# Bas|ket>ball: A Game for Young Students Learning Quantum Computing

It is no secret that quantum computing has recently become one of the trendiest topics within the physics community, gaining financial support and good press at an ever increasing pace. The new technology not only promises huge advances in information processing, but it also – in theory – has the potential to crack the encryption that currently protects sensitive information inside governments and businesses around the world. Consequently, quantum research has extended beyond academic groups and has entered the technical industry, creating new job opportunities for both experimentalists and theorists. However, in order for this technology to become a reality, we need qualified engineers and scientists that can fill these positions.

Increasing the number of individuals with an interest in this field starts with educating our youth. While it does not take particularly advanced mathematics to explain the basics of quantum computing, there are still involved topics such as quantum superposition, unitary evolution, and projective measurement that can be difficult to conceptualize. In order to explain these topics at a middle and high school level to encourage more students to enter this area, we decided to design an educational game called Bas|ket>ball, which allows students to directly engage with quantum computing concepts outside of the classroom while being physically active.

After playing the game with students in our local Quantum Information High (QIHigh) Program at Stevens Institute of Technology, we realized that the game is a fun learning tool worth sharing with the broader physics community. Here, we describe a non-gender specific activity that can be used to effectively teach the basics of quantum computing at a high school level.

Quantum Basketball is something that helps you understand a very confusing topic, especially for a ninth grader! In the QI-High Program at Stevens, I was approached with a challenge of learning about quantum computing, and while I was hesitant at first, my mentors made the topic so much more understandable by relating it to a sport that I love!

Grace Conlin, Freshman Student from High Tech High School

## The Rules of Bas|ket>ball

The game can have up to 10 student players and only requires one basketball. Each player acts as a quantum bit (qubit) in a quantum register and is initialized to the |0> position. During each turn, a player will perform one of the allowed quantum gates depending on their position on the court. A diagram of the court positions is displayed at the bottom.

There are four options of quantum gates from which players can choose to move around the court:

1. X Gate – This single qubit gate will take a player from the |0> to the |1> position, and vice versa.
2. Hadamard Gate – This single qubit gate will take a player from the |0> to the (|0> + |1>) / $\sqrt{2}$ position and the |1> to the (|0> – |1>) / $\sqrt{2}$ position, and vice versa.
3. Control-Not Gate – This two-qubit gate allows one player to control another only if they are in the |1> position, or in superposition between |0> and |1>. The player in the |1> position can move a player back and forth between the |0> and |1> positions. The player in the superposition can choose to entangle with a player in the |0> position.
4. Z Measurement – The player takes a shot. The player measures a 1 if he/she makes the shot and measures a 0 if he/she misses. Once the player shoots, he/she has to return back to the |0> position no matter what was measured.

The first player to measure ten 1’s (make ten shots) wins! In order to make the game more interesting, the following additional rules are put in place:

1. Each player has one SWAP gate that can be utilized per game to switch positions with any other player, including players that are entangled. This is an effective way to replace yourself with someone in an entangled state.
2. Up to five players can be entangled at any given time. The only way to break the entanglement is to make a Z Measurement by taking a shot. If one of the entangled players makes a shot, each player entangled with that player receives a point value equal to the number of individuals they are entangled with (including themselves). If the player misses, the entanglement is broken and no points are awarded. Either way, all players go back to the |0> position.

## Example Bas|ket>ball Match

For example, let’s say that we have three student players. Each will start at the red marker, behind the basketball hoop. One by one, each student will choose from the list of gate operations above. If the first player chooses an X-gate, he/she will physically move to the blue marker and be in a better position to make a measurement (take a shot) during the next turn. If the second player chooses to perform a Hadamard gate, he/she will move to the green marker. Each of the students will continue to move around the court and score points by making measurements until 10 points are reached.

However, things can get more interesting when players start to form alliances by entangling. If player 1 is at the green marker and player 3 is at the red marker, then player 1 can perform a C-Not gate on player 3 to become entangled with them. Now if either player takes a shot and scores a point, both players will be awarded 2 points (1 x the number of players entangled).

We believe that simple games such as this, along with Quantum TiqTaqToe and Quantum Chess, will attract more young students to pursue degrees in physics and computer science, and eventually specialize in quantum information and computing fields. Not only is this important for the overall progression of the field, but also to encourage more diversity and inclusion in STEM.

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