Marin Ivezic
Three words carry most of the weight in quantum computing announcements: supremacy, advantage, and utility. Coverage treats them as interchangeable labels for one event, the moment a quantum computer beat a classical one. They aren’t interchangeable. Each names a distinct claim, each claim has to clear a different bar, and the difference decides whether an announcement changes anything for the person reading it.
In October 2019, Google reported that Sycamore, a 53-qubit superconducting processor, finished a sampling task in 200 seconds that the team estimated would take the best available supercomputer 10,000 years. Nature published the result. IBM contested the classical estimate within days, and later classical work cut it much further still. And in December 2019, a group of quantum researchers wrote to Nature asking the field to abandon the word “supremacy” altogether. One announcement, three separate arguments, and only one of them was about physics.
What Supremacy Actually Claimed
John Preskill, a theoretical physicist at Caltech, coined the term in a 2012 essay, “Quantum Computing and the Entanglement Frontier.” His definition set a deliberately narrow bar: a programmable quantum device performs a computation that would be extremely difficult to carry out on a conventional supercomputer. The task doesn’t have to be useful. That exclusion isn’t a loophole, it’s the design. Preskill wanted a demonstration that the hardware class had crossed a computational line, kept separate from the much longer question of what to do with it.
Sycamore’s task was random circuit sampling. The processor runs a randomly chosen sequence of quantum gates and reports the bit strings it measures. The distribution of those bit strings is the result, and reproducing that distribution on a classical machine gets exponentially harder as qubit count and circuit depth grow. Nobody wants the output. It has no downstream use. It was chosen because it is hard to fake, which is what a supremacy demonstration needs and all it needs.
The Fragile Half of the Claim
A supremacy result is a comparison, and a comparison has two sides. The quantum side is measured on hardware. The classical side is an estimate of what the best known classical algorithm would require, and that estimate is an open research target for everyone who disagrees with it.
IBM published a rebuttal within days of the Google paper, arguing that a Summit-based simulation using disk storage more aggressively would finish in about 2.5 days rather than 10,000 years. Later work went considerably further. Tensor-network methods, classical algorithms that exploit structure in a circuit so the full quantum state never has to be held in memory, have since cut the estimated classical cost of Sycamore-scale sampling by many orders of magnitude.
Vendors quote the classical number as though it described their hardware. It describes the comparison, and the comparison has a research community actively working to move it. A supremacy claim is provisional by construction, and the provisionality is rarely printed alongside the headline figure.
The word itself drew a separate objection. In December 2019, a Nature correspondence signed by 13 quantum researchers argued that “supremacy” carries political freight the field does not need, and proposed “quantum advantage” in its place. Much of the community adopted the substitution. Swapping the word left the evidence bar exactly where it was, and that is where the confusion we still deal with began.
Advantage Raises the Bar
Used strictly, quantum advantage is the harder claim. It requires a task someone actually wants performed, and a quantum result that beats the best available classical method on a dimension somebody pays for: time, cost, accuracy, or energy consumption.
Shor’s algorithm is the standard illustration of an advantage that hasn’t arrived. Published in 1994, it factors large integers in polynomial time, which would break RSA and elliptic-curve public-key cryptography. The algorithm isn’t in dispute. The hardware is. Running it against a 2048-bit key needs millions of physical qubits organised into a far smaller number of error-corrected logical qubits, and that requires fault tolerance: error correction that removes errors faster than the additional hardware introduces them, so a computation can run long enough to finish without noise swamping the answer.
Google Quantum AI reported in Nature in 2023 that increasing the surface-code distance on a Sycamore-class processor lowered the logical error rate, the scaling behaviour error correction has to show before fault tolerance is possible. That is progress toward the machine class an advantage claim will eventually need. It is not an advantage claim, and Google did not present it as one.
Utility Is a Claim About the Instrument
IBM introduced a third framing in June 2023, in a Nature paper on a 127-qubit Eagle processor simulating a two-dimensional Ising spin model. The team used error mitigation, which estimates how noise distorts a measured quantity and subtracts that distortion, paying for the correction with many additional circuit runs rather than with extra qubits.
The claim was carefully bounded. The device produced trustworthy results at a scale where brute-force classical simulation is impractical, so it can serve as a scientific instrument before fault tolerance exists. Several groups reproduced the results classically within months, using tensor-network and related approximation techniques. The utility claim survived that better than a supremacy claim would have, because it never asserted the classical route was closed. It asserted usefulness, and usefulness isn’t exclusive. Of the three words, utility asks the least of the hardware and promises the least to the buyer.
Four Questions for Any Benchmark Announcement
We teach candidates to run any benchmark announcement through the same four questions before deciding whether it touches a plan.
What was the task? A contrived benchmark can support a supremacy or utility claim and nothing else. If nobody outside the lab wants the output, the result describes hardware capability and says nothing about applications.
Who computed the classical baseline, and how? A vendor’s own estimate of classical difficulty is the number most likely to move. Independent scrutiny of the classical side is worth more than another qubit on the quantum side.
Physical or logical qubits, demonstrated or announced? Physical qubits are the hardware. Logical qubits are error-corrected groups of physical ones, and the ratio between them currently runs into the hundreds or thousands. A roadmap date is not a result.
What would falsify it? A supremacy claim dies to a better classical algorithm. An advantage claim dies to a better classical algorithm or to a cheaper conventional method. A utility claim survives both, which is precisely why it promises less.
Run those four over October 2019 and the reading resolves quickly. Contrived task, vendor-computed baseline, 53 physical qubits and no logical ones, and a falsification condition that improved classical simulation later met. The Sycamore result was a genuine hardware milestone. It was never a reason to change a cryptographic migration date, and a great deal of coverage read it as though it were.
Which Word a Company Chooses
The word a company selects tells you which claim it is prepared to defend. Supremacy is a statement about a contrived task measured against a contested baseline. Advantage is a statement about a useful task, and no clean, uncontested public demonstration exists yet. Utility is a statement about the machine’s value as a research instrument, with no assertion that classical methods have been beaten.
Reading these claims precisely is a working skill for anyone who briefs a board, sizes a budget, or sets a migration schedule. Quantum Academy’s Certified Quantum Technology Professional (CQTP) program covers benchmark reading alongside hardware modalities, error correction, and algorithm classes. Program details, including syllabus and assessment format, are at quantumacademy.com/.
For the migration-planning side of the same question, meaning what a hardware result does and does not do to a post-quantum cryptography (PQC) timeline, the migration methodology published at pqcframework.org is the better starting point, and PostQuantum.com publishes deeper technical analysis of individual benchmark claims as they appear.