One of the secrets to building the world's most powerful computer is probably perched by your bathroom sink. At IBM's Thomas J. Watson Research Center in New York State's Westchester County, scientists always keep a box of dental floss--Reach is the preferred brand--close by in case they need to tinker with their oil-drum-size quantum computers, the latest of which can complete certain tasks millions of times as fast as your laptop. Inside the shimmering aluminum canister of IBM's System One, which sits shielded by the same kind of protective glass as the Mona Lisa, are three cylinders of diminishing circumference, rather like a set of Russian dolls. To work properly, this chip requires super-cooling to 0.015 kelvins--a smidgen above absolute zero and colder than outer space. Most materials contract or grow brittle and snap under such intense chill.

Quantum computing technology is advancing rapidly and is on track to solve extraordinarily complex business problems through enhanced optimization, machine learning, and simulation. Make no mistake, the technology promises to be one of the most disruptive of all time. In fact, I believe quantum computing will hand a significant competitive advantage to the companies that can successfully leverage its potential to transform their business and their industries. While quantum technologies are still maturing, companies are already preparing, with spending on quantum computing projected to surge from $260 million in 2020 to $9.1 billion by 2030, according to research from Tractica. Companies are pursuing the promise of quantum aggressively, as evidenced by the recently announced combination of Honeywell Quantum Solutions and Cambridge Quantum Computing.

In game theory, an Evolutionarily Stable Set (ES set) is a set of Nash Equilibrium (NE) strategies that give the same payoffs. Similar to an Evolutionarily Stable Strategy (ES strategy), an ES set is also a strict NE. This work investigates the evolutionary stability of classical and quantum strategies in the quantum penny flip games. In particular, we developed an evolutionary game theory model to conduct a series of simulations where a population of mixed classical strategies from the ES set of the game were invaded by quantum strategies. We found that when only one of the two players' mixed classical strategies were invaded, the results were different. In one case, due to the interference phenomenon of superposition, quantum strategies provided more payoff, hence successfully replaced the mixed classical strategies in the ES set. In the other case, the mixed classical strategies were able to sustain the invasion of quantum strategies and remained in the ES set. Moreover, when both players' mixed classical strategies were invaded by quantum strategies, a new quantum ES set emerged. The strategies in the quantum ES set give both players payoff 0, which is the same as the payoff of the strategies in the mixed classical ES set of this game.