# Superposition and Interference

Let's discuss the wave-like property of qubits, interference, and its connection to superposition and see how we can use it in our quantum algorithms.

## We'll cover the following

Two lessons back, we introduced the idea that quantum mechanics allows qubits to exhibit both **wave-like** and **particle-like** properties. In this lesson, we shall focus on the former and see how wave properties become useful in formulating accurate quantum algorithms. But before that, let’s recap wave theory.

## Wave theory

As you recall from your high school or college classes, waves are **disturbances** or **vibrations** in a **medium** that **transport** **energy** from one point to another. There are two types of waves, **transverse** and **longitudinal**. In transverse waves, the **displacement** of the medium is **perpendicular** to the direction of wave motion. But in longitudinal waves, the displacement of the medium is parallel. We’ll limit ourselves to discussing transverse waves as they are relevant to our subject matter.

We typically define waves using their **wavelength**, **speed**, and **frequency**. The **speed** is obviously the rate at which the wave travels between two points. The **frequency** is the number of vibrations per unit time. The **wavelength** is the distance between two consecutive **troughs** or two consecutive **crests**. Places of **high amplitude** are called **crests** while places of **low amplitude** are called **troughs**. We define their **amplitude** as the greatest displacement from the mean position. The wavelength $\lambda$, speed $c$, and frequency $f$ are related by the following equation:

$c = f\lambda$

Looking at the equation above, **frequency** and **wavelength** are inversely proportional to each other, meaning that an increase in one causes a decrease in the other, and vice versa. In other words, lower frequencies mean longer wavelengths, and higher frequencies mean shorter wavelengths.

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