What is Quantum Supremacy? The Complete 2026 Guide to the Quantum vs Classical Milestone

Quantum supremacy, also commonly known as quantum advantage, is the milestone at which a programmable quantum computer solves a specific computational task that no classical computer can solve in any feasible amount of time, whether or not that task is practically useful. The phrase quantum supremacy was coined by Caltech physicist John Preskill in 2012, and it became one of the most-watched and most-contested benchmarks in computing when Google claimed to have reached it with its Sycamore processor in 2019. This guide answers what quantum supremacy is, how it differs from quantum advantage and quantum utility, how researchers actually prove it, and how the frontier has moved from Sycamore in 2019 to Google’s Willow chip and China’s Zuchongzhi 3.0 in 2024 and 2025.

Quantum supremacy in plain English

Imagine a race where the finish line is not a useful destination but simply a point that proves your new vehicle can go somewhere no other vehicle can reach. Quantum supremacy is that kind of finish line: a quantum computer completes a task so quickly that the most powerful classical supercomputers on Earth would need thousands or even septillions of years to match it. The task itself is usually artificial, chosen because it is easy for quantum hardware and brutally hard for classical hardware, so the result is a proof of capability rather than a product anyone would buy.

The everyday confusion is that “supremacy” sounds like quantum computers have taken over computing. They have not, and that is the most important thing to understand about the term. A processor that achieves quantum supremacy on a sampling benchmark still cannot run a spreadsheet, train a neural network, or break the encryption protecting your bank account, because those are different problems that current quantum machines handle poorly or not at all.

A useful analogy is the first flight of a new rocket engine on a test stand. Firing the engine proves the technology works and produces the expected thrust, even though the test stand goes nowhere. Quantum supremacy demonstrations are the test-stand firings of quantum computing, evidence that the physics scales as hoped, with the real missions still to come.

What is quantum supremacy, exactly?

The formal definition of quantum supremacy is the point at which a controllable quantum system performs a well-defined computational task that is beyond the reach of any classical computer within a practical time budget. The task does not need to be useful, and in every demonstration to date it has not been; the only requirement is that the classical cost of reproducing the result grows so fast with problem size that no existing or near-future supercomputer could finish it. Preskill framed it as a clear scientific signpost, a way to mark when quantum devices cross from “interesting but classically simulable” into genuinely new computational territory.

Three conditions have to hold for a credible claim. First, the quantum device must actually run the task and produce verifiable output, not just be projected to do so. Second, the best known classical algorithm for the same task, running on the best available hardware, must require an infeasible amount of time or memory. Third, the gap has to survive scrutiny, because classical methods improve and a result that looked impossible can become tractable, which is why the quantum supremacy frontier is best read as a contested, shifting boundary rather than a one-time finish line.

Why the task is deliberately useless

Newcomers are often surprised that the headline quantum-supremacy tasks have no application. The reason is strategic: the easiest way to beat classical computers is to pick a problem that plays to quantum hardware’s strengths and classical hardware’s weaknesses, even if nobody needs the answer. Random circuit sampling fits this description perfectly, because sampling from the output of a deep random quantum circuit is something quantum hardware does natively while classical simulation costs scale exponentially with the number of qubits.

Choosing a useful task instead would make the demonstration far harder, since useful problems often have structure that clever classical algorithms can exploit. The history of the field shows this repeatedly: the moment a quantum result targets a structured, useful problem, classical researchers tend to find a shortcut. Supremacy benchmarks avoid that trap by being structureless on purpose, which is also why they are so often described as a stepping stone rather than the goal itself.

Supremacy, advantage, and utility

The vocabulary around this milestone is genuinely confusing because three overlapping terms get used, sometimes interchangeably and sometimes with sharp distinctions. Quantum supremacy is the strict version, meaning a task no classical computer can do in feasible time. Quantum advantage is the broader and now more popular phrase, often used for the same idea but increasingly reserved for cases where the quantum approach is meaningfully better on a task people might actually care about.

Quantum utility is a third framing, introduced by IBM in 2023, describing quantum computers becoming useful scientific tools before full fault tolerance arrives, even if classical methods can still keep pace. The distinctions matter because vendors choose their words carefully, and a “utility” claim is a weaker statement than an “advantage” claim, which is in turn weaker than strict “supremacy” on a verifiable task. Reading any announcement carefully for which word it uses tells you a great deal about how strong the underlying result really is.

Why “supremacy” became controversial

The word itself has been a flashpoint. In 2019 a group of thirteen researchers published a correspondence in the journal Nature arguing that “supremacy” carries unwelcome connotations and should be retired in favour of “quantum advantage.” The debate was partly about science communication and partly about the political weight of the word, and it split the community without ever fully resolving.

Preskill responded directly in a widely read 2019 Quanta Magazine column titled “Why I Called It Quantum Supremacy.” He explained that he rejected “advantage” precisely because it sounded too mild, implying a quantum computer with a slight edge rather than one that decisively outclasses every classical machine on the chosen task. Both words remain in active use in 2026, with “advantage” dominant in marketing and “supremacy” still common in technical discussion of the strict milestone.

How researchers prove it

Proving quantum supremacy requires a task that quantum hardware can run and that classical computers provably struggle to reproduce. Two families of benchmark have carried almost every claim so far, and both are sampling problems, meaning the quantum computer produces a stream of random-looking outputs whose statistical distribution is the hard part to fake. Sampling problems are attractive because their classical hardness rests on well-studied results in computational complexity theory.

The first and most important benchmark is random circuit sampling. A processor applies a randomly chosen sequence of one-qubit and two-qubit gates to all its qubits, then measures them, and repeats this millions of times to build up a sample of output bit-strings. The output distribution is highly structured by quantum interference, and the best classical methods for reproducing it cost time and memory that grow exponentially with the number of qubits and the circuit depth, which is why random circuit sampling is often described as the classically hardest benchmark a quantum computer can run today.

The procedure is short to state, even though reproducing its output is exactly what defeats classical machines. Random circuit sampling runs in three steps and then leans on sheer repetition:

1. Apply a random sequence of one-qubit and two-qubit gates to n qubits, where the circuit depth is the number of gate layers.
2. Measure all qubits at the end, recording one n-bit output string.
3. Repeat the run millions of times to build up an estimate of the output distribution.

The classical cost of reproducing that distribution scales roughly as 2 to the power of n, the number of qubits. It climbs further with circuit depth, which is what pushes large random-circuit instances beyond the reach of any supercomputer.

Verification is the subtle part, because the whole point is that classical computers cannot easily reproduce the distribution. Researchers use a statistical measure called the linear cross-entropy benchmark, often written linear XEB, which scores how strongly the measured samples favour the high-probability outputs predicted for the ideal circuit. A score near the ideal value, combined with a classical cost estimate for spoofing that score, is the evidence offered for supremacy, and disputes over supremacy claims very often come down to disputes over the spoofing cost.

Gaussian boson sampling

The second benchmark family is boson sampling, and specifically Gaussian boson sampling, which runs on photonic hardware rather than superconducting qubits. Photons are sent through a large network of beam splitters and phase shifters, and the pattern of where they are detected follows a distribution governed by a matrix quantity called the hafnian, which is famously hard to compute classically. China’s Jiuzhang experiments used Gaussian boson sampling, giving the field a photonic route to supremacy that is independent of the superconducting random-circuit route.

Boson sampling has its own verification challenges and its own classical-spoofing literature, so it is not inherently more or less convincing than random circuit sampling. Having two physically distinct benchmark families is healthy for the field, because it means a supremacy claim does not rest on a single hardware platform or a single complexity-theory assumption. Both routes share the same vulnerability, however, which is that improved classical algorithms can erode the claimed gap after the fact.

The milestones, 2019 to 2025

The quantum-supremacy story is best told as a sequence of competing claims between Google and the University of Science and Technology of China, with IBM playing the role of skeptic and classical challenger. Each milestone widened the claimed gap or moved to new hardware, and several were later contested by improved classical simulations. The table below summarises the major demonstrations and the figures their authors reported at the time of announcement.

Google Sycamore, 2019

Google’s October 2019 Nature paper was the shot heard around the field. The 53-qubit Sycamore processor sampled a random circuit in roughly 200 seconds, and the team estimated that the Summit supercomputer at Oak Ridge would need about 10,000 years to produce a comparable sample. This was the first formal claim of quantum supremacy, and it generated enormous attention precisely because of the scale of the claimed gap.

The result also drew an immediate rebuttal from IBM, which set the tone for everything that followed. The lesson the community took away was that a supremacy headline is the start of an argument, not the end of one, because the classical baseline is never fixed. That dynamic has shaped every subsequent demonstration.

Jiuzhang and Zuchongzhi

China’s USTC group answered in December 2020 with Jiuzhang, a photonic processor that performed Gaussian boson sampling with 76 detected photons and claimed a gap measured in hundreds of millions of years against the best classical methods of the day. Because Jiuzhang used photons rather than superconducting qubits, it established a second, independent platform for supremacy claims. The same group then pushed superconducting hardware with the Zuchongzhi 2.1 processor in 2021.

The most striking recent Chinese result is Zuchongzhi 3.0, published as a Physical Review Letters cover article in 2025. The 105-qubit processor reported single-qubit, two-qubit, and readout fidelities of 99.90, 99.62, and 99.13 percent, and an 83-qubit random-circuit experiment that its authors estimated to run roughly 10^15 times faster than the leading classical supercomputer. The team placed the classical cost on the Frontier machine at billions of years for the same task.

Google Willow and Quantum Echoes

Google returned in December 2024 with Willow, a 105-qubit chip that delivered two distinct results in one announcement. Its random-circuit-sampling benchmark was completed in under five minutes, with the team estimating that Frontier would need on the order of 10^25 years, a figure far larger than the age of the universe. The Willow processor paired this with a separate and arguably more important demonstration of below-threshold quantum error correction, showing logical error rates that fell as the code grew, which is covered in our error-correction guide.

In October 2025 Google went further with an algorithm it calls Quantum Echoes, running on a 65-qubit subset of Willow. The technique uses out-of-time-order correlators, a kind of quantum echo that sends a signal into the system, perturbs it, and reverses the evolution to read the amplified response. Google described the result as the first verifiable quantum advantage, about 13,000 times faster than classical simulation on a task with connections to molecular structure, which matters because verifiability has been one of the weakest points of earlier sampling claims.

The classical fightback

No account of quantum supremacy is honest without the classical counterattack, because the classical baseline has moved almost as fast as the quantum hardware. Within weeks of Google’s 2019 claim, IBM argued that a smarter use of Summit’s huge secondary storage could reproduce the Sycamore sample in about 2.5 days rather than 10,000 years, with higher fidelity. The 10,000-year figure assumed a particular classical method, and a better method shrank it dramatically.

The pattern continued and deepened. Researchers including Pan Zhang and collaborators developed tensor-network algorithms that, running on GPU clusters, reproduced the statistics of Google’s 2019 circuits far faster than the original estimate suggested, eroding the gap to the point where the original supremacy claim is now widely regarded as superseded. Tensor-network and related methods have also been the main tool for challenging boson-sampling claims, so neither benchmark family has been immune.

The clearest example of the classical fightback came against IBM’s own 2023 quantum-utility experiment. IBM’s 127-qubit Eagle result, published in Nature, was matched within months by several classical teams: tensor-network simulations reproduced the dynamics to high accuracy, and a method based on efficient tensor-network simulation ran comparable calculations on modest hardware. IBM had been careful to call its result “utility” rather than “advantage,” and the rapid classical response showed exactly why that caution was warranted.

Why it matters, and what it does not mean

Quantum supremacy matters because it is experimental proof that quantum computers can do something genuinely beyond classical reach, which validates decades of theory about why quantum systems are hard to simulate. Before 2019 it was possible to argue that quantum computers might never scale to a regime classical machines could not follow, and the supremacy demonstrations closed off that pessimistic position. They show the exponential resource cost of classical simulation is real and that quantum hardware can operate in that regime.

What supremacy does not mean is that quantum computers are now broadly useful or that they threaten classical computing in general. The benchmark tasks are deliberately useless, the demonstrations run on noisy hardware without full error correction, and a supremacy result on random circuit sampling tells you nothing about whether the same machine can factor a number or simulate a drug molecule. Treating a supremacy headline as evidence that encryption is about to fall, or that practical quantum advantage has arrived, is a common and serious misreading.

The honest summary is that supremacy is a scientific milestone with limited engineering meaning on its own. It is necessary on the road to useful quantum computing, because a machine that could never beat classical hardware on anything would be a dead end, but it is nowhere near sufficient. The gap between beating a supercomputer at random sampling and delivering commercial value remains large, and closing it is the central challenge of the field.

From supremacy to useful advantage

The frontier in 2026 has shifted from bare supremacy toward two harder goals: results that are verifiable, and results that are useful. Verifiability addresses the deepest weakness of random-circuit-sampling claims, which is that nobody can fully check the output without the very classical computation that is supposed to be infeasible. Google’s 2025 Quantum Echoes result was framed around exactly this point, offering a task whose answer another quantum computer could in principle reproduce and confirm.

Usefulness is the larger prize and depends on quantum error correction. Today’s processors are noisy, and noise limits how deep a circuit can run before errors swamp the signal, which is why supremacy benchmarks favour shallow random circuits rather than long, structured algorithms. Willow’s below-threshold error-correction result pointed the way by showing that adding more physical qubits can lower the logical error rate, the property a fault-tolerant machine needs, and you can read more in our guide to quantum error correction.

The destination everyone is racing toward is useful, fault-tolerant quantum advantage, meaning a quantum computer that beats classical methods on a problem people genuinely want solved, such as simulating chemistry, optimising logistics, or running Shor’s factoring algorithm at scale. That had not been achieved as of 2026, and most credible roadmaps place it years away. Quantum supremacy was the first checkpoint on that road, and the more demanding checkpoints of verifiability and usefulness are where the contest now sits.