Quantum Computing: A Soccer Analogy

Creighton University soccer player Ricky Lopez-Espin, photographed by Mark Kuhlmann, courtesy of Creighton Athletics.

The essence of quantum computing is explained using a soccer or association football analogy, giving the correct sense that quantum computers are faster than traditional computers at solving some problems, not all problems.

Quantum computing has been explained in popular articles using a variety of means, with varying levels of accuracy. One particularly problematic approach is when “quantum parallelism” is abused, suggesting that quantum computers are faster simply because they try all possible solutions at once. This gives the false notion that quantum computers are just massively parallel classical computers, and so they can solve all problems quickly via brute-force. In reality, while quantum computers are faster at solving some problems, they are not faster at solving all problems.

This misunderstanding is so prolific that the banner of Scott Aaronson’s popular quantum computing blog reads, “If you take just one piece of information from this blog: Quantum computers would not solve hard search problems instantaneously by simply trying all the possible solutions at once.” That is, the reporting on quantum computing has been so bad that the most important piece of information that readers can garner from Aaronson’s blog is not what quantum computers can do, but what they cannot do.

More accurate articles correct for the misunderstanding that quantum parallelism brings by stressing that even though quantum computers do compute in parallel, only one result is outputted. Thus, one does not obtain all possible results at once, meaning a quantum computer is not simply a massively parallel computer. This correction may come too late, however, with readers maintaining their initial, inaccurate interpretation of quantum parallelism.

Alternative approach to explaining the essence of quantum computing, which avoids the false conclusion that quantum computers can quickly solve all problems in parallel, is using an analogy to soccer or association football.

In soccer, players generally cannot use their hands. As a result of this rule, the sport looks a certain way, with athletes mostly using their feet to control and kick the ball.

Now if the rules were changed so that players could use their hands, soccer would look very different. In some cases, it would be faster or easier for athletes to use their hands to hold, throw, or catch the ball. In other cases, however, it would still be better to kick the ball. For example, most soccer players can kick the ball across the field faster than they can throw the ball or run with it. So, to get the ball across the field as quickly as possible, it may still be better to use one’s feet.

Analogously, the essence of quantum computing is to change the rules so that a computer can now use its “hands.” That is, the rules of the game are changed from the laws of classical physics to the laws of quantum physics. As a result, a quantum computer can solve some problems faster by using its “hands.” For other problems, using one’s “feet” is better, so a quantum computer is no faster for these problems.

This raises the question of what it means for a computer to use its “hands.” Now would be the appropriate time to discuss the facets of quantum mechanics that make it different from classical mechanics, including quantum parallelism or superposition, measurement, the use of complex numbers as probability amplitudes, and entanglement. By leading the explanation with the soccer analogy, any oversimplification of these concepts will be confined by the initially correct understanding that quantum computers are faster at some problems, but not all, in the same way that using one’s hands in soccer may be better in some instances, but not all.