Student Guide

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)
    Game background

    Dr. Schrödinger is conducting a classic quantum experiment! He has built a steel chamber in which he has placed a Geiger counter along with a tiny bit of radioactive substance, an amount so small that perhaps in a matter of minutes one of the atoms will decay, but perhaps, with equal probability, none of the atoms will decay. If this does happen, the counter tube will discharge, then through an electromagnet activated by a signal, release a hammer that shatters a flask of sleeping gas.

    Dr. Schrödinger leaves the office for the night to feed his cat.

    You are his lab assistant, and you are certain that if one of the atoms decays, the flask would surely break inside the steel chamber and the gas would put everything inside the chamber to sleep. As you ponder upon the experimental details, you hear a sudden “Meow!” coming from the steel chamber.

    Oh no, Schrödinger’s Cat must have sneaked inside the chamber searching for food!

    You must quickly use your knowledge of quantum and Save Schrödinger’s Cat!

    How to win

    • The purpose of the game is to start from one of the Challenge Scenarios. Place the cat token as indicated in each scenario and then figure out and place down the right sequence of Quantum Gates to create a quantum path for the cat token to arrive from the initial state (given in the Challenge Scenario) to our desired final state: a single blue cat token on the Awake state. This will stabilize the atom and keep Schrödinger’s cat awake.

      You win a Challenge if you manage to obtain on the last card a single, blue-colored token at the end of an uninterrupted sequence of quantum gate cards.

      All quantum gates you placed should remain in place until you solve the Challenge Scenario. They represent the Quantum Algorithm you create to achieve the final state (blue cat token on the Awake state) out of an initial state given by the Challenge Scenario. There is more than one way to solve a problem!

    Game components
      1. The colors in the game represent the quantum phase. There are two types of tokens: four blue-red tokens (blue on one side and red on the other), four green-gold tokens (green on one side and gold on the other). These eight tokens, through their position and color, represent quantum states of the atom that decide the fate of Schrödinger’s Cat.
      2. The Color Legend table (titled Color Legend) shows the rules for phase interactions.
      3. The Quantum Interference table (titled Quantum Interference) shows the behavioral rules of what happens to the quantum state inside an H gate. You will need an H gate when you want your tokens to be in a superposition of both SLEEP and AWAKE or create phase interference between the tokens. Use the Quantum Interference table only to calculate the quantum state of your cat inside an H gate.
    Game setup
    Rules of the game

    • Place on a flat surface one of the Challenge Scenarios to start and the Final State card that shows the winning condition.

    • Place the cat token(s) as indicated by the Challenge Scenario.

    • Pick from the quantum gate cards those that you believe will bring the token closer to the Final state. Place these gates one below each other, from the Scenario card to the Final state card.

    • Navigate the quantum gates with the token. Follow the paths as indicated by the arrows. If one of the paths is a different color, look at the Color Legend and change the color of the token as indicated by the Color Legend.

    • Try to find the right combination of quantum gate cards to reach the Final State. The final combination of gates used is your quantum algorithm. Try to find the optimal one (to reach the Final State with the least number of gates).

    • A special case: The H gate:

      You can create additional tokens, combine them, or remove tokens using the H gate. This gate has two arrows pointing out from each state and two arrow pointers arriving to each state. For each state on the H gate, add another identical copy of the same token(s) that are already present on that state to be able to travel both arrows simultaneously. When the tokens collide, use the Quantum Interference table to calculate what tokens are left.

    Two examples of navigating quantum gate cards

    Case 1: blue cat token on Awake state entering a Z gate, followed by an X gate. The output will be a red cat on the Sleep state.

    ZX sequence

    • Place blue token on the Z gate’s AWAKE state.

    • Token will navigate a red path; flip it according to the Color Legend.

    • The now red token enters X gate on the AWAKE state.

    • Token crosses from the AWAKE state to the SLEEP state, through a blue path (according to the Color Legend).

    HH sequence

    • Place blue token on the H gate’s SLEEP state.

    • There are two arrow pointers in the SLEEP state within the H gate. You must duplicate your token on the board (add another one in this case). Tokens now navigate both paths of blue color (nothing changes according to Color Legend) at the same time.

    • In this step, you must repeat step (2) from both SLEEP and AWAKE states of the second H gate, to have four tokens in total. Take notice that one of the paths from the AWAKE state is of red color, which will flip one copy of the token from blue to red.

    • Use the Quantum Interference table to calculate what happens to the colliding cats from step (3)! Two blue cats colliding will leave a single blue one, while a blue and a red cat will result in no cats.

    Color legend table

    These are the rules for what happens to a cat token when it navigates a path of a specific color. Remember there are two types of tokens (blue-red and green-gold).

    • The blue path is neutral. It preserves the color of the token.

    • The red path will always flip the token.

    • A green cat going through a green path will result in a red cat.

    • A gold cat going through a green path will result in a blue cat

      A gold cat going through a green path will result in a blue cat.

    • If you know a thing or two about Complex Numbers, it could be easier to think of multiplication between complex numbers. For convenience, a blue cat is 1+0i, a red cat is -1+0i, a green cat is 0+i, a gold cat is 0-i. If you know that (0+i)*(0+i)= -1+0i, this is just as saying a green cat goes through a green path and comes out red (rule 3).

    Observations

    • After you decide to place an H gate, you will notice that because of how the paths within this gate are laid out, your cat tokens will collide like what you see here.

    • Now look at the following table. In this example we have two cases: blue + blue on the SLEEP state and blue + red on the AWAKE state. The table shows you the outcome. Replace or remove the tokens as indicated in the following table.

      For our example, we are left with a single blue cat.

    If you know a thing or two about Complex Numbers, these are the rules for addition! Example: blue + gold cats = form a blue and a gold cat together 1+0i+(0-i)=1-i.

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