This is the teacher guide for this lesson. A student-focused guide to assist learners as they perform the activity is available.
Teacher Guide
Quantum Circuits
How does a quantum computer work?
This resource was originally published in PhysicsQuest 2021: Introduction to the World of Quantum.
How does a quantum computer work?
- Quantum state card pieces from the link "game" in Overview
Thousands of scientists around the world are working hard to develop quantum computers – machines that can solve certain problems that are far beyond the reach of the world’s best supercomputers. Famous examples of these kinds of problems include code breaking and simulating complex molecules. Unlike ordinary computers, quantum computers exploit the laws of quantum mechanics. Like ordinary computers, the way a quantum computer works can be understood in terms of a few simple logic operations that act on bits of information. By combining many such operations to form logic circuits, one can solve interesting problems. This document contains a detailed explanation of pictorial rules that can be used to design and analyze quantum logic circuits, along with a few practice problems to help students become familiar with the basic rules of quantum logic.
- Total time45 - 60 minutes
- Education levelGrades 6 - 12
- Content AreaQuantum mechanics
- Educational topicQuantum circuits
For the purpose of this activity, we substituted math by using pictorial rules, where shapes and colors will represent the different components of the computer, such as the bits and gates. We can represent programming a computer by stacking the many types of gates together to form a “logic circuit.” If we design this circuit in the right way, then we can perform useful computations where, for every input bit string we consider, the answer is given by the output bit string.
In addition to representing classical information processing (like in today’s computers), we can also use these pictorial rules to describe quantum information processing. We called the quantum states “mists” (these mists are represented by a cloud outline). These misty states enable computations that are not feasible with classical computers. We can use gates for both classical and quantum circuits with the mist. However, the Hadamard gate is purely quantum and not possible on a classical computer. We can use the Hadamard gate with the mist creating a phenomenon known as quantum superposition (producing mist from non-mist in pictorial rules) and quantum entanglement (turn mists into non-mists in pictorial rules).
We show using the visuals from this activity why in quantum mechanics, phase will always contain information behind events that lead to different outcomes.
Key terms
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.
- Bits: Today’s computers store information as strings of 0’s and 1’s, which comprise a set of bits. (Not to be confused with bytes, which are units of measurement of information for electronic devices). The 1 bit would be an electric signal (when a switch is on), while the 0 bit would represent an off switch.
- Gates: Modern computers process information using “logic gates” (or just “gates”) that take a bit string as input and produce a new bit string as output. Gates are electronic components that can be used to transport electricity, and therefore an on/off signal, based on a determined rule. The output of the gate would be determined by the rule. There are different types of gates. For example, the NOT gate inverts the input. This means that if a positive charge came in through the gate, the output then would be a negative charge. The output of the identity gate is the same as the input, i.e., it does not change the signal. There are gates that process multiple bits at the same time, such as SWAP, that change the signal of all the input bits, and the controlled-NOT (CNOT) gate. This gate applies NOT to one input bit conditional on the signal of the other input bit, specifically if the conditional is different, then the output of the NOT side of the gate will change.
- Circuits: A set of physical components that form a path around which electricity can flow. Circuits are formed by a source of electricity, such as a battery and components, such as wires, that allow electric current to pass through them easily, called conductors.
- Quantum bits or Qubits: Quantum computers use qubits instead of classical bits to process information. Qubits have different properties than bits: They can take the 0 and 1 values like classical bits, but they can also be in superposition states, where the qubit is both 0 and 1 state at the same time.
- Superposition: A physics principle in which two or more signals can be (or do) opposite things at the same time. For example a qubit can be both 0 and 1 simultaneously, a combination of those two states.
- Entanglement: Another physics phenomenon in which two or more bits are connected, so that what happens to one bit affects what happens to the others.
Objective
Students will complete different challenges using the classical and quantum gates to see if they can arrive at the desired final state.
Before the experiment
Before the activity students should know::
- Quantum mechanics is different from the usual rules of nature they see and usually only applies to very small objects.
- 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.
- Some things have a definite outcome (same thing always happens), whereas some have a chance of a few different things happening.
Setting up
Before letting students work on the challenges, go over the pictorial rules and work with them on the examples provided on the game instructions. Then let them do the initial challenge that only involves classic gates before introducing them into the H and S quantum gates.
Watch the PhysicsQuest workshop video on quantum circuits.
Teacher tip
- 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.
Conclusion
After the activity students should know:
- How classical logic works.
- How quantum logic works.
- How to build and analyze quantum circuits.
- A nice introduction to quantum information using the pictorial formalism described here can be found in the book Q is for Quantum by Terry Rudolph. A PDF copy of Part I of the book is available for free at qisforquantum.org. Keep in mind that the book uses a slightly different notation (‘NOT’ instead of ‘X’ and ‘PETE’ instead of ‘Hadamard’). Also, all qubits are represented by circles instead of different shapes.
- An introduction to quantum superposition can be found in a six-minute excerpt from a video called Dr. Quantum - Double Slit Experiment.
- MS-PS4.AWave Properties
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)