This is the teacher guide for this lesson. A student-focused guide to assist learners as they perform the activity is available.

# Save Schrödinger's Cat

How are quantum logic gates different from the logic gates used in normal computers?

This resource was originally published in PhysicsQuest 2021: Introduction to the World of Quantum.

How are quantum logic gates different from the logic gates used in normal computers? What are the key phenomena that make people excited about quantum computing? Can you describe quantum interference after playing this game?

- Game cards (see the game pieces in Teacher guide, Setting up)

Modern computers are all built to use the same logic and the same assessment criteria to understand each other. Instructions the computers use for achieving tasks are called logic circuits and the result of executing any such circuit will always have just one of the two states: False or True. We can call these two states any way we want, including Asleep and Awake. The building blocks of these circuits are the logic gates and arrangements of logic gates are called circuits. A programmer’s job is to build circuits that expand what computers are able to do: construct circuits that flip between False and True in ways that have not been done before by building more elaborate arrangements of logic gates to construct even more advanced logic circuits. In the activity “Save Schrodinger’s Cat,” the pupils play the role of a programmer that instead of writing code, has a powerful visual method to work with logic gates and create circuits. They will build circuits by placing gates in a sequence to prevent the outcomes given by the Challenge Scenarios from happening to our beloved cat. We want our cat to always be in the Awake (True) state after each challenge scenario. How to get there is completely up to them and their ability to master various logic gates and come up with useful circuits to achieve this goal.

Save Schrödinger’s Cat is about how the logic of quantum mechanical systems is fundamentally different from classical mechanics (the rules most “everyday” physics you encounter follows). The key difference we highlight here is the idea of interference, classically, giving more than one way for something to happen can only increase its likelihood. For example, if you want to know the chances that your jacket will be wet when you come home this evening, you might look at the chance that it will rain, discovering that the neighbor’s sprinkler has also been acting funny and you might get your jacket wet that way, can only increase the chances that you come home wet, never decrease it. Quantum mechanically this is completely different, possibilities can interfere with each other, and adding a new way to get an outcome can reduce the chance of it happening, even to the point where it never happens at all.

- Total time60 - 90 minutes
- Education levelGrades 6 - 12
- Content AreaQuantum mechanics
- Educational topicQuantum science

If you have pupils asking about the underlying mathematics of the activity, you can refer to this. In fact, you could use Save Shrödinger’s Cat to get the pupils excited about linear algebra and complex numbers if the time is right. The rules of the game allow you to work with quantum computing using just visual clues, without having to understand the underlying mathematics. However, if pupils are interested in how the mathematics work, here we present what the activity does:

This activity is based on the fundamental rules of play of an educational video game called Quantum Odyssey. Quantum Odyssey is an interactive software meant to make quantum computation an enjoyable experience and to teach people without a background in quantum physics, coding, or linear algebra how to construct real quantum algorithms, using a no code, fully visual, and gamified method. The mission behind Quantum Odyssey is explained in this short video.

These are the key terms that students should know by the END of the two lessons. They do not need to be front loaded. In fact, studies show that presenting key terms to students before the lesson may not be as effective as having students observe and witness the phenomenon the key terms illustrate beforehand and learn the formalized words afterwards. For this reason, we recommend allowing students to grapple with the experiments without knowing these words and then exposing them to the formalized definitions afterwards in the context of what they learned.

However, if these words are helpful for students on an IEP, ELL students, or anyone else that may need more support, please use at your discretion.

- Probability: The likelihood that something happens, for example, the chance that I flip a coin and it lands on heads is ½.
- Probability amplitude: The quantum version of probability which allows for interference between different outcomes.
- Quantum interference: The quantum mechanical effects which allow probabilities to decrease or completely cancel out when new ways of reaching that outcome are added. We offer pupils the quantum interference table to calculate the outcomes.
- Quantum phase: The property which determines how probability amplitudes add. The same phase means they add together more strongly than classical probabilities, opposite phases (difference of - 1) mean they cancel, and “orthogonal” phases (phase difference of plus or minus one imaginary unit) mean they add in the same way classical probabilities do. In this game we use colors to do the math rather than traditional equations. We offer pupils the color legend table to calculate how the phases interact with each other.

Students will begin to explore a powerful visual method used for writing algorithms (circuits) on quantum computers.

Quantum mechanics is different from the usual rules of nature they see, and usually only applies to very small objects. The activity Save Schrödinger’s Cat attempts to bridge the quantum mechanical state of an atom (that can be in superposition) with a classical object (the cat). Measurement forces both the atom and the cat to collapse to one of the possible states however pre-measurement the fates of the cat and the atom are interlinked.

If you try something many times you can get an idea how likely different outcomes are, for example if a coin has landed on heads 20 times in a row it probably isn’t a fair coin. We show using the visuals from this activity why in quantum mechanics, phase will always contain information behind events that lead to different outcomes. See the video "Why Probability in Quantum Physics is Not What You'd Expect: Quantum Odyssey videogame."

Some things have a definite outcome (same thing always happens), whereas some have a chance of a few different things happening.

In the Student Guide, students are asked to complete different challenges using the classic and quantum gates to see if they can arrive at the desired final state. The idea of this experiment is that students start to form ideas about the difference between classical mechanics and quantum mechanics.

Print out

*game cards*and cut them out.Read through instructions in the Student Guide.

Before letting students work on the challenges, work with them on the examples provided on the game instructions. Then let them do the initial challenges that only involve classic gates before introducing them into the H and S quantum gates.

- Suggested
*STEP UP Everyday Actions*to incorporate into activity:- When pairing students, try to have male/female partners and invite female students to share their ideas first.
- As you put students into groups, consider having female or minority students take the leadership role.
- Take note of female participation. If they seem to be taking direction and following along, elevate their voice by asking them a question about their experiment.

- Consider using white boards so students have time to work through their ideas and brainstorms before saying them out loud.
- As students experiment, roam around the room to listen in on discussion and notice experiment techniques. If needed, stop the class and call over to a certain group that has hit on an important concept.

Consider using the RIP protocol (Research, Instruct, Plan) for lab group visits and conferring.

Consider culturally responsive tools and strategies and/or open ended reflection questions to help push student thinking, evidence tracking, and connections to their lives.

After the activity, the students should know:

- That interference is a key part of what makes quantum different.
- Adding a new way to get a result quantum mechanically can reduce the chances of something happening, and even make it never happen.
- Changing a quantum phase between two possibilities can change the outcome – there is no classical analogy of this.
- That even complicated math can be understood by drawing pictures rather than using equations.
- How quantum gates can be combined together to create quantum effects and how to use different sets of gates to achieve the same outcome.

- Real world connections:
- Have students explore these online quantum games and activities from Quander.

- Suggestions for drawing, illustrating, presenting content in creative ways:
- Have students play with this Phet simulation to visualize this experiment. Have them write about how the visualization helped them understand the concept more deeply.

### Credits

Coordination, Research, Text, and Editorial Review: Jessica Eskew, Jamie Liu, Leah Poffenberger, Catherine Tabor, Laurie Tangren, and Rose Villatoro

Graphic Design and Production: Meghan White

Cover Illustration: Annamaria Ward

Activity 3, "Save Schrodinger’s Cat,” is created by the team behind Quarks Interactive SRL. Concept: Laurentiu Nita

Design & Art: Ar. Judit Balazs-Becsi

Writing: Dr. Nicholas Chancellor, Dr. Helen Cramman, Dr. Laura Mazolli Smith, and Andrei Voicu Tomut

Activity 4, "Quantum Circuits," was created by our partners at Virginia Tech Sophia Economou and Edwin Barnes. Supported by the National Science Foundation (grant nos. 1741656 and 1847078)

PhysicsQuest is sponsored in part by the Eucalyptus Foundation.

Updated in 2023 by Sierra Crandell, MEd, partially funded by Eucalyptus Foundation

Extension by Jenna Tempkin with Society of Physics Students (SPS)