Start with codebreaking. Officials in America, Britain, France and other rich countries are chivvying firms to upgrade to new sorts of cryptography that are thought to be resistant to quantum computers. America’s standards agency recommends making the switch by 2035. But there may be less time than they had thought. In March Oratomic outlined how better error correction might allow attacks on existing cryptography using only tens of thousands of physical qubits, rather than the hundreds of thousands that researchers had thought would be necessary. Soon afterwards researchers at Google outlined a way to break in minutes the codes that protect cryptocurrencies, using just 1,200 logical qubits. Google was worried enough about its own findings to abandon the norm in computer-security research for publishing results openly. Instead, it published a “zero-knowledge proof”, a mathematical construct that allows others to confirm its results without revealing its methods. The firm also announced that it would aim to complete its internal upgrade to post- quantum cryptography by 2029. Even that might be too late to keep prying eyes completely away. Western intelligence agencies have been warning for several years about foreign adversaries using a strategy called “harvest now, decrypt later”, in which juicy data can be captured and stored offline, to be unscrambled when a quantum computer that can do the job is ready. (Whether Western spies are doing something similar themselves is left to the reader’s imagination.) Switching to new sorts of cryptography will be hard but doable for giant firms like Google, Amazon and Microsoft that have strong central control of their infrastructure, says Brian LaMacchia, who used to run Microsoft’s programme on security and cryptography, and is now president of the Farcaster Group, a consultancy. But there is a “long tail” of vulnerable systems that either cannot be upgraded at all, or are run by organisations that lack the know-how. “Think of every piece of connected medical equipment in a hospital,” he says. “You’ll never get all that upgraded and re-certified. Or banks and cash machines, or credit cards, or toll roads, or sewage- treatment works, and so on.” Happily, quantum computers will have constructive effects as well as destructive ones. The original rationale for developing them, as outlined by
Richard Feynman, an American physicist, in 1982, was to better simulate quantum mechanics itself. Quantum mechanics governs the chemical reactions that take place in factories, pharmaceutical labs, or living organisms. But the complexity of the maths needed to simulate the process increases exponentially with the number of particles involved. That means that accurately modelling even relatively simple chemical interactions is beyond the reach of classical machines. “If you want to model something like hydrogen and oxygen coming together to form water—that’s very difficult to do classically,” says Dr Cubitt. Instead, classical machines must rely on a rougher approximation called “Density-Functional Theory” which won one of its pioneers a Nobel prize in 1998. “DFT solves many problems perfectly well,” says Dr Cubitt. “Sometimes, though, it falls flat on its face. It predicts that silicon will be a semiconductor, but it gets the band-gap [a semiconductor’s defining property] completely wrong.” Dr Cubitt cites superconductivity, the behaviour of electrons in new solar-panel materials, or the properties of cathodes in batteries as examples of areas in which existing methods fall short. Quantum computers can efficiently simulate such interactions because they are quantum-mechanical systems themselves. Once the behaviour and interactions of all the particles in a reaction (primarily the electrons around the various atoms) have been encoded into a machine’s qubits, the computer can be made to evolve according to the same quantum-mechanical rules that govern the real molecule. That avoids the need to carry out the enormous numbers of equations that would choke a classical machine that tried to simulate what was happening mathematically. The hope is that quantum computers could replace today’s rough-and-ready simulations with something closer to how an engineer can model a bridge, says Dr Cubitt —“where the object will behave exactly as the computer predicts it will”.
That promise is why McKinsey forecasts that the chemical and pharmaceutical industries will offer some of the biggest opportunities for quantum computers (see chart 2). Several firms are already experimenting. In April, for instance, Wellcome, a big medical-research charity, announced that a team of researchers at Algorithmiq, a startup based in Milan, the Cleveland Clinic, an American hospital, and IBM had won a $2m prize for developing a mixed, quantum-plus-classical simulation of the behaviour of an anti-cancer drug that is activated when light is shone on it. The team’s hybrid system was, according to Algorithmiq, better able to model the interactions between electrons in the drug’s atoms after the drug absorbed a photon than any classical machine would have been. What makes both cryptography and simulating quantum mechanics stand out is that the speedups on offer from quantum computers are both enormous and a sure thing. But there exists an entire “third continent” of problems, says Dr Aaronson, where speedups are either more modest, less certain, or both. Financiers, for instance, use “Monte Carlo” simulations to model the likely performance of a portfolio of assets by generating thousands of plausible future scenarios and seeing how the portfolio performs under each of them.
In 2018 a trio of researchers at Xanadu published a paper demonstrating the use of a quantum algorithm for pricing financial instruments. On paper, the idea looks attractive: the algorithm involved is a derivative of an existing one that has already been shown to offer a significant speedup over classical methods. But actually readying the computer to perform its calculations takes time, and one roundup of quantum finance, published in Nature Reviews Physics in 2023, acknowledged that it was still unclear whether a quantum approach would actually beat a classical one in practice. Another candidate for quantum-minded financiers is the Quantum Approximate Optimisation Algorithm (QAOA). It can be applied to constrained-optimisation problems, such as building a portfolio of financial instruments in which the likelihood of gain must be maximised while the probability of big losses minimised. Ashley Montanaro, one of Dr Cubitt’s fellow founders at Phasecraft, says the firm’s work suggests QAOA can indeed offer a substantial speedup, but only in some cases. And, he says, the extra steps required to prepare the quantum computer may be enough to overwhelm the faster calculations in practice. A paper published in 2025 by Eric Stopfer and Friedrich Wagner, of the Fraunhofer Institute for Integrated Circuits, in Germany, assessed QAOA with real-world data and found that classical approaches usually outperformed it—although they noted that the modest powers of today’s quantum hardware limited the size of the problems they could test. These sorts of uncertainties should be chipped away with time. As quantum hardware becomes more advanced, more and more firms will start experimenting with it. “The original idea for quantum computers was simulating quantum mechanics,” notes Dr Aaronson. “It was an unexpected miracle that they turned out to be good for anything else.” If there are more unexpected miracles lurking out there, then the more people that look for them, the more likely they are to be found. ■ This article was downloaded by zlibrary from https://www.economist.com/science-and-technology/2026/07/29/quantum-computers- promise-mathematical-superpowers
Science & technology | Super positioning AI and quantum computers will be frenemies The two technologies look more complementary than rivalrous Jul 30th 2026 IN 2013 GOOGLE and NASA, America’s space agency, launched a quantum computing lab. The idea was to use a specialised quantum computer built by D-Wave, a Canadian firm, to improve the onerous task of training of machine-learning algorithms. Alas, the lab was ahead of its time not just once, but twice over. Neither machine learning—soon to be rechristened “artificial intelligence”—nor quantum computing were then mature technologies, as D-Wave’s boss, Alan Baratz, now concedes. A paper published in Nature Physics the year after the lab was founded showed that D-Wave’s machine was no better at AI work than a normal graphics- processing unit (GPU).
Yet the fates of AI and quantum computing remain entwined. Some see them as complementary: advances in AI have boosted attempts to build quantum computers, even as progress in quantum algorithms have suggested novel ways of improving AI. Others see the technologies as competitors. To listen to modern AI labs, by the time they are up and running there may not be many useful problems left for quantum computers to tackle. The truth is less dramatic. There are three ways that AI and quantum computers overlap: first, in the problems they try to solve; second, in the way each can be used to build the other; and third, in the resources for which they are competing. And in each of those, co-operation seems to be the winning strategy. The most promising use-case for quantum computers is simulating quantum mechanics itself—which in practice means things like materials science, chemistry and biology. The calculations necessary to simulate even fairly simple chemical reactions are so demanding that even supercomputers are limited to error-prone rough approximations. A sufficiently powerful quantum computer could allow true, high-fidelity simulations of reality at its most fundamental level. But AI firms such as Isomorphic Labs or CuspAI are already working on systems that aim to solve the same challenges, relying on pattern recognition for predictions rather than super-accurate simulations. CuspAI’s cofounder Chad Edwards was previously a senior leader at Quantinuum, a quantum computing startup based in Cambridge, until the pace of progress in AI convinced him to switch sides. Sometimes the conflict runs the other way. In March, Chinese researchers demonstrated a small-scale quantum system that could outperform classical approaches to weather forecasting. The paper was covered by the press in Hong Kong as a blow against the AI industry that risked making expensive data-centres obsolete. Such zero-sum thinking is a mistake, says David Cox, IBM’s vice-president for AI models. Quantum computers will always have a place, he says, because “no other kind of computer…can do the things that a quantum computer can do.” An AI model trying to predict chemical reactions has first