# First encounters with quantum computing: can games teach quantum reasoning?

Lead Research Organisation:
Durham University

Department Name: Physics

### Abstract

Quantum computing is expected to have far-reaching benefits as well as potential security concerns for a wide range of industries in coming years. At present, there is little understanding of, or expertise in, the skills required for effective quantum computational reasoning outside specialists in physics and mathematics. The goal of this work is to conduct a pilot project in collaboration with participants from across a range of ages and sectors to develop an understanding of how non-specialists develop their understanding of counter-intuitive quantum computational concepts and whether this can be assisted through the use of a visual game-like interface. Our project partner Quarks Interactive have developed a game which visually, rather than mathematically, represents the most common model of quantum computing; the gate model which is universal in the sense that it can model all quantum information processing. This project will allow us to develop and test the effectiveness of this game as a learning tool, as well as to assess its relative performance with different groups. The game consists of a visual Plinko (grid of pins) board like system where coloured balls travel down the board following different tracks. Players are tasked to solve increasingly complex puzzles using picture tiles to change the path the balls take down the board, or to introduce actions on the balls. Behind the scenes each picture tile accurately represents a quantum mechanical rule and the player's sequence of tiles is writing a functioning quantum algorithm. However, crucially, the player does not have to have any knowledge of the complex mathematics behind the scenes to be able to successfully complete the puzzles. The puzzles therefore enable the player to develop an intuition about quantum mechanics as well as generating genuine quantum computing algorithms, which can be implemented on quantum computers. Developing a more effective way for quantum non-specialists across diverse industries to develop intuition about quantum mechanics is crucial for businesses to understand the implications of quantum computing for their own context and to stay ahead of the game as quantum computing advances. Additionally, management and government will increasingly be expected to make decisions related to quantum computing and will have to become quantum literate to avoid falling victim to misconceptions and hype.

Higher levels of quantum literacy will enable citizens from a wide variety of backgrounds to bring the potential benefits of exponentially faster and more complex data processing to their own businesses, industries and disciplines, enabling them to re-imagine the possibilities for data analysis and problem solving in their fields. At present, a relatively small number of quantum computing experts have this knowledge and understanding. The benefit of a broader range of citizens being able to access this understanding than is currently possible when quantum computing must be learned through maths and physics, is therefore a wider understanding of the potential applications of quantum computing in diverse areas of society, which currently do not benefit from this technological revolution. Quantum literacy equates to a different way of understanding reality and therefore, a potentially different way of conceiving of problems in a range of diverse fields.

A quantum computing visualization learning tool could also have an important function in engaging the next generation of learners in the building blocks of quantum computing at an earlier age. We aim to discover whether learning through this puzzle visualization process also potentially increases engagement and motivation in groups who are traditionally under-represented in more advanced study of computer science, mathematics and physics.

Higher levels of quantum literacy will enable citizens from a wide variety of backgrounds to bring the potential benefits of exponentially faster and more complex data processing to their own businesses, industries and disciplines, enabling them to re-imagine the possibilities for data analysis and problem solving in their fields. At present, a relatively small number of quantum computing experts have this knowledge and understanding. The benefit of a broader range of citizens being able to access this understanding than is currently possible when quantum computing must be learned through maths and physics, is therefore a wider understanding of the potential applications of quantum computing in diverse areas of society, which currently do not benefit from this technological revolution. Quantum literacy equates to a different way of understanding reality and therefore, a potentially different way of conceiving of problems in a range of diverse fields.

A quantum computing visualization learning tool could also have an important function in engaging the next generation of learners in the building blocks of quantum computing at an earlier age. We aim to discover whether learning through this puzzle visualization process also potentially increases engagement and motivation in groups who are traditionally under-represented in more advanced study of computer science, mathematics and physics.

### Technical Summary

The quantum puzzle visualization tool is based on an entirely graphical version of the matrix-vector representation of the Hilbert spaces of full systems. Because the translation for matrices to visual elements is exact, this representation is also exact. From this visualisation tool the players will be able to learn about fundamental principles behind quantum mechanics such as superposition and interference. Because high level tools for quantum computing are not yet fully developed, understanding the underlying building blocks is crucial, unlike in classical computing where much of the low level behaviour of the computer can be abstracted away. The dynamics of classically counter-intuitive processes such as phase amplification can be understood in such a way that even if the mathematics is hard to grasp, they can be intuitively understood by engaging with the visual tool and solving puzzles. The visualization tool is of something real i.e. quantum circuits, which include non-Clifford gates and are therefore universal for quantum computing. The fact that the game is a full exact representation of quantum mechanics necessarily limits the systems to small sizes (if the game itself could exactly simulate large quantum computers, we would not need large quantum computers), however these small sized examples can build intuition for larger systems which could not be represented in the game. This is a gateway to further learning because it presents complex numbers and linear algebra in a much more accessible way than through equations. These representations mean that the phase interference which is crucial to quantum mechanics can be understood visually and allows the users to develop a visual, rather than mathematical, mental model of these processes. Testing how effective this model is is one of the aims of our proposal.

### Planned Impact

This project has the potential to ensure that end users of quantum computing are able to become quantum literate and engage with the concepts behind quantum computing much earlier, and to a much greater extent than they would otherwise be able to. A direct result of this is that these end users will be able to use their intimate knowledge of important problems and the current cutting edge classical techniques to develop highly optimal applications of quantum computing, when compared to what could be developed by quantum physicists who are newcomers to the application domains. Therefore, quantum machines can be developed more effectively for maximum benefit within individual industrial applications and the transition from being academically funded research to industrially focussed applications can occur much sooner.

Additionally the methods studied here can help educate future decision makers, such as managers and members of government who have to make decisions related to quantum computing. By increasing quantum literacy in this group, we can ensure that companies and governments make the right choices going forward, and are less likely to invest in apparently exciting but technically unsound avenues toward quantum computation, and perhaps more importantly have the ability to recognize areas where there is truly immense potential and shape policy and/or investments to support these areas. By being quantum literate, these important decision makers can also maintain realistic expectations of time scales and the rate of development of the technologies, such literacy is likely to help reduce the potential of a "quantum winter", where excessive enthusiasm leads to unrealistic expectations for the field and a corresponding reduction in investment when these expectations are not met.

Understanding the optimal age at which it becomes appropriate to introduce the concepts of quantum computing within the education system also means that there is potential to develop skills in this area from a much earlier stage. This project has the potential to provide policy makers and teachers with the ability to introduce the concepts of quantum computation within the school computer science curriculum without the need for complex mathematical knowledge, thus advancing the level of skill in this area before students enter the workforce or Higher Education.

Raising the level of quantum literacy in the general public will also elevate the public discourse on quantum computing in arenas such as popular science publications and will lesson the incentives for both the quantum computing industry and academics to over-hype results since the public is less likely to be convinced. This can again help reduce the potential for "quantum winter". This higher level of quantum literacy also means that members of the public will be more likely to go into professions requiring expertise related to quantum mechanics which includes, but is not limited to, quantum computing.

These related fields include but are not limited to materials science, physics, chemistry, and nanotechnology. Quantum mechanical effects are becoming increasingly important as technology moves to smaller scales (in the case of nanotechnology) or as research into exotic states of matter such as superconductors becomes more important. Other fields such as physics and chemistry have aspects which are fundamentally quantum. Individuals who are not only quantum literate, but have been exposed to quantum laws from an early age and have true quantum intuition are likely to be better equipped to handle difficult quantum problems such as high temperature superconductivity, or understanding the action of complex molecules, even in the absence of quantum computers.

Additionally the methods studied here can help educate future decision makers, such as managers and members of government who have to make decisions related to quantum computing. By increasing quantum literacy in this group, we can ensure that companies and governments make the right choices going forward, and are less likely to invest in apparently exciting but technically unsound avenues toward quantum computation, and perhaps more importantly have the ability to recognize areas where there is truly immense potential and shape policy and/or investments to support these areas. By being quantum literate, these important decision makers can also maintain realistic expectations of time scales and the rate of development of the technologies, such literacy is likely to help reduce the potential of a "quantum winter", where excessive enthusiasm leads to unrealistic expectations for the field and a corresponding reduction in investment when these expectations are not met.

Understanding the optimal age at which it becomes appropriate to introduce the concepts of quantum computing within the education system also means that there is potential to develop skills in this area from a much earlier stage. This project has the potential to provide policy makers and teachers with the ability to introduce the concepts of quantum computation within the school computer science curriculum without the need for complex mathematical knowledge, thus advancing the level of skill in this area before students enter the workforce or Higher Education.

Raising the level of quantum literacy in the general public will also elevate the public discourse on quantum computing in arenas such as popular science publications and will lesson the incentives for both the quantum computing industry and academics to over-hype results since the public is less likely to be convinced. This can again help reduce the potential for "quantum winter". This higher level of quantum literacy also means that members of the public will be more likely to go into professions requiring expertise related to quantum mechanics which includes, but is not limited to, quantum computing.

These related fields include but are not limited to materials science, physics, chemistry, and nanotechnology. Quantum mechanical effects are becoming increasingly important as technology moves to smaller scales (in the case of nanotechnology) or as research into exotic states of matter such as superconductors becomes more important. Other fields such as physics and chemistry have aspects which are fundamentally quantum. Individuals who are not only quantum literate, but have been exposed to quantum laws from an early age and have true quantum intuition are likely to be better equipped to handle difficult quantum problems such as high temperature superconductivity, or understanding the action of complex molecules, even in the absence of quantum computers.