# Superposition and Interference

In this video, Rodney Van Meter and his student Shinnosuke Ozawa show how superposition of waves creates constructive and destructive interference.

One of the most important concepts you must grasp to understand quantum computing is the superposition and interference of waves. Since waves are moving through space, you can have more than one wave passing through one place at the same time. When that happens, the wave add up, or superimpose on one another.

In addition to the video, we have prepared a set of applications for you to play with, and we have made the 3-D models in the video available.

## One-dimensional interference

In the upcoming application, you will have the opportunity to see the following behaviors:

1. constructive interference
2. destructive interference
3. “beats” with different frequencies

This will be followed by a quiz with questions that can be answered using the application.

## 2-dimensional interference

Interference can happen in more than one dimension. If we have two sources that are each sending out a sine wave, it might look something like this, if the waves stay the same height as they move away:

After the 1-D interference application and quiz, you will see an application demonstrating 2-D interference, as well.

To aid the vision-impaired, or for those who just enjoy 3-D printing, we have created some 3-D printable models representing some of the key concepts. You saw these models in the video, feel free to print your own.

Most 3-D printing software can handle a file type known as STL. Here, we provide an STL file for you to print, or the source code in a language called OpenSCAD, if you would like to modify the shape.

• A single wave source radiating in two dimensions, with (1/r) decay of amplitude
• Two wave sources radiating in two dimensions demonstrating interference, with (1/r) decay of amplitude

## (N)-dimensional interference

Humans can’t effectively visualize more than three dimensions, but in fact a quantum computer creates interference across many different variables, which we can treat as separate dimensions. We will see this effect when we discuss quantum algorithms in Week 3.

# 重ね合わせと干渉

ビデオの内容に加えて、みなさんが実際に手を動かして学んでいただけるアプリや3Dモデルを用意していますので試してみてください。

## 一次元の波の干渉

このあとのステップで紹介するアプリでは、以下のような波の特徴を見ることができます。

1. 波の強め合い（建設的干渉）
2. 波の弱め合い（相殺的干渉）
3. 異なる周波数の波による波のうなり（ビート）

これはそのアプリを使ってクイズに答えると非常にわかりやすく理解できるかと思います。

## 二次元の波の干渉

• 1/rで振幅が減衰する二次元上の単一波
• 1/rで振幅が減衰する、二次元上の2つの波の干渉