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 include code breaking and simulating complex molecules. Unlike ordinary computers, these machines 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 together 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.

**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.

**AFTER the activity students should know:**

- How classical logic works
- How quantum logic works
- How to build and analyze quantum circuits

- How does a quantum computer work?

For the purpose of this activity, we substituted math by using pictorial rules, where shapes and colors that 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.

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

Quantum Circuits Activity Video

**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 phenomena in which two or more bits are connected, so that what happens to one bit affects what happens to the others.

- 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.