Games played under the laws of quantum mechanics dissipate less energy than their classical equivalents. This is the finding of researchers at Singapore’s Nanyang Technological University (NTU), who worked with colleagues in the UK, Austria and the US to apply the mathematics of game theory to quantum information. The researchers also found that for more complex game strategies, the quantum-classical energy difference can increase without bound, raising the possibility of a “quantum advantage” in energy dissipation.

Game theory is the field of mathematics that aims to formally understand the payoff or gains that a person or other entity (usually called an agent) will get from following a certain strategy. Concepts from game theory are often applied to studies of quantum information, especially when trying to understand whether agents who can use the laws of quantum physics can achieve a better payoff in the game.

In the latest work, which is published in Physical Review Letters, Jayne Thompson, Mile Gu and colleagues approached the problem from a different direction. Rather than focusing on differences in payoffs, they asked how much energy must be dissipated to achieve identical payoffs for games played under the laws of classical versus quantum physics. In doing so, they were guided by Landauer’s principle, an important concept in thermodynamics and information theory that states that there is a minimum energy cost to erasing a piece of information.

This Landauer minimum is known to hold for both classical and quantum systems. However, in practice systems will spend more than the minimum energy erasing memory to make space for new information, and this energy will be dissipated as heat. What the NTU team showed is that this extra heat dissipation can be reduced in the quantum system compared to the classical one.

Planning for future contingencies

To understand why, consider that when a classical agent creates a strategy, it must plan for all possible future contingencies. This means it stores possibilities that never occur, wasting resources. Thompson explains this with a simple analogy. Suppose you are packing to go on a day out. Because you are not sure what the weather is going to be, you must pack items to cover all possible weather outcomes. If it’s sunny, you’d like sunglasses. If it rains, you’ll need your umbrella. But if you only end up using one of these items, you’ll have wasted space in your bag.

“It turns out that the same principle applies to information,” explains Thompson. “Depending on future outcomes, some stored information may turn out to be unnecessary – yet an agent must still maintain it to stay ready for any contingency.”

For a classical system, this can be a very wasteful process. Quantum systems, however, can use superposition to store past information more efficiently. When systems in a quantum superposition are measured, they probabilistically reveal an outcome associated with only one of the states in the superposition. Hence, while superposition can be used to store both pasts, upon measurement all excess information is automatically erased “almost as if they had never stored this information at all,” Thompson explains.

The upshot is that because information erasure has close ties to energy dissipation, this gives quantum systems an energetic advantage. “This is a fantastic result focusing on the physical aspect that many other approaches neglect,” says Vlatko Vedral, a physicist at the University of Oxford, UK who was not involved in the research.

Implications of the research

Gu and Thompson say their result could have implications for the large language models (LLMs) behind popular AI tools such as ChatGPT, as it suggests there might be theoretical advantages, from an energy consumption point of view, in using quantum computers to run them.

Another, more foundational question they hope to understand regarding LLMs is the inherent asymmetry in their behaviour. “It is likely a lot more difficult for an LLM to write a book from back cover to front cover, as opposed to in the more conventional temporal order,” Thompson notes. When considered from an information-theoretic point of view, the two tasks are equivalent, making this asymmetry somewhat surprising.

In Thompson and Gu’s view, taking waste into consideration could shed light on this asymmetry. “It is likely we have to waste more information to go in one direction over the other,” Thompson says, “and we have some tools here which could be used to analyse this”.

For Vedral, the result also has philosophical implications. If quantum agents are more optimal, he says, it is “surely is telling us that the most coherent picture of the universe is the one where the agents are also quantum and not just the underlying processes that they observe”.

• This article was amended on 19 November 2025 to correct a reference to the minimum energy cost of erasing information. It is the Landauer minimum, not the Landau minimum.

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When you look back at the early days of computing, some familiar names pop up, including John von Neumann, Nicholas Metropolis and Richard Feynman. But they were not lonely pioneers – they were part of a much larger group, using mechanical and then electronic computers to do calculations that had never been possible before.

These people, many of whom were women, were the first scientific programmers and computational scientists. Skilled in the complicated operation of early computing devices, they often had degrees in maths or science, and were an integral part of research efforts. And yet, their fundamental contributions are mostly forgotten.

This was in part because of their gender – it was an age when sexism was rife, and it was standard for women to be fired from their job after getting married. However, there is another important factor that is often overlooked, even in today’s scientific community – people in technical roles are often underappreciated and underacknowledged, even though they are the ones who make research possible.

Human and mechanical computers

Originally, a “computer” was a human being who did calculations by hand or with the help of a mechanical calculator. It is thought that the world’s first computational lab was set up in 1937 at Columbia University. But it wasn’t until the Second World War that the demand for computation really exploded; with the need for artillery calculations, new technologies and code breaking.

In the US, the development of the atomic bomb during the Manhattan Project (established in 1943) required huge computational efforts, so it wasn’t long before the New Mexico site had a hand-computing group. Called the T-5 group of the Theoretical Division, it initially consisted of about 20 people. Most were women, including the spouses of other scientific staff. Among them was Mary Frankel, a mathematician married to physicist Stan Frankel; mathematician Augusta “Mici” Teller who was married to Edward Teller, the “father of the hydrogen bomb”; and Jean Bacher, the wife of physicist Robert Bacher.

As the war continued, the T-5 group expanded to include civilian recruits from the nearby towns and members of the Women’s Army Corps. Its staff worked around the clock, using printed mathematical tables and desk calculators in four-hour shifts – but that was not enough to keep up with the computational needs for bomb development. In the early spring of 1944, IBM punch-card machines were brought in to supplement the human power. They became so effective that the machines were soon being used for all large calculations, 24 hours a day, in three shifts.

The computational group continued to grow, and among the new recruits were Naomi Livesay and Eleonor Ewing. Livesay held an advanced degree in mathematics and had done a course in operating and programming IBM electric calculating machines, making her an ideal candidate for the T-5 division. She in turn recruited Ewing, a fellow mathematician who was a former colleague. The two young women supervised the running of the IBM machines around the clock.

The frantic pace of the T-5 group continued until the end of the war in September 1945. The development of the atomic bomb required an immense computational effort, which was made possible through hand and punch-card calculations.

Electronic computers

Shortly after the war ended, the first fully electronic, general-purpose computer – the Electronic Numerical Integrator and Computer (ENIAC) – became operational at the University of Pennsylvania, following two years of development. The project had been led by physicist John Mauchly and electrical engineer J Presper Eckert. The machine was operated and coded by six women – mathematicians Betty Jean Jennings (later Bartik); Kathleen, or Kay, McNulty (later Mauchly, then Antonelli); Frances Bilas (Spence); Marlyn Wescoff (Meltzer) and Ruth Lichterman (Teitelbaum); as well as Betty Snyder (Holberton) who had studied journalism.

Polymath John von Neumann also got involved when looking for more computing power for projects at the new Los Alamos Laboratory, established in New Mexico in 1947. In fact, although originally designed to solve ballistic trajectory problems, the first problem to be run on the ENIAC was “the Los Alamos problem” – a thermonuclear feasibility calculation for Teller’s group studying the H-bomb.

Like in the Manhattan Project, several husband-and-wife teams worked on the ENIAC, the most famous being von Neumann and his wife Klara Dán, and mathematicians Adele and Herman Goldstine. Dán von Neumann in particular worked closely with Nicholas Metropolis, who alongside mathematician Stanislaw Ulam had coined the term Monte Carlo to describe numerical methods based on random sampling. Indeed, between 1948 and 1949 Dán von Neumann and Metropolis ran the first series of Monte Carlo simulations on an electronic computer.

Work began on a new machine at Los Alamos in 1948 – the Mathematical Analyzer Numerical Integrator and Automatic Computer (MANIAC) – which ran its first large-scale hydrodynamic calculation in March 1952. Many of its users were physicists, and its operators and coders included mathematicians Mary Tsingou (later Tsingou-Menzel), Marjorie Jones (Devaney) and Elaine Felix (Alei); plus Verna Ellingson (later Gardiner) and Lois Cook (Leurgans).

Early algorithms

The Los Alamos scientists tried all sorts of problems on the MANIAC, including a chess-playing program – the first documented case of a machine defeating a human at the game. However, two of these projects stand out because they had profound implications on computational science.

In 1953 the Tellers, together with Metropolis and physicists Arianna and Marshall Rosenbluth, published the seminal article “Equation of state calculations by fast computing machines” (J. Chem. Phys. 21 1087). The work introduced the ideas behind the “Metropolis (later renamed Metropolis–Hastings) algorithm”, which is a Monte Carlo method that is based on the concept of “importance sampling”. (While Metropolis was involved in the development of Monte Carlo methods, it appears that he did not contribute directly to the article, but provided access to the MANIAC nightshift.) This is the progenitor of the Markov Chain Monte Carlo methods, which are widely used today throughout science and engineering.

Marshall later recalled how the research came about when he and Arianna had proposed using the MANIAC to study how solids melt (AIP Conf. Proc. 690 22).

Edward Teller meanwhile had the idea of using statistical mechanics and taking ensemble averages instead of following detailed kinematics for each individual disk, and Mici helped with programming during the initial stages. However, the Rosenbluths did most of the work, with Arianna translating and programming the concepts into an algorithm.

The 1953 article is remarkable, not only because it led to the Metropolis algorithm, but also as one of the earliest examples of using a digital computer to simulate a physical system. The main innovation of this work was in developing “importance sampling”. Instead of sampling from random configurations, it samples with a bias toward physically important configurations which contribute more towards the integral.

Furthermore, the article also introduced another computational trick, known as “periodic boundary conditions” (PBCs): a set of conditions which are often used to approximate an infinitely large system by using a small part known as a “unit cell”. Both importance sampling and PBCs went on to become workhorse methods in computational physics.

In the summer of 1953, physicist Enrico Fermi, Ulam, Tsingou and physicist John Pasta also made a significant breakthrough using the MANIAC. They ran a “numerical experiment” as part of a series meant to illustrate possible uses of electronic computers in studying various physical phenomena.

The team modelled a 1D chain of oscillators with a small nonlinearity to see if it would behave as hypothesized, reaching an equilibrium with the energy redistributed equally across the modes (doi.org/10.2172/4376203). However, their work showed that this was not guaranteed for small perturbations – a non-trivial and non-intuitive observation that would not have been apparent without the simulations. It is the first example of a physics discovery made not by theoretical or experimental means, but through a computational approach. It would later lead to the discovery of solitons and integrable models, the development of chaos theory, and a deeper understanding of ergodic limits.

Although the paper says the work was done by all four scientists, Tsingou’s role was forgotten, and the results became known as the Fermi–Pasta–Ulam problem. It was not until 2008, when French physicist Thierry Dauxois advocated for giving her credit in a Physics Today article, that Tsingou’s contribution was properly acknowledged. Today the finding is called the Fermi–Pasta–Ulam–Tsingou problem.

The year 1953 also saw IBM’s first commercial, fully electronic computer – an IBM 701 – arrive at Los Alamos. Soon the theoretical division had two of these machines, which, alongside the MANIAC, gave the scientists unprecedented computing power. Among those to take advantage of the new devices were Martha Evans (whom very little is known about) and theoretical physicist Francis Harlow, who began to tackle the largely unexplored subject of computational fluid dynamics.

The idea was to use a mesh of cells through which the fluid, represented as particles, would move. This computational method made it possible to solve complex hydrodynamics problems (involving large distortions and compressions of the fluid) in 2D and 3D. Indeed, the method proved so effective that it became a standard tool in plasma physics where it has been applied to every conceivable topic from astrophysical plasmas to fusion energy.

The resulting internal Los Alamos report – The Particle-in-cell Method for Hydrodynamic Calculations, published in 1955 – showed Evans as first author and acknowledged eight people (including Evans) for the machine calculations. However, while Harlow is remembered as one of the pioneers of computational fluid dynamics, Evans was forgotten.

A clear-cut division of labour?

In an age where women had very limited access to the frontlines of research, the computational war effort brought many female researchers and technical staff in. As their contributions come more into the light, it becomes clearer that their role was not a simple clerical one.

There is a view that the coders’ work was “the vital link between the physicist’s concepts (about which the coders more often than not didn’t have a clue) and their translation into a set of instructions that the computer was able to perform, in a language about which, more often than not, the physicists didn’t have a clue either”, as physicists Giovanni Battimelli and Giovanni Ciccotti wrote in 2018 (Eur. Phys. J. H 43 303). But the examples we have seen show that some of the coders had a solid grasp of the physics, and some of the physicists had a good understanding of the machine operation. Rather than a skilled–non-skilled/men–women separation, the division of labour was blurred. Indeed, it was more of an effective collaboration between physicists, mathematicians and engineers.

Even in the early days of the T-5 division before electronic computers existed, Livesay and Ewing, for example, attended maths lectures from von Neumann, and introduced him to punch-card operations. As has been documented in books including Their Day in the Sun by Ruth Howes and Caroline Herzenberg, they also took part in the weekly colloquia held by J Robert Oppenheimer and other project leaders. This shows they should not be dismissed as mere human calculators and machine operators who supposedly “didn’t have a clue” about physics.

Verna Ellingson (Gardiner) is another forgotten coder who worked at Los Alamos. While little information about her can be found, she appears as the last author on a 1955 paper (Science 122 465) written with Metropolis and physicist Joseph Hoffman – “Study of tumor cell populations by Monte Carlo methods”. The next year she was first author of “On certain sequences of integers defined by sieves” with mathematical physicist Roger Lazarus, Metropolis and Ulam (Mathematics Magazine 29 117). She also worked with physicist George Gamow on attempts to discover the code for DNA selection of amino acids, which just shows the breadth of projects she was involved in.

Evans not only worked with Harlow but took part in a 1959 conference on self-organizing systems, where she queried AI pioneer Frank Rosenblatt on his ideas about human and machine learning. Her attendance at such a meeting, in an age when women were not common attendees, implies we should not view her as “just a coder”.

With their many and wide-ranging contributions, it is more than likely that Evans, Gardiner, Tsingou and many others were full-fledged researchers, and were perhaps even the first computational scientists. “These women were doing work that modern computational physicists in the [Los Alamos] lab’s XCP [Weapons Computational Physics] Division do,” says Nicholas Lewis, a historian at Los Alamos. “They needed a deep understanding of both the physics being studied, and of how to map the problem to the particular architecture of the machine being used.”

Overlooked then, overlooked now

Credited or not, these pioneering women and their contributions have been mostly forgotten, and only in recent decades have their roles come to light again. But why were they obscured by history in the first place?

Secrecy and sexism seem to be the main factors at play. For example, Livesay was not allowed to pursue a PhD in mathematics because she was a woman, and in the cases of the many married couples, the team contributions were attributed exclusively to the husband. The existence of the Manhattan Project was publicly announced in 1945, but documents that contain certain nuclear-weapons-related information remain classified today. Because these are likely to remain secret, we will never know the full extent of these pioneers’ contributions.

But another often overlooked reason is the widespread underappreciation of the key role of computational scientists and research software engineers, a term that was only coined just over a decade ago. Even today, these non-traditional research roles end up being undervalued. A 2022 survey by the UK Software Sustainability Institute, for example, showed that only 59% of research software engineers were named as authors, with barely a quarter (24%) mentioned in the acknowledgements or main text, while a sixth (16%) were not mentioned at all.

The separation between those who understand the physics and those who write the code, understand and operate the hardware goes back to the early days of computing (see box above), but it wasn’t entirely accurate even then. People who implement complex scientific computations are not just coders or skilled operators of supercomputers, but truly multidisciplinary scientists who have a deep understanding of the scientific problems, mathematics, computational methods and hardware.

Such people – whatever their gender – play a key role in advancing science and yet remain the unsung heroes of the discoveries their work enables. Perhaps what this story of the forgotten pioneers of computational physics tells us is that some views rooted in the 1950s are still influencing us today. It’s high time we moved on.

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A few weeks ago, I experienced a classic annoyance of modern life: one of my computer games stopped working. The cause? An “update” to the emulator that translates old games into programs that today’s machines can execute. In my case, this update broke the translation process, and the tenuous thread of hardware and software connecting my laptop to the game’s 30-year-old code was severed.

For individuals, failures like this are irritating. But for the wider digital ecosystem, they’re a real problem – so much so, in fact, that Vint Cerf, who’s known as one of the “fathers of the Internet”, made them the subject of his talk at last week’s Heidelberg Laureate Forum (HLF) in Heidelberg, Germany.

“My big worry is that all this digital stuff won’t be there when we would like it to be there, or when our descendants would like to have it,” Cerf said.

How it used to work

Historically, the best ways of preserving information involved writing it on durable materials such as clay tablets, high-quality paper, or a form of animal skin known as vellum. These media, Cerf observed, “have one thing in common: they don’t require electricity to be stored and preserved.”

Digital media, in contrast, are much less robust. “Many of them are magnetic, and the magnetic material wears away after a while,” Cerf explained. Consequently, some old tapes are now so fragile that attempting to read them can actually lift the magnetic material off the surface: “You read it once and that’s it. It’s now transparent tape,” he said.

Being able to read data is just the beginning, though. As my broken computer game shows, you also need programs and equipment that can persuade those data to do things. “That’s often the thing that goes first,” Cerf told me in a press conference after his talk. For example, when Cerf recently tried to retrieve data from an old three-and-a-half-inch floppy disk, he discovered that doing so would require three additional components: a drive that could read the disk, a program that could open the files stored on the disk and an old computer that could run the program. “I needed a whole lot of software help and several stages in order to make that digital content useful,” Cerf said.

Creating ‘digital vellum’

As for how to fix this problem and create a digital version of vellum, Cerf, who has been the “Chief Internet Evangelist” at Google since 2005, listed three ideas that he finds interesting. The first involves a New Jersey, US-based company called SPhotonix that does research and development work in the UK and Switzerland. It’s using lasers to write bits of data into chunks of quartz crystal, which is a very long-lasting medium. However, each crystal is roughly the size of a hockey puck, and Cerf thinks that “real work” still needs to be done to organize the information the material holds.

The second idea is partly inspired by the clay tablets that proved so successful at preserving cuneiform writing from ancient Mesopotamia. Cerabyte, a start-up with facilities in Austria, Germany and the US, has developed a ceramic material that its founders claim could “store all data virtually forever”.

The third idea, and the one that seems to appeal most to Cerf, is to write digital information into DNA. That might sound like an inherently fragile medium, but as Cerf pointed out, “It’s actually a very robust molecule – otherwise, life wouldn’t have persisted for several billion years.” Provided you dehydrate the DNA first, he added, it lasts for “quite a long time”.

The question of how to read such information is not an easy one, and Cerf doesn’t have an answer to it. He is, however, hopeful that someone will find one. At the HLF, where he is such a revered figure that even the journalists want to take photos with him, he issued a call to arms for the young researchers in the audience. “I want you to appreciate the scope of the work that is required to preserve digital things,” Cerf told them. Without that work, he added, “recreating a digital environment in 100 years is not going to be a trivial matter.”

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