits quantum hardware. Speedups on optimisation, machine learning or drug discovery remain forecasts. They depend on error-corrected machines that do not exist yet. Quantinuum targets universal fault tolerance by 2029-2030, and IBM targets its Starling system in 2029. Treat these dates as engineering targets published by vendors, not commitments.
What exactly has been demonstrated?
Why care? "Quantum advantage" is the phrase in almost every big quantum headline. It means a quantum computer finishing a task that the best ordinary, or classical, computers cannot match in any sensible time. Knowing what it really covers helps you read those headlines.
Every claim so far has the same shape. First, 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 hard for ordinary computers. The hardness is only a strong guess. And classical algorithm designers have often narrowed or closed the gap after the press release. It is like a speed record set before rivals have tried a new shortcut. The record is real on the day. It may not last.
The claims fall into three families:
- Sampling tests (Sycamore 2019, Willow 2024). The machine outputs bitstrings, strings of 0s and 1s, from a scrambled random circuit. The output is useless, and the classical run times are argued over.
- Checkable physics numbers (Quantum Echoes, October 2025). The machine measures a number that describes how information spreads and scrambles. Another quantum computer can reproduce and check it.
- Simulations beyond checking (IBM and partners, July 2026). The machine simulates quantum materials where classical methods disagree with each other. So nobody can check the quantum answer classically either. Trust has to come from consistency checks instead.
Why do big circuits get so hard to copy? Work the numbers. A simulation of n qubits tracks 2^n amplitudes, numbers that say how strongly the machine leans toward each result. 3 qubits need 2^3 = 8. 50 qubits need 2^50, about a million billion. At 16 bytes each, that is about 18 million billion bytes of memory. Clever shortcuts can avoid storing them all, which is exactly how past claims were knocked down.
What has never been shown, anywhere, is a quantum computer beating classical computing on a task with its own 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 target keeps moving. A claim of advantage is really a claim about the whole future of classical algorithms, made on the day it is published. Sycamore's "10,000 years" became days within two years, as a method called tensor-network contraction improved. 10,000 years is about 3.65 million days, so that was a speedup of roughly a million times. By 2024 the same circuits ran on a single CPU node.
That is not a scandal. It is how science is supposed to argue back and forth. But it means you should read any fresh claim with a built-in delay. The classical community's answer takes months to years to arrive.
Checking cuts both ways too. Random-circuit outputs cannot be checked at full size. So the 2019 and 2024 claims rest on fidelity, a score for how close the output is to perfect, estimated from smaller circuits. Quantum Echoes was designed to fix exactly this. It produces a number that others can reproduce on their own. That makes it the strongest claim so far. 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 its own value. Someone would pay for the answer even if quantum computers did not exist.
- A speedup that survives the full bill. Count everything: error-mitigation overhead, time waiting in the cloud queue, and the classical work before and after.
- A result that survives years of classical attack, not just months.
IBM's public Quantum Advantage Tracker invites classical researchers to knock down standing claims. That is a healthy step on the third point. Most researchers expect the first full yes to need fault-tolerant machines, computers that fix their own errors as they run. They are built from logical qubits, reliable qubits made from many error-prone ones. Machines like that 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 tests.
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.