Headlines tend to describe quantum computers as simply much faster computers, ready to transform everything from finance to medicine. The truth is narrower and more interesting. A quantum computer is a specialist. For a handful of problems it could be astonishingly better than any ordinary machine. For most of what we use computers for, it offers nothing at all.

A specialist, not a faster everything

Quantum computers are not faster at everything; they promise big speedups only for problems with special structure that interference can exploit. Sending email, streaming video and running spreadsheets will stay on ordinary chips.

Shor's algorithm

The discovery that turned quantum computing from curiosity into a field came in 1994. Peter Shor, then at Bell Labs, showed that a quantum computer could find the prime factors of a large number dramatically faster than any known classical method. Shor's algorithm, published in 1994, could efficiently factor large numbers and solve related problems, which would break RSA and elliptic-curve public-key encryption. Those systems protect much of the internet. The algorithm works by turning factoring into a search for the repeating period of a number pattern, a job interference handles beautifully. Two cautions apply. Running it on numbers used in real encryption needs a large, error-corrected machine that does not yet exist. And nobody has proved that no fast classical factoring method exists; it is simply that none has been found despite decades of effort.

Grover's algorithm

In 1996 Lov Grover, also at Bell Labs, found a quantum method for searching without any helpful structure, such as checking every combination of a lock. Grover's algorithm searches an unstructured collection in about the square root of the number of steps a classical search needs, a quadratic speedup. A million possibilities would take about a thousand quantum steps rather than up to a million. That is real but modest. Each quantum step is slow and, once error correction is added, expensive, so researchers at Google and elsewhere have argued that quadratic speedups alone are unlikely to beat classical computers in practice for a long time.

Simulating nature

Feynman's original idea may prove the most valuable. Chemistry and materials science are governed by quantum mechanics, and classical computers must use approximations that fail for some important molecules. Many researchers think simulating molecules and materials is the most promising use of quantum computers, because those systems are themselves quantum. Targets often named include catalysts for making fertilizer with less energy, better battery materials and new superconductors. These are hopes, not results; so far no quantum computer has solved a chemistry problem of commercial value that classical methods could not.

Hard problems stay hard

Many famous puzzles, such as finding the shortest route through hundreds of cities, belong to a class computer scientists call NP-complete. There is no evidence that quantum computers can efficiently solve NP-complete problems in general, and most experts doubt they can. Quantum methods may still offer modest gains on some optimization tasks, but claims that they will "solve logistics" deserve suspicion.

The race for quantum advantage

In 2012 the physicist John Preskill coined the phrase "quantum supremacy" for the moment a quantum device does something no classical computer can do in reasonable time; many now prefer "quantum advantage." In 2019 Google reported that its 53-qubit Sycamore chip had reached that point. Google's 2019 experiment used a task, random circuit sampling, chosen because it is hard for classical computers rather than because it is useful. Google estimated a supercomputer would need 10,000 years; IBM replied that better classical methods could do it in about two and a half days, and later classical simulations narrowed the gap further. In December 2024 Google's Willow chip ran a harder version of the same kind of task. These experiments are genuine scientific milestones, but they are not useful calculations.

Watching for dequantization

Quantum claims can also collapse from the classical side. In 2018 Ewin Tang, then a teenage undergraduate, showed that a classical algorithm could match a celebrated quantum algorithm for recommendation systems, the kind of task that suggests films or products. A speedup that had seemed exponential disappeared. The lesson is simple: a quantum result means little until it is compared against the best classical method, not a weak one.

Worked example: reading a press release

Imagine a company announces that its quantum computer "solved a delivery routing problem 1,000 times faster than a classical computer." How should a careful reader respond? First, ask which classical method was used for comparison. Routing problems are attacked by highly tuned classical software, and beating an untuned rival proves little. Second, ask about size: a problem small enough for today's machines is usually small enough for a laptop to solve in seconds. Third, ask whether the quantum part did the hard work or whether classical computers did most of the steps. Fourth, remember that routing is close to the NP-complete family, where no large quantum speedup is expected. Fifth, ask whether independent researchers have checked it. None of this means the work is worthless; it may be a useful test of hardware. But measured against this level, the announcement probably shows a promising experiment, not proof that quantum computers have changed logistics.