The information age
We live in a time that is often called "The information age". This is because we share and use an enormous amount of information in our lives.
Books, memes, videos, tweets, and texts are all forms of information. Information can be in various forms. Even a coyote's howling to let others on their pack about a potential danger is a kind of information!
Less than 100 years ago, people mostly relied on sharing information on paper or by word-of-mouth. This is no longer the case; most of the human's knowledge is now being shared and spread using computers. This raises a question: How are all these different types of information presented, stored, and shared using computers?
In today's computers information in books, memes, tweets and videos can all be stored as zeros and ones.
We call these zeros and ones bits. Bits can join each other and make series of bits to represent the information we want. The information which is stored using a series of bits is called binary information.
Time to ask yourself, as information can be presented in different forms, what are some forms of information presented to you in your everyday life?
Quantum Bits
The information you are familiar with (the information in texts, videos, and pictures) is one kind of information, called classical information.
However, not everything is accurately described using classical information. This is where we require quantum information.
Remember that classical information can be built out of units called bits. Similarly, quantum information is built out of qubits (quantum bits!). In this section, we will explore what qubits are, and how they are different than bits.
To begin exploring qubits and quantum information, it will be useful to have a picture that represents a qubit.
Recall that bits can have two states, which we can call 0 or 1. We can also label the two states with something else though. For example, blue or yellow dots.
Another choice we can make is to label bits with up or down,
Classical bits bit can be stored as a 0 or 1, as "True" or "False", as a blue or yellow dot, high or low voltages and so on. Likewise, there are many different ways to store a qubit. Some examples are using photons (a particle of light), using superconductors, or using the spin of a small particle, like an atom or electron. Spin is a property of particles (just like mass and charge) that we can determine using magnets. We can visualize the spin using the arrow picture.
As a starting point, we will look at 4 different states a qubit can be in. We'll label these by drawing arrows in four different directions, like this:
We'll call these up, down, left, and right. By understanding these four "quantum" states, we will find out that qubits are strange yet powerful!
Stern-Gerlach Experiment
Stern-Gerlach ExperimentWe just told you that you can think of a qubit as an up arrow, or a down arrow, or anything in between. This is a weird concept, but one that is easier to understand experimentally. We will be learning more about spin using magnets. The simulation we build below is based on a very important experiment in quantum mechanics, known as the Stern-Gerlach experiment.
You can see the simulator below. Ensure that the simulator is opened in a separate tab.
Let's start out by getting to know the components of the simulator.
The source. This is a box that will shoot spins out. The spins have a qubit stored on them, like we discussed in the last section. The qubits can be up, down, left or right.
A magnet. This has one place atoms can go in and two places they could come out. You can turn the magnet using the button to its left. Start out with the magnet set straight up and down.
A blocker. This is blocking one of the places the atoms can come out of the magnet. You can switch the blocker position by selecting "up" or "down" in the top menu.
More Spins
Now that we have our setup ready, its time to actually conduct our experiments. The aim of our experiment is to understand the quantum mechanics of qubits using spin qubits. You can play around with the simulator we have built and frame your own conclusions regarding qubits! The questions below will help you in the process. Here's the simulator again for you to use when you answer the questions below: Simulator.
Clicking on the magnets will show or hide the percent of qubits that went each direction through the magnet. Note that the magnet can be rotated. In the questions and subsequent discussions, we will refer to the magnet in the vertical position as being aligned with the z-axis and when it is completely horizontal, we will say that the magnet is aligned with the x-axis.
Stern-Gerlach Observations
The magnets in the simulation let you check if the qubit is up or down when the magnet is placed along the z-axis, and left or right if the magnet when placed along the x-axis. We call this a measurement.
When the magnet was placed vertically (along the z-axis), we noticed that upon conducting a measurement
- A spin-up qubit will turn out to be up 100% of the time.
- A spin-down qubit will turn out to be down 100% of the time.
When the magnet was placed horizontally along the x-direction, we observed that upon measurement
- A left-qubit will turn out to be left 100% of the time
- A right-qubit will turn out to be right 100% of the time (verify this!)
This makes sense! Vertical spins (up and down) are not affected by a vertical magnet, and horizontal spins are not affected by a horizontal magnet.
However, things are different when you pass a left qubit through a magnet along the z-direction. Now, there's a 50-50 chance the qubit will go up or down!
In the quantum world, we understand this by saying the left state is a superposition of up and down. Superposition is a way to describe a particle being in a combination of known states. In the case of a right or right qubit going through a vertical magnet, we can think of "left" as being a bit of up and a bit of down. By measuring the qubit, we can force the qubit into either up or down.
Challenge with two magnets
Now we're going to up the challenge level, and put in two magnets! Click on the top menu of the simulator to adjust the number of magqubits! The questions below will help you in the process. Here's the simulator again for you to use when you answer the questions below: Simulator.
Clicking on the magnets will show or hide the percent of qubits that went each direction through the magnet. Note that the magnet can be rotated. In the questions and subsequent discussions, we will refer to the magnet in the vertical position as being aligned with the z-axis and when it is completely horizontal, we will say that the magnet is aligned with the x-axis.
Once you've done this, explore the simulator by trying out different arrangements of magnets and sending in different kinds of spins. You can take hints from the video below gives a nice overview of the experiments that you have conducted using the Stern-Gerlach simulator.
Stern-Gerlach (QC with Geering Up)
Superposition and Measurement
Quantum Superposition
We said that the left state is a superposition of up and down.
In the quantum world we have a way of describing this using math. We write
Left = Up - Down
Why are up and down subtracted instead of added? Good question! We can actually do either one. However, it is best to pick one way and stick to it. We will be using left being the subtracted one. Then, if we add them, we get the "right" state
Right = Up + Down
If you don't understand this idea of superposition right away, that is okay! We will come back to this idea in the future and try it again.
Quantum Measurement
Remember that we are thinking about four states a qubit can be in, up, down, left, right
When we pass a spin through a magnet with a blocker, the spin can go in only one of two directions. Finding out which direction is goes means we have performed a quantum measurement. In the simulation there are two different ways of measuring the qubit. Putting the magnet in the vertical position let you measure if the spin would go up or down. Putting the magnet in the horizontal position let you check if the magnet would go left or right.
We found that an up qubit going through an up-down magnet goes up, and similarly a left qubit going through a left-right magnet goes left. However, a left qubit going through an up-down magnet behaves randomly - it has a 50-50 chance of going up or down.
In the simulation with two magnets, you might have learned that if you send a left qubit into an up-down magnet and it goes up, it will then be an up qubit afterward. The quantum measurement actually pushes the qubit to be either an up or a down qubit, even though it goes in as a left qubit.
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